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♣ This paper was part of my Ph.D. thesis at the University of Cambridge (Trinity College). I am particularly grateful to Prof. William Brown (University of Cambridge) and Prof. David Perez Castrillo (Universitat Autònoma Barcelona) for the helpful comments and valuable suggestions. I have also gained much from discussions with Dr. Robert Evans (University of Cambridge).

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This paper investigates the ineffectiveness of output-related pay such as the contract system in the US iron and steel industry during the second half of the nineteenth-century. The high rate of technological innovation along with the extensive bargaining power of the old industrial crafts made output-related pay a sub-optimal solution. Thus, the simple trade-off between incentive and risk, which is crucial to the agency problem, is not a sufficient explanation. Consequently, the analysis of the interaction between technological change, bargaining powers, and payment systems of a specific historical event can be conducive to a better understanding of the agency problem and the use of incentive pay.

Keywords: Incentive Contracts, Moral Hazard, Bargaining, Technological Change.

JEL Codes: J21, J33, M52.

Please do not quote without permission of the author

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11.. II NNTTRROODDUUCCTTII OONN Agency theory, in its standard specification, investigates the choice between different payment schemes according to the classical trade-off between risk and incentives. If monitoring workers’ effort is expensive, the best choice is to offer payment by results. However, if this embodies a high risk the incentive component should be reduced because workers, as they are more risk-averse, can be inefficient in bearing risk compared to their employers. This theory captures several stylised facts; however the provision of incentives is more sophisticated than the theoretical understanding envisages. For example, agency theory neglects the role of bargaining and consequently the importance of power in the outcome of a compensation scheme. The case of the contract system in the developing years of the American iron and steel industry is precisely one of those circumstances in which payment by results suffered severely from conflicting labour relationships that eventually rendered the provision of those incentives ineffective. In particular, the high rates of technological change experienced by this industry did nothing but exacerbate the ‘labour problem’, thereby playing a very important role in the decline of the incentive provision and revolutionising the industrial relations of the period.

The purpose of this paper is therefore to examine the potential problems of the adoption of payment by results and its hidden costs, specifically those that marked the contract system in the American iron and steel industry in its early stages. Payment by results, as established for skilled workers in the booming period of the iron and steel industry in the United States, was so costly as to be unsustainable in the long run. The American iron and steel industry in the second half of the nineteenth century was marked by the conflict between the old industrial crafts, with its legacy of rules, traditions, and pay systems on the one hand and, on the other hand, the new concepts of industrial capitalism, with its hierarchies, a rational work organisation, tight market competition, and, not least, high rates of technological change.

The system of contracting out production to highly skilled workers, which was in all likelihood inherited from the putting-out systems of the early English industrial revolution, was doomed to fail under the pressure of the many factors characterising the new stage of industrial capitalism that made this type of incentive very costly. However, this payment system was the building block of the labour relationships between companies and workers in large parts of the iron and steel industry. It gave sizeable profit and operational margins to skilled workers who contracted their work directly with the companies by being paid for the amount of metal produced and by performing their tasks with the help of small gangs.

Initially, firms responded positively to this system because it was considered a partnership between skilled hands and capital, and also it could displace some risk to the workers. Firms soon realised that it was simply unprofitable. Among the most important strains on this incentive system was the high level of technological change that marked the period and that considerably increased output for a given effort level. The main issue at stake was the division of surplus from this higher output. Furthermore, the piece rate that rewarded contractors was geared to the price of the final product (e.g., the bar iron), with a minimum base below which the piece rate could not fall. The large fluctuations in demand and the stagnant low prices put further strain upon the system. With strong trade unions backing the interests of contractors, re-negotiations were extremely costly and were marked by strikes and lockouts.

Agency theory envisages only two types of conflicting interests between principals and agents. On the one hand, the cost of effort, which is not internalised by the principal

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but negatively affects workers’ utility, and on the other hand, the wage cost which, evidently, increases workers’ utility but diminishes that of the firms. However, the case that will be examined in the following pages reveals that the agency contract hides other conflicts that should be accounted for when designing a payment mechanism. Firstly, re-negotiation of the rates can be very costly. When there is a high level of technological change, rates quickly become obsolete. Thus, if workers have sufficient bargaining power, setting new rates generates conflicts. Secondly, piece rates are ‘sticky’. Providing explicit incentives sometimes means giving away part of the technological gains to workers because rates cannot be adjusted immediately after the change in the technology or techniques has taken place, and thus under-investment is likely to occur. Thirdly, competition in the product market considerably penalises those firms that pay by the piece. Indeed, firms paying workers fixed wages can immediately benefit from the gains stemming from improved machinery, without incurring additional re-negotiation costs. This difference is exacerbated when trade unions have strong bargaining power within piece rate firms and drive piece rates upwards.

These and other considerations are neglected by the current literature on incentive pay, and they also play a marginal role in the literature of the economic history of the iron and steel industry.1 Hence, an analysis of the contract system with its pros and cons is particularly interesting as it could unveil in greater depth the mechanisms that characterise incentive pay and the role played by institutions such as organised labour. Finally, this work also seeks to challenge the agency theory such that theory can be subjected to some degree of qualitative testing and then extended in order to respond to further contractual issues.

This paper is arranged in two parts: one descriptive and the other theoretical. The first part is devoted to the historical analysis of the contract system. In particular, the next section presents the main characteristics of the iron and steel industry such as the figures involved in the production process, the industrial relations, and the payment systems. Then, an investigation of the technological changes and the evolution of the markets related to the industry will be carried out so as to describe those factors that were critical to the failure of the contract system. Following this, the strains on the contract system will be identified, especially the struggle between capital and labour that undermined the old ways of organising work as well as the long-established institutions such as the contract system with its sliding scale mechanism. The second part will introduce the principal-agent theory, which will be intertwined with technological change and workers’ bargaining power. The subsequent model and its extensions will help to explain why incentive pay may not be the solution to the ‘labour problem’ but that it can turn into a sub-optimal choice when high technological change is coupled with strong trade-unionism. Sophisticated computer simulation techniques are going to be used in order to understand diagrammatically the intertwined effects of the main variables, which are not readily intelligible from the common algebraic tools used for static analysis. Finally, concluding remarks will address further issues related to the theoretical investigation and the historical account.

1 For extensive historical accounts see Clark (1929, Vols. II and III) and Temin (1964).

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PPAARRTT II

TTHHEE HH II SSTTOORRYY OOFF TTHHEE CCOONNTTRRAACCTT SSYYSSTTEEMM :: RRII SSEE AANNDD FFAALL LL

22.. TTHHEE PPAAYYMM EENNTT SSYYSSTTEEMM SS II NN TTHHEE EEMM EERRGGEENNTT II RROONN AANNDD SSTTEEEELL II NNDDUUSSTTRRYY In the second half of the nineteenth-century the production of iron and steel went through the following stages. The first stage was the same for both metals; it consisted of removing most of the impurities from the iron ore through a smelting procedure carried out under intense heating in blast furnaces. The product of the blast furnaces is called pig iron, whose chemical composition was allowed to vary according to the desired type of final product. At this stage, the pig iron could not commonly be employed for commercial use and had to be refined. The refining of pig iron gave rise to wrought iron or steel. Bessemer converters and open-hearth furnaces were used to refine pig iron into steel whereas puddling furnaces yielded wrought iron. The final stage consisted of shaping these metals by rolling them according to their usage.

The production of iron required heavy manual work. In the puddling furnaces the pig iron was melted together with oxidising agents and then stirred manually through a hole in the furnace door by means of a long iron rod until the impurities were separated. The molten iron was then removed in a pasty mass which was further refined and rolled. Puddling was very hard work and high skill levels were required. There were always at least two men, and sometimes three, to tend a single furnace and they took turns at working the metal due to the intense heat coming from the furnace.

The invention of the Bessemer converter in 1856 allowed for the continuous and large production of steel ingots as never before. In a Bessemer production process no direct heat or manual stirring was required as the pig iron was transformed into steel by adding further chemical compounds and blowing hot air into the converter. The molten mass was then poured into an iron ladle and, finally, into ingot moulds ready to be either hammered or rolled. In this process the blower was the most important worker after the foreman. He determined the time to turn down the converter for the pouring and shut off the blast. This was the greatest responsibility as incorrect timing could spoil the metal. Consequently, the introduction of the Bessemer converters reduced, but did not eliminate, the demand for skilled workers who played a major role in the production and refining of the metal.

The production of steel in open-hearth furnaces came about two decades later and it can be considered as a logical development of the puddling process. It was to some extent merely a mixing process; pig iron and steel-scrap were melted together at very intense heat to produce a steel of intermediate properties. It dispensed with the need for the manipulation of iron as was practised in the puddling furnaces. This method was more flexible and accurate than Bessemer steel because it could convert any quality of iron into steel and the purification took place more slowly. Therefore, the process could be stopped when the proportions of certain elements had reached the required levels. Three men were usually employed at an open-hearth furnace: the first helper or melter, the second helper and the cinder-pit man. The foremen or boss melter was typically in charge of three to five furnaces.

Puddling particularly, along with heating, blowing, shearing, and rolling, were all trades that needed highly skilled industrial craftsmen. These workers enjoyed high prestige in their communities and were at the top of the industrial craft hierarchy. The great majority had British origins and they had brought with them to America the work practices established in their original nations, in particular the trade-union traditions of their native country and the custom to be paid, as the forge men who preceded them, by the tonnage of

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product (Clark 1929, II). A relatively unskilled labour force usually assisted them by performing heavy manual labour: lifting, pushing, hoisting, carrying, and wheeling raw materials from one operation to the next. Skilled workers, both individually or in teams, controlled the production process and made iron and steel by using the employers’ capital. They contracted directly with the owners of the plants over the characteristics of the final product and the value of their industry and effort. The most common form of payment was the so-called contract system. Skilled workers were paid on the base of the tonnage produced, and in turn they paid helpers out of their own pay cheques. As a rule, contractors did not pay their helpers piece rates, but sub-contracting was not uncommon (BITA 1902). The hiring and firing of the helpers was also under contractors’ responsibility.

Skilled workers had an interest in protecting their craft exclusiveness, their know-how, in institutionalising the contract system and extending it to a national scale. In 1837, five years after the introduction of puddling in Pittsburgh – which became the most important iron industrial district in the whole country – a successful strike was inaugurated by the boilers (a type of puddler) to prevent a reduction of wages. Similar labour interruptions continued at frequent intervals thereafter. In 1858, the puddlers formed the first union movement in Pittsburgh, the Sons of Vulcan. This organisation grew out of the panic of 1857 that threatened the industry, and which caused repeated reductions in the tonnage rates. The price of puddling steadily declined from $7 a ton in the early 1830s to less than $4 at the outbreak of the Civil War. During the conflict prices and wages increased and the rate reached $9 a ton, but suffered a slight reduction as soon as peace was declared (Clark 1929, II). In 1865, after continued disputes over the tonnage rate, the Sons of Vulcan went on strike largely to affirm principles over unionism, wages, and work organisation. The workers’ battle was successful and in 1866, after a general lockout to enforce a reduction of wage rates, the employers of Pittsburgh recognised the union and signed a scale of wages, the sliding scale system, linking the puddling rate to the selling price of bar iron. This was the first example of collective bargaining in the United States. This system quickly spread in the whole iron and steel industry, although it was never fully developed in the steel industry, whereas in the iron industry it was very widespread (Doeringer 1968). Often the steel companies paid part of the helpers’ wages or provided some helpers for certain skilled workers, so that a hybrid system became prevalent (Stone 1974).

Adjustments to the piece rates were made every other month, based on the average prices of the past two months. Due to the time lag in the adjustment process, the workers knew some time in advance that their piece rate was to change. When the price of bar iron went up, puddlers’ wages were adjusted upwards. When the price went down, the wages dropped correspondingly. Wages could not go below a certain base level, which was fixed by bargaining, however much the price of bar iron might fall. By contrast, there was no upper bound on the piece rates when prices went up.

The contract system was largely copied from a similar mechanism used in some parts of the British iron and steel industry (Doeringer 1968). The sliding scale system was an arrangement for sharing the risks and profits of production between skilled workers and iron masters. Both the skilled workers and the manufacturers derived their own advantages from this approach. The skilled workers could be remunerated according to their capacity and level of effort. The post-war boom in demand for iron automatically improved the earning positions of the Sons of Vulcan (Doeringer 1968). The employers in turn had a better understanding of their accountancy due to the link between efficiency and remuneration. Employers could also transfer part of the risk to contractors. As noted by Andrew Carnegie at the outset of the scheme, the sliding scale system was ‘the solution of

5

the capital and labor problem because it really makes them partners – alike in prosperity and adversity’ (Stone 1974: 31).

As will be discussed below, the demand for iron was particularly unstable and prices fluctuated widely, and with this mechanism ironmasters could automatically reduce their costs during recessions. Apparently, the need for annual negotiations with the ironworkers was partially reduced by the automatic periodic adjustments of the sliding scale in response to the changes in market conditions. This was to mean a reduction in conflicts and production stoppages in critical periods of high demand. Finally, the contract system was also a means to relieve the manufacturers from managerial responsibility over labour issues and leave contractors to deal with their own men as to the division of labour and the pace of work.

However, there were two important setbacks to the sliding scale mechanism that arose some time after its introduction. Firstly, it implied that any surplus gained from a higher turnout was fully captured by the ironworkers if tonnage rates were left unchanged. Secondly, the risk-sharing idea behind the automatic adjustment was only apparent because much depended on the minimum base. For the workers a high minimum base granted a high coverage from the risk of the downward fluctuations of the price of bar iron and other reference prices for the sliding scale, thus transferring the risk almost entirely to the manufacturers. Therefore, on the one hand, a rapid technological change set off a dispute over the massive gains stemming from the increased output, and on the other hand, the low prices of the final products to which the sliding scale was indexed made the sliding scale essentially inoperative. In other words, both the supply and the demand side brought to light the inconsistencies of the contract system, and it is in these two directions that we turn our attention next.

33.. CCHHAANNGGEESS II NN TTEECCHHNNOOLL OOGGYY AANNDD EEVVOOLL UUTTII OONN OOFF TTHHEE MM AARRKK EETTSS After the Civil War, the United States was a country with unparalleled

opportunities to grow at a rate never experienced before by any other industrialising country. Its immense primary resources were still available to be exploited and the population was steadily increasing due to the large influx of immigrants. The iron and steel industry was at the forefront of this industrial development. This industry experienced an impressive technological change that induced a likewise remarkable increase in output. On the demand side, we can distinguish two important driving forces that caused the large-scale technological change. Firstly, the growing demand for railway construction can be considered the main factor leading to rapid technological change. This growth particularly characterised the years following the Civil War until the panic of 1873 and then the five-year period ending in 1882 (see Figure 1-A). Between 1860 and 1885, the demand for railroads constituted more than one-third of all rolled iron and steel. Secondly, two protectionist tariffs, the Morrill tariff of 1862 and the McKinley tariff of 1890, fostered the internal expansion by opening up to home manufacturers the prospect of the establishment of new branches of the trade as well as the expansion and consolidation of the trade already secured. Among other minor driving forces there was the vast increase in the demand for telegraph wires, steel ploughs, mowing machines and harvesters, which kept pace with tracklayers in the invasion of the Western prairies until 1875 (Clark 1929, II).

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On the supply side, the introduction of the Bessemer process for steel production represented one of the most important technological innovations that marked the future economic evolution of the country.2 Steel products were far superior to wrought iron in terms of malleability, tensile strength, and cost of manufacture; as a result, steel products were suitable for a wide range of applications.

The continuous turnout of steel allowed by the Bessemer process necessitated increasing supplies of pig iron coming from the blast furnaces (see Figure 1-B). Increasingly bigger blast furnaces started to be built in groups and in connection with the steel plants such that pig iron could be converted into steel without cooling. Bridge (1903) reported the results obtained by two blast furnaces, Lucy and Isabella. Both increased their production from a daily average of 50 tons each in 1872, when they went into blast, to 87 tons in 1873, 112 tons in 1874, 217.5 tons in 1881, and over 300 tons each in 1883. The higher turnout of blast furnaces was also due to, and accompanied by, the introduction of several labour- and cost-saving innovations. The utilisation of coke as a fuel and the Whitwell hot-blast stove significantly economised the fuel consumption of the furnaces and enabled them to attain and sustain higher temperatures (Clark 1929, II). The pig casting machines, consisting of a series of cast iron moulds arranged on a long chain, superseded the sand bed. The manner of elevating and charging the stock changed considerably with the introduction of the automatic hoist, which operated from the ground, carrying carts full of raw material to the furnace top and into the hopper. Overall in the late nineteenth-century, electric trolleys, electric travelling cranes, and mechanical ladle cars transformed the working environment of the industry.

The average size of iron and steel establishments and their productivity from 1869 to 1899 exhibited a large increase (see below Table 1). Average pig iron output per establishment experienced a thirteen-fold increase while output in steelworks and rolling mills rose more than seven times.3 During the same period, capital investments rose considerably, from $145,000 to $643,000 for blast furnaces, and from $156,000 to $967,000 for steelworks and rolling mills (Temin 1964). This substantial rise in investments, coupled with a significant increase in output per worker, indicates that a

2 Gold, Peirce, and Rosegger (1970) put the commercial diffusion of the Bessemer converter at the top of their list of the technological innovations discovered in 1860–1970 in terms of their contribution to output growth. 3 Iron mills are also included under ‘steelworks and rolling mills’.

Production of Rails

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Pig Iron and Steel Production

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Total Pig Iron Total Steel

Graph A. Source: Temin (1964) Graph B. Source: Temin (1964)

FFiigguurree 11.. EEvvoolluuttiioonn ooff PPiigg II rroonn,, SStteeeell ,, aanndd RRaaii llss iinn UUSS

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process of substitution of capital for labour was taking place. Output per worker increased fivefold and more than twofold respectively in blast furnaces and in iron and steel rolling mills as a consequence of a rapid technological change arising especially during the 1880s and 1890s.4 The data on steelworks and rolling mills do not distinguish rolled iron from rolled steel. However, the large increase in productivity and size is fundamentally ascribable to steelworks rather than to iron mills.

Table 1. AAVVEERRAAGGEE SSIIZZEE OOFF EESSTTAABBLLIISSHHMMEENNTTSS AANNDD PPRROODDUUCCTTIIVVIITTYY IINNDDIICCAATTOORRSS..

Output/Capital (tons/$)

Census-Year Output (thousands of tons)

Output per Worker

(tons)

BBllaasstt FFuurrnnaacceess

1869 0.035 5 70.4

1879 0.038 10 82.0

1889 0.068 29 263.6

1899 0.101 65 369.3

SStteeeellwwoorrkkss aanndd RRooll ll iinngg MMii ll llss

1869 0.019 3 25.2

1879 0.026 7 32.8

1889 0.021 12 42.2

1899 0.023 23 55.8

Source: After Temin 1964: 166, Table 7.1.

In 1860, there were only 13 establishments in the USA producing steel, employing a total of 748 workers to produce a few hundreds tons of steel a year using an antiquated method of production, the crucible process. After the Civil War the iron and steel industry began to expand rapidly. However, it was only in the 1870s that the progressive introduction of the Bessemer converters in the production of steel took place, and by 1890 there were 110 Bessemer converters along with 167 open-hearth mills producing 4.3 million tons of steel per year, most of this through the Bessemer converters. In 1902, the total production of steel reached almost 15 million tons, with the open-hearth process output catching up with the Bessemer process (Figure 2-A). The open-hearth process, which started later than the Bessemer converters, enjoyed several improvements especially in the 1890s, and one worth noting is the Wellman charging machine which did away with almost all the manual aspects of steel production.

4 Allen (1979: 917, Table 2) reports similar findings on output per worker.

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The expansion of steel manufacturing significantly reduced the need for wrought iron and its refined products. From 1877 steel overtook iron in the production of rails, and less than a decade later all railroads were solely made from steel. In 1886 rolled steel production overtook rolled iron production (Figure 2-B). The years 1890 to 1910 were the pivotal period for the U.S. steel industry. During these two decades steel replaced iron as the building block of industrial society. The proportion of iron in the total quantity of rolled iron and steel produced in the country fell from 43 percent to 8 percent. Before the end of the century most rolling mills were equipped to handle steel. The evolution of rolled iron production was also mirrored by the more stable technological path followed by wrought iron compared to steel. The attempts to mechanise puddling in order to reduce the need for puddlers, such as the Dank’s rotary machine, only partially succeeded and not until the turn of the century puddling underwent substantial changes (Clark 1929, II). These relegated puddlers to a marginal position when facing internal competition from other ironworkers, as well as in bargaining with their employers.

As a whole, technological change severely undermined the contract system and the underlying piece rate scheme. On the one hand, the resulting increase in output per unit of labour needed prompt changes in piece rates if companies wanted to get the profits from their investments in new technologies and face competition from internal non-unionised firms. On the other hand, the skill content was diminishing, thereby reducing the bargaining power of skilled workers and their differential earnings with respect to unskilled positions.

However, rapid technological change was not the only factor that demanded re-negotiation of rates. The minimum base was particularly important especially when prices suffered from large fluctuations. As a matter of fact, fluctuations were more sudden and violent in the United States than in any other large industrial country. If we divide iron and steel consumption into two classes, consumption for maintenance and consumption for development, the latter was relatively more important in the domestic market of the United States than in that of any other major iron-producing nation. It was this class of consumption that fluctuated most (Clark 1929, III) and the prices of iron and steel particularly suffered from this instability. As discussed above, the sliding scale system was a measure that attempted to deal with the large price fluctuations brought about by the Civil War. A look at the evolution of iron and steel prices (Figure 3) sheds some light on the factors that jeopardised this mechanism.

Steel Production by Process Used

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Graph A. Source Temin (1964) Graph B. Source Temin (1964)

FFiigguurree 22.. CCoommppaarriissoonn wwii tthhiinn SStteeeell PPrroodduuccttiioonn aanndd bbeettwweeeenn RRooll lleedd MMaatteerriiaallss

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Before 1866, when the sliding scale system became the mechanism to share risks and profits between ironmasters and skilled ironworkers, the price of iron experienced a significant increase due to the high demand for warfare equipment and the Morrill tariff. The high price of iron allowed for massive profits, accruing especially to the ironmasters, with puddlers and rollers bargaining individually to capture a share of these. The request for an automatic mechanism that could adjust the earnings of the workers to the increasing profits was seen as a fair and necessary agreement to deal with the labour problem and the growing symptoms of organised labour.

However, the high price epoch did not last long, largely as a result of the technological changes and the increasing competition. The price of iron and steel steadily declined especially after the 1873 worldwide depression. From 1880 onwards, the market price for iron and steel product was falling drastically, so that the price for bar iron was actually below the minimum specified in the union’s sliding scale, even though the negotiated minimum rates were also declining (see Table 2 below). This meant that employers were paying a higher percentage of their income in wages than they would have if the sliding feature of the sliding scale were fully operative, or if they had had the power to reduce wages unilaterally in the face of declining prices (Doeringer 1968, Stone 1974).

The figures in Figure 3 and Table 2 only illustrate average yearly data and do not capture the full extent of the fluctuations in prices. For example, in January 1892 a major fall in the price of structural steel occurred, followed in February by a similar decline in the price of barbed wire. A steel-billet pool was formed to hold prices at $25. But less than two years later the price had fallen further, to between $16 and $17. Throughout this low-price era the pig-iron market was steadily subjected to a strain of exceptional severity by the pressure of competition from southern States (Clark 1929, II and III). The British Iron Trade Association (BITA) characterises this period as one where ‘prices fell to a lower point than had ever before been known in the history of American industry’ (BITA 190: 284) with the excess capacity that the expansion of the lucrative market engendered. In the years 1888–1893 more new plants were brought into operation than had ever been seen before and to such an extent that led to a glut of the markets. This was also due to the discovery and exploitation of new iron ore fields, especially of the Mesaba range, which tended to reduce the costs of production and which induced an enlargement of the scale of production in order to exploit these new lucrative ores (BITA 1902).

Price of Iron and Steel Products

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Price of Iron Price of Steel

FFiigguurree 33.. PPrriiccee ppeerr ttoonn ooff II rroonn aanndd SStteeeell -- SSoouurrccee TTeemmiinn ((11996644))

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Table 2. SSCCAALLEE MMIINNIIMMUUMMSS AANNDD PPIITTTTSSBBUURRGGHH BBAARR IIRROONN PPRRIICCEESS

Year Scale Minimum Bar Iron Price per Pound

1880 2.5¢ 2.4¢ 1881 2.5 2.3 1882 2.5 2.4 1883 2.5 2.0 1884 2.5 1.7 1885 2.0 1.6 1886 2.0 1.7 1887 2.0 1.9 1888 2.0 1.8 1889 2.0 1.7 1890 2.0 1.8 1891 2.0 1.7 1892 2.0 1.6 1893 2.0 1.5 1894 1.5 1.2 1895 1.1 1.2 1896 1.1 1.2 1897 1.1 1.1 1898 1.1 1.1 1899 1.3 1.9 1900 1.5 2.1

Source: Doeringer 1968: 266, Table III.

44.. TTHHEE SSTTRRAAII NNSS OONN TTHHEE PPAAYYMM EENNTT SSYYSSTTEEMM Control over the surplus stemming from increasing output levels, the owners’ need to be directly in charge of the production process in order to contain costs and sustain competition and, not least, the extremely low prices of iron and steel together placed serious strains on the contract system and its sliding scale mechanism. In particular, it was clear that the earnings of skilled occupations tended to rise if the workers could keep their tonnage payment rate unchanged. The output of iron and steel works was rapidly increasing on account of the introduction of improved machinery, so that at the same rate per ton the workmen could make more money. Paradoxical situations could arise ‘where new machinery increased output, they [the workers] often demanded all the benefit of that increase, and would not accept a reduction in the tonnage rate. As a result, a roller would sometimes earn more money in a year than his superintendent’ (Fitch 1911: 104).

Workers’ earnings increased steadily throughout the 1870s, though not quite in the same ratio as output (Fitch 1911). Employers constantly endeavoured to lower the tonnage rate in order to secure additional profits from the expensive machinery they installed, while workers almost invariably resisted any attempt to modify the scale to their disadvantage, even at the cost of a strike.

The expectations of social peace after the introduction of the sliding scale system soon failed, and relations between labour and capital became quite stormy until the 1890s when the trade unions suffered several defeats that effectively drove them out of the industry until the 1930s. In 1867, one year after the introduction of the new system, due to the fall in prices a demand was put to the puddlers in the Pittsburgh district to accept a reduction of wages. This being refused, strikes occurred at Troy, and among the Welsh puddlers employed at the Tredegar Works, at Richmond. At that time, sympathetic strikes

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were still unknown and thus the rest of the workers in the mills continued to work as long as the material on hand lasted or fresh supplies could be had (Bridge 1903, Krause 1992).

During the depression following the panic of 1873, several strikes occurred in different parts of the country: a strike of the heaters at the rolling mills in Chicago and Milwaukee in 1873; a strike at the Pennsylvania Steel Works and among the Troy puddlers the following year; and a puddlers’ strike at Pittsburgh in 1875. The outcome of these disputes was the reduction of the tonnage rates and the introduction of new devices that attempted to reduce the power of skilled workers. For example, it was not uncommon that manufacturers sent some emissaries to Europe and brought many skilled workers from there in order to substitute for the defiant workers at home. Clark maintains that ‘while the labor unrest of this period may not have directly suggested the efforts to perfect mechanical puddling that then occurred, it is probable that this series of strikes and lock-outs encouraged the adoption of such improvements as soon as they appeared in the market’ (1929, II: 260). This was symptomatic of the divergences between old industrial craftsmen and new iron capitalism.

The first defeats in the struggle for holding tonnage rates encouraged the skilled workers to strive for unity and overcome the sectarianism that marked the first period of organised labour. In Pittsburgh in 1876, the Heaters Union, the Roll Hands Union, and the Sons of Vulcan merged to form the Amalgamated Association of Iron and Steel Workers. This gave more power to workers and a greater recognition at the national level. Given the increasing turnout and the tighter collaboration among workers, strikes became quite costly for unionised firms vis-à-vis their competitors.

In 1877 Pittsburgh manufacturers gave, among their reasons for granting the demands of their puddlers for higher wages, the fact that western competitors took advantage of Pittsburgh strikes to keep in operation and extend their markets, under an agreement with their workmen that any increase of wages at Pittsburgh would, as soon as accepted by employers there, be introduced at the western mills. (Clark 1929, II: 178)

In a 2 January 1885 interview Andrew Carnegie anxiously claimed that:

They [the unions] allow other Bessemer mills to work at less wages than we pay…we cannot do it, and must close rather than sell rails at less than cost… I do not know when they [Braddock and Homestead plants] will be started, but not until the rail market improves and we can run and sell at a profit, or until the Amalgamated Association gains control of the other mills in the country and makes better wages in those establishments. (Fitch 1911: 113)

The renewal of the scales ending on 1 June 1882 brought about four months of stoppages. The Amalgamated Association asked for an advance over the scale of 1881–82, but the main issue at stake was the minimum base price. The strike ended unsuccessfully for the Amalgamated Association and the workers eventually had to accept the old scales without substantial changes. Through 1880s and 1890s the Amalgamated Association strengthened its power and succeeded to unionise and apply the sliding scale system in all iron mills in Allegheny County. However, trade unions were not so important east of the Alleghenies where labour conditions continued to vary considerably from those in the Pittsburgh district and farther west. Neither were they a power in the growing iron and steel region of southern Tennessee and northern Alabama. Unionism in the steel industry was also never as widespread as in the iron mills. By 1891, the Amalgamated Association represented 25 percent of all steelworkers.

The actions of the Amalgamated Association culminated in 1889 with a contract at Carnegie’s Homestead mill that gave the skilled workers authority over every aspect of steel production (Bridge 1903, Fitch 1911). Yet, the bargaining over the contract renewal at Homestead in 1892 marked the start of the end of collective bargaining as well as that of

12

the prominent role of skilled workers, thereby accelerating the abandonment of the contract system. The companies were urging that the improved machinery at workers’ command made the work easier and the output greater than at similar works. In the words of Bridge (1902: 208):

When the scale for 1889 was signed for the 119-inch plate-mill, it was based on rolling plates direct from ingots, and the output was about 2,500 tons a month. But when the ingots were first passed through the 32-inch slabbing-mill – the great machine that had developed out of Zimmer’s little Universal mill – and then through the 119-inch plate-mill, the tonnage of the latter was more than doubled. With the sweet unreason of the toiler, the men who operated the 119-inch plate-mill refused to share with their employers the cost of running the slabbing-mill, and demanded just as much for rolling plates from slabs as they had been getting for rolling plates from ingots; insisting, moreover, upon receiving all the benefit of the investment that had gone into this million-dollar machine. Similarly in the open-hearth department. When the 1889 scale was signed, this was a comparatively new business; and in three years it had been vastly improved. Tonnages had increased; labor had been made easier by the substitution of machines; but the benefits had mainly gone to the workmen.

Homestead became the turning point of a system that had been based until then on the industry and skills of industrial craftsmen but since then had given way to the centralised work organisation of big corporations. We can infer this process from the Amalgamated Association membership figures. The highest membership figures were in 1891 with 24,068 members. After the disastrous strike at Homestead Steel Works, the membership fell to 13,613 in 1893, and fluctuated between 15,000 and 10,000 until the First World War. After the Homestead defeat, employers began to pay day-wages, but once the threat of trade unionism faded away completely, piecework gradually replaced the contract system (Stone 1974). It was applied to all operations that called for a considerable amount of skill or wherever the work was above the level of unskilled labour. The tonnage rates started to be fixed by mutual agreement between employer and the workman or workmen who performed the work without trade union intervention. Foremen employed by the company progressively replaced the leading figure of the independent contractor. They earned a base salary and a bonus linked to the output of the furnaces under their supervision.

The technological development experienced by the iron and steel industry lessened the value to the employer of all workers and at the same time made the job of every individual, skilled and unskilled, to a greater or lesser degree insecure. A de-skilling process was active. In 1895, it was estimated that it would have taken 60,000 skilled puddlers one year to refine sufficient iron to supply the country, had iron been used in place of steel. In contrast, the same quantity of metal could be provided from Bessemer converters with the service of only 3,000 men and those, with few exceptions, less skilled than puddlers (Clark 1929, III). BITA notes that ‘the tendency in the American steel industry is to reduce by every possible means the number of highly-skilled men employed and more and more to establish the general wage on the basis of common unskilled labour. This is not a new thing, but it becomes every year more accentuated as a result of the use of automatic appliances which unskilled labour is usually competent to control’ (1902: 317). A new category of semi-skilled workers came into being. They were a workforce that possessed little or no general mechanical or metallurgical knowledge, but were able to perform relatively complex tasks, such as the operation of cranes and other mechanical appliances.

As a consequence of the reduction in the skill differentials, the earnings differentials had to be correspondingly narrowed so as to make them more consistent with differentials in skill requirements for the different jobs. In the Pittsburgh district between

13

1892 and 1907 daily earnings of unskilled steelworkers rose by about 20 percent while those of the skilled workers fell by as much as 70 percent. By contrast, average prices increased by 22 percent (Fitch 1911). The earnings reduction was accompanied by a general increase in working hours, from three shifts of eight hours to two shifts of twelve hours. In the Carnegie Steel Company in Allegheny County in 1907, only 120 out of 17,000 employees worked an eight-hour day, the remainder were on a two-shift day.

In summary, what was originally conceived as the solution for the labour problem – the contract system – turned out to be an inefficient instrument both as a compensation method and as a control device for industrial relations. The end of the contract system dissolved trade unionism, and as a result the power of skilled workers over bargaining and workplace issues came to an end. Furthermore, the same job of skilled workers was gradually transformed into a less critical production factor by altering the ratio between capital and labour. Hence, the high rates of technological change challenged the contract system at its roots, and the sliding scale system with its binding minimum base exacerbated the labour problem.

PPAARRTT II II

TTHHEEOORREETTII CCAALL PPRREEDDII CCTTII OONNSS

55.. AAGGEENNCCYY TTHHEEOORRYY ,, TTEECCHHNNOOLL OOGGII CCAALL CCHHAANNGGEE,, AANNDD WWOORRKK EERRSS’’

BBAARRGGAAII NNII NNGG PPOOWWEERR This section focuses on the role of technological change within a principal-agent model in order to understand to what extent a piece rate pay scheme, such as the contract system, is not an optimal compensation scheme when compared with a fixed pay scheme. By using some well-established theoretical tools I shall attempt to theoretically substantiate the observation that high rates of technological change together with strong trade unions make output-related pay particularly costly for the employer who then cannot sustain it in the long term.

When technological change occurs the production function changes, thus iIn a piece rate contract, and the employer needs to update the rates. If the employer does not update the rates, workers would change their effort according to the new technology. Since principals and agents have conflicting objectives we expect that workers would profit from the new technology at the expense of the employer. For example, workers may be induced to exert low effort levels due to income effects. In other circumstances, workers may exert the same effort level as before the introduction of the technological innovation and consequently earn more.5 Therefore, according to the specification of workers’ utility functions, workers gain from technological innovations without paying the price for their introduction. Firms, in turn, want to reduce the benefits to workers and gain the whole surplus stemming from their investment. In other words, firms would like to grant to workers the same reservation utility as before the introduction of the new technology.

Hence, technological innovation should give rise to the re-negotiation of rates. Piece rate workers oppose a simple adjustment of the rates which would only take into account the improved technology by keeping workers to their old participation constraint. Piece rate workers want to get the benefits of the technological advancement as well, particularly by forcing the firms to hold the old rates. In contrast, firms would like to adjust

5 Both effects cannot arise from a CARA (constant-absolute risk aversion) utility function because this does not allow for income effects.

14

the rates so that they get the whole benefit from the technological innovation.6 This is exactly what happened in the iron and steel industry in the second-half of the nineteenth-century in the United States when the contract system was in force. The high and enduring rate of technological innovation made piece rates quickly obsolete. Additionally, the steady low prices of the final output, to which the piece rates were tied, made inoperative the sliding scale system; thus, the minimum base became binding for long periods, thereby exacerbating the conflict between principals and agents. In effect, the minimum base became the actual rate to be negotiated and practically identified the level of reservation utility that workers claimed and defended through their bargaining power. In sum, well-organised workers drove rates to sub-optimal levels because they made rates re-negotiation extremely costly in terms of strikes, lockouts, and output restrictions. Consequently, actual and ‘incidental’ labour costs went up draining resources from the introduction of new technology, and also making the competition with non-unionised firms and fixed pay firms difficult.

However some questions arise. Do fixed pay schemes need to be updated as well once technological change occurs? Do they suffer from the same re-negotiation costs as piece rate payment schemes do? In principle, rates must be changed with fixed pay as well in order to adjust effort to the new optimal levels. However, suppose there is no re-negotiation. In the fixed pay case, effort levels would remain the same because they are contractually stated, but output rises due to technological change. Conversely, in the piece rate pay case, workers reduce (or otherwise adjust) their effort levels and gain the extra surplus from technological change. Thus, ceteris paribus, if contracts are not re-negotiated, under fixed pay the employer receives the full surplus from technological change even if he cannot get it optimally (i.e., by changing the effort rates) whereas under piece rate pay not only would workers gain from the higher turnout, but they have the possibility to adjust their effort, which is not stated in the contract, and get part, if not all, of the surplus from the new technology. Therefore, the conflict arising from technological change is more marked in the piece rate case than in the fixed pay case. Consequently, in principle, fixed pay firms should encounter fewer problems when rates must be changed. However, whether or not to have re-negotiation depends heavily on the bargaining power of trade unions and on the share of the ‘pie’ stemming from the new technology they can seize.

The following analysis relies on agency theory and its ability to highlight the conflicting objectives between workers and employers. A serious limitation of agency theory is the absence of any bargaining structure: the employer optimises by leaving the worker with no surplus through a binding participation constraint. However, we can account for workers’ bargaining power by using a repeated moral hazard model and allowing the second-period reservation utility to change. The size of the change would depend on workers’ power and the extent of technological change. Holding the first period rates is also another way of affecting the standard outcome of the agency theory in a way that is useful for the investigation.

First, a two-period model that grants a certain bargaining power to the worker is presented. Technological change occurs in the second period and it is multiplicative in the production function. Workers have the possibility to reject the contract in the second period (i.e., once the new technology has been introduced) if the contract does not grant

6 Once again, the type of adjustment (whether it is a reduction or an increase) of the intensity of incentives depends on the workers’ utility function. In our case, we are going to use the CARA utility function because it is the only one that allows closed-form solutions, and its tractability is simple. In any case, this specific type of utility function does not affect the final results.

15

them the same utility, provided that rates are left unchanged. Therefore, the employer must take into account this possibility when making the proposal. This is a model that compares a piece rate pay with fixed pay when a fully rational employer can offer a single contract with a set of rates for each period without writing a new contract once technology has changed. This employer can be considered a ‘forward-looking’ or ‘long-term’ manager, and is one who knows exactly the amount of technological change that is going to be introduced in the second period.7 Subsequently the model is extended by allowing for more than two periods and by introducing a more general cost-of-effort function. Then, the analysis is enriched by different contractual structures, which are compared with each other. In particular, three cases are considered. One case is without trade unions, and represents a sort of benchmark for the other two because the employer cannot do better than that. The other two cases depict different roles for trade unions. In one case, as in the model initially introduced, the bargaining power of trade unions originates from a positive second-period reservation utility, and two rates, one for each period, are set. The last case assigns to trade unions the power to hold the rates to their first period level, thus the employer can choose only one set of rates. Finally, the contractual structures are also analysed according to the time-span of the contract itself, thereby allowing for two types of managers, a long-term and a short-term manager, the latter being unaware of the technological change occurring in the second period, thus proposing contracts period by period.

5.1. The Model

Piece Rate Pay Contract

The principal is risk-neutral and makes a take-it-or-leave-it offer of a share of output for each period. The agent is risk-averse, and if he does not accept the contract the principal earns zero profits. The production function is linear on effort e, which is unobservable to the employer and which is hit by a random component θ, the latter being unobservable by both parties. The level of output y is verifiable (i.e., observable by both parties and also by a potential third party), and is such that y = e + θ, where E(θ)=0 and var(θ)=σ2.

Agents cannot save or borrow, which means that they must consume their entire income by the end of the period. This will make the formalisation much easier. The agent has an exponential utility function of the CARA type. The fixed part of the compensation is expressed by α, whereas β corresponds to the piece rate. The cost of effort c(e) is assumed to be equal to ½e2, such that it is a function of effort and it is increasing at an increasing rate.8 The coefficient of absolute risk-aversion r is a positive constant. The resulting utility function for the agent is the following:

U = –exp{–r[α+βy – c(e)]}

Maximising an exponential utility function is equivalent to maximising its certainty-equivalent. We assume that technological change, which affects the second period production function, is linearly multiplicative on effort and is represented by k (≥1), such that y2 = ke2 + θ. Consequently, k is set equal to one in the first period. Thus, the certainty-equivalents for each period are the following:

CE1 = α1 + β1e1 – ½rσ2β12 – ½e1

2

7 This hypothesis is relaxed further below when a short-term manager is introduced. 8 This type of function has a unitary second-order derivative. This is a simplifying assumption that is relaxed further below.

16

CE2 = α2 + β2ke2 – ½rσ2β22 – ½e2

2

The principal, by maximising his profits, encounters two types of constraints. One is the participation constraint, which establishes that the contract must be at least as good as any possible alternative that is available to the worker. Specifically, the certainty-equivalent of the first period is set equal to zero. For the second period, the employer must take into account a different lower bound, which depends on the wage claims arising with the introduction of new technology. Therefore, a certain bargaining power is granted to workers, who will be able to retain the surplus accruing from the improved technology when first period’s rates are left unchanged. Hence, the second period certainty-equivalent must be at least equal to the certainty-equivalent calculated at α1, β1, and at an effort level that represents the best effort exerted by the worker and realised according to the new level of technology.

The second type of constraint stems from the agent’s maximisation over his certainty-equivalents. This is the incentive-compatibility constraint, which imposes the best effort choice among those available to the agent for each period and which gives the following results:

β1 = e1 and kβ2 = e2

Thus, the principal must choose those α1, α2, β1 and β2 that maximise expected profits over two periods by taking into account overall four constraints. We replace the parameter rσ2 with ε in order to simplify the expression. An increase in the value of ε means either a higher workers’ risk-aversion or a higher variability of output. The principal’s problem is the following:

Principal’s Problem

[ ]2211

2

11ok

2111

ok11

22

22222

21

21111

22221111,,,

and

),(e2

1

2

1),(e

2

1

2

1

02

1

2

1

s.t.

)e(2121

eke

keke

ee

kekeeMax

==

−−+≥−−+

≥−−+

−−+−−

ββ

βαεββαβαεββα

εββα

βαβαββαα

The expression ek°(α1,β1) is worker’s optimal effort level calculated at the first-period rates by taking into account the technological change occurring in the second period (i.e., ek

°=β1k). The right-hand side of the second-period participation constraint corresponds to the surplus accruing to the worker due to his bargaining power. The optimal contract is the following:

22

242*22

2*2

22*12

*1

)(2

)(1

)(2

1

1

εε

αε

β

εε

αε

β

+−−−

=+

=

+−

=+

=

k

kkk

k

k

kk

The contract proposal is a sort of map of rates which varies according to the technological change occurring between the two periods.9 As predicted by the standard 9 It may happen that α is negative. This result is plausible. For instance, in case of no production, skilled ironworkers could lose money because they gathered their own production inputs at their expense.

17

principal-agent theory, ‘risk’ (i.e., ε) has a negative impact on the intensity of incentives, β. The optimal β1 decreases as k increases, whereas β2 gets asymptotically close to one. This pattern is not surprising given the specification adopted for the workers’ utility function, wherein there are no income effects. Indeed, the optimal effort levels chosen by the agent are such that e2 is higher than e1, because technological improvements make worthwhile an increase in labour productivity in order to exploit the higher capital productivity. This increase is greater the greater is technological change.

ε

ε

+=

+=

2

3*2

2*1

1

k

ke

ke

There is another reason why e2 is higher than e1. Since the first-period piece rate affects the second-period participation constraint, the employer is induced to reduce β1 because a higher β1 would increase workers’ surplus for the second period. As a result, a low β1 reduces the leverage effect on e1. In the extreme case, if k is particularly high, it is convenient to shift the whole production process to the second period because the product value of the first period is trivial when it is compared with the second period’s. Higher β1’s can only cause higher costs in terms of higher reservation utility in the second period.

The overall expected profits with piece rates ΠPR are increasing in k and decreasing in ε as it can be easily inferred from the expression below.

( )εβαβα+

+=−−+−−=Π

2

4

22221111 2

1

k

kkekeeePR

Fixed Pay Contract

According to the principal-agent model, a fixed pay contract can be realised under two circumstances. One is fixed pay with monitoring, where the employer can perfectly observe effort. The employer bears the cost of monitoring but gains from a perfect observability of effort because workers cannot adopt any moral hazard behaviour. Hence, the employer can enforce a specific effort level through a forcing contract. This means that the principal can claim before the court the fulfilment of the contract, which prescribes the effort level to be supplied in exchange for a fixed pay level. The second circumstance arises when the principal gives in to moral hazard, which occurs when effort control is prohibitively expensive or impossible to perform. In this case, the principal guarantees minimum earnings that are compatible with the low effort level exerted by the agent who profits from the lack of control. In this modelling, the first type of contract is chosen because it is a better way of comparing it with the piece rate case. Moreover, there is no need to take into consideration the low effort level parameter; however we must bear in mind that monitoring is costly and should be deducted from the overall profits as a sort of lump sum allocated to effort control.

Following the same logic for piece rate pay, workers would hold the first period’s rates and ask for the utility accruing once technological change has occurred.10 However, in this case, workers would gain nothing from holding the rates because their pay is fixed and is not linked with the production level. Thus, the right-hand side of the second period’s

10 In a fixed pay contract the contractual rates are defined by the fixed salary but also by the effort level to be supplied.

18

participation constraint is zero. In other words, ‘sticky’ rates have no impact on workers’ utility with fixed pay unless workers make an explicit request on the share of technological gain.11

In order to hold the worker to the job, the principal must provide a fixed pay that satisfies the participation constraint for each period. Analytically,

02

1 and 0

2

1 222

211 ≥−≥− ee αα

These constraints are both binding and are inserted into the objective function of the principal. The whole expression is maximised according to the effort levels of each period. Thus, the principal offers a fixed pay contract that adjusts the rates according to the new level of technology achieved in the second period. The result is the following,

2*2

*2

*1

*1

2

1 e

2

1 1

kk

e

==

==

α

α

Expected profits are as follows:

( )12

1 2 +=Π kFP

Comparison Between the Two Payment Schemes

By comparing the two cases we can explore in what circumstances piece rates are preferable to fixed pay and vice versa as technological change occurs. Therefore, we must analyse the size of the difference between ΠFP and ΠPR. Once again, we should bear in mind that the fixed pay case does not take into account the monitoring costs. Analytically we have

( )( )ε

εε+

−++=Π−Π=Π

2

2

2

11

k

kD PRFP

DΠ turns out to be increasing in k and ε, as shown in Figure 4-A, where DΠ is depicted for two levels of risk. As k increases, fixed pay becomes ceteris paribus more profitable with respect to piece rate pay as one can see from the increasing curves. This is a very important result. By paying by fixed pay the employer collects the entire surplus of the increased productivity, and this gets larger during periods of high technological and technical enhancement. As mentioned before, piece rate profits increase with technological improvements but the resulting surplus must be shared with the worker. Additionally, the more important the risk component the less favourable is piece rate pay. This last result is in line with the normal predictions of the principal-agent theory. Thus, the gap between the two payment schemes becomes larger as ε and/or k increase as highlighted from Figure 4-A.

11 Further below, a higher bargaining power is assigned to workers, such that they can gain a positive surplus from technological change. It can be argued that, in order to make a fair comparison, fixed pay workers should get the same surplus as piece rate workers; however, we must take into account the bargaining mechanisms that occur for each specific contractual arrangement, and it is for precisely this reason that fixed pay workers do not have the same contractual terms as piece rate workers.

19

monitoring costs

fixed pay preferable

piece rate pay preferable

Graph A. Comparison of the two payment systems Graph B. Comparison with monitoring costs

FFiigguurree 44.. CCoommppaarriissoonn bbeettwweeeenn FFiixxeedd PPaayy aanndd PPiieeccee RRaattee PPaayy

However, these results do not take into account the role of monitoring costs which would reduce fixed pay profits. Therefore, there may be jobs where monitoring costs are rather high; as a result, piece rate pay could outperform fixed pay up to a certain level of k. In Figure 2.4-B, the horizontal line depicts a possible amount for monitoring costs, which should be subtracted to the fixed-pay profits. For those values of k such that the DΠ lies above this line, fixed pay is still preferable. Yet, the difference-in-profits function tends asymptotically to a finite value as k→∞, which means that for high levels of monitoring costs, piece rate pay can be preferable however large k might be.

Extensions to the Basic Model

We can deduce two routes by which technological change can affect a payment system. One is the number of times technological improvements occur. The other is the magnitude of technological change itself. We have just analysed a two-period model in which we can alter k in order to determine the impact of different magnitudes of technological enhancement on payment systems. This means that we took into account only a single technological wave occurring between two periods. However, we may be interested in analysing several technological advances that take place over several periods. In the same fashion as depicted by the two-period model each single technological shock gives rise to a sort of ‘re-negotiation’ in which a worker would not give up the surplus he could earn with a higher productivity of capital. Hence, it is interesting to see how an increase in the number of periods would affect the final outcome of the model by bearing in mind that the employer is a long-term manager who perfectly predicts the magnitude and the number of technological shocks.

Firstly, in order to allow comparison between different periods we must set the same technological change between the first and the last period; in other words, the level of technology that is achieved in the last period is exactly the same for each case. Secondly, within each case the same increment of technology between periods is assumed. Finally, the overall duration of the contracts must be the same.12 As a consequence, technological level (TL) at period i is as follows:

12 In the optimisation problem, additional periods increase profits because they are simply added. Thus, I had to divide the overall profits of each contract by the number of periods, t, in order to make the comparison possible.

20

t1,...,ifor )1(

)1)(1(1 =

−−−

+=t

kiTLi

The parameter k denotes the level of technology in the last period whereas t corresponds to the number of periods or, alternatively, the number of possible re-negotiations minus one. At period one technology is set to one. For example, for a three-period model technological level would be TL1=1, TL2=(1+k)/2, TL3=k, for a four-period model TL1=1, TL2=(2+k)/3, TL3=(1+2k)/3, TL4=k, and so on for an increasing number of periods. Thus, by following the same procedure as in the two-period model, we can obtain the profits for the three-period and four-period models. As to piece rate pay, Figure 5-A shows the curves of profits according to the number of technological waves. Each profits curve denotes the average profits when different numbers of re-negotiations are hypothesised in the piece rate pay scheme. The main prediction is that as the number of periods increases, profits under piece rates get lower, and the difference between fixed pay profits and piece-rate profits gets larger the higher the total technological advancement k over the whole time span.

Graph A. Average profits as t changes (ε=0.1). Graph B. Comparison as t grows (ε=0.1).

FFiigguurree 55.. CCoommppaarriissoonn bbeettwweeeenn SSeevveerraall RRee--nneeggoottiiaattiioonnss

This pattern can be attributed to the ‘re-negotiation’ cost. Even if the production function, as well as the rates, is immediately adjusted according to the improved technology, each time the employer must divert additional surplus to the worker. Furthermore, as inferred from the basic two-period model, at high levels of k, the bulk of the production process is moved to the last period, but with additional periods, the last period is increasingly shorter. This also explains the reduction of profits for greater t’s. Fixed pay follows a similar pattern. When more periods are added, profits per period tend to be lower, but the difference is less noticeable than in the piece rate case. However, the pattern for the fixed pay case is exclusively due to the form of the production function and the cost-of-effort function, because in the fixed pay contract there is no rate re-negotiation. Figure 5-B shows the difference in profits between the two payment schemes (i.e., (ΠFP–ΠPR)(t)). A greater number of technological waves occurring in a specific time span considerably reduces the chances to adopt piece rate pay with respect to fixed pay as one may notice from the larger difference in profits. Additionally, as k increases, a rapid technological change makes piece rate pay an increasingly inferior option.

Another simple extension introduces a more general cost-of-effort function. So far, c(e) was set equal to ½e2, so that the second-order derivative is equal to one. However, a more general form can be introduced by letting the second-order derivative assume a

21

different value, for example the parameter c. Consequently, the cost-of-effort function will be c(e)=½ce2. The difference in profits in a two-period model will be:

)(2

1

2

1

)(2

1

2

12

2

2

42

kcc

ck

ckcc

k

c

kD PRFP +

−+=

+

+−

+=Π−Π=Π

εε

ε

Suppose c=1, the same result as in the basic model is obtained. Figure 2.6 depicts the pattern of the difference-in-profits curves for two different values of c.

FFiigguurree 66.. DDii ff ffeerreennccee iinn PPrrooffii ttss ffoorr ddii ffffeerreenntt vvaalluueess ooff cc

For harder jobs (i.e., high c), the difference between the two payment schemes becomes trivial and, when monitoring costs are added to the fixed pay scheme, piece rate pay may prevail. From the above expression we realise that the difference-in-profits

function is upward bounded, and its limit is 2c2

1 ε+ . Consequently, as c increases and/or ε

decreases relatively low monitoring costs are enough to make piece rates preferable. It is worthwhile noting that c can represent the worker’s ability to perform a specific task. The higher the ability the lower is c. Consequently, when analysing the output-related pay applied to skilled workers in the iron and steel industry, we should take into account that c was relatively lower for them than for other ironworkers. Thus, this is an important result: when technological change occurs, skilled workers should be paid fixed pay.

5.2. Choice under Different Workers’ Bargaining Power Structures

In this section the main model is extended in order to incorporate different degrees of workers’ bargaining power and introduce two different types of manager. The purpose is to establish under what institutional conditions fixed pay is preferable to piece rate pay. Additionally, the differences in profits with technological change and without technological change for each compensation scheme are compared, so as to understand which system gives a competitive advantage when introducing an improved technology. If we show that the difference in profits with and without technological change under fixed pay is higher than the difference in profits with and without technological change under piece rate pay, we have provided evidence that the gain accruing from technological change is higher under fixed pay than under piece rate pay. A major feature of this comparison is that the difference in profits of fixed pay cancels out the monitoring costs,

22

which are supposed to be the same both for the case with technological change and for that without technological change. Therefore, the comparison between the two payment systems can be analysed without making any conjecture over monitoring costs.

Six different cases can arise according to the type of manager and the bargaining power of trade unions. The employer can be of two types:

1. A forward-looking or long-term manager (as that of the previous model);

2. A conservative or short-term manager.

The long-term manager knows how much technological change will be introduced in the second period and incorporates this information in the contract from the first period. The short-term manager offers a contract period by period, as technological change is unknown. Thus, with a short-term manager, the first contract makes only a provision for the first period without any reference to the technological change occurring in the second period. We assume that the type of manager is independent of workers’ power but it is related, for example, to the level of knowledge of technological change, personal returns to the manager, duration of the period in office.

Three different institutional structures can occur.

a. The no-trade-unions case (NTU);

b. Trade unions affecting negotiation of rates (NR);

c. Trade unions leading to sticky rates (SR).

In the NTU case workers have no power whatsoever in affecting bargaining and contractual outcomes, and consequently they get no surplus from the introduction of the new technology. The employer optimally proposes two rates, one for each period: (α1,e1) and (α2,e2) for fixed pay, (α1,β1) and (α2,β2) for piece rate pay. The long-term manager chooses these rates at the beginning of the first period, whereas the short-term manager updates rates immediately after technological change has occurred. Overall profits are the same for both the long-term manager and the short-term manager. This means that in non-unionised firms, long-term managers cannot profit from their knowledge in advance over technological change relatively to their short-term colleagues.

The NR case arises when trade unions are able to reduce employers’ surplus by imposing that a share of the surplus stemming from technological change accrues to workers. The long-term manager incorporates workers’ claims in the whole two-period contract; thus second period rates are negotiated before the beginning of the first period. A short-term manager does not (or cannot) anticipate workers’ claims arising from technological change already in the first period. The short-term manager deals with them only once the innovation has occurred, therefore second period rates are negotiated at the end of the first period. Hence, the outcome of the first period is taken as given and workers’ bargaining power is only introduced in the rate re-negotiation of the second period in the form of a positive reservation utility, whose size depends on technological change.

In the piece rate case, the NR bargaining structure corresponds to what has been presented in the model of the previous section with a long-term manager: trade unions’ claims would set the second-period reservation utility to be equal to the surplus stemming from technological change by holding the first-period rates constant and correspondingly adjusting effort to the new production function. As already examined in the previous section, the piece rate case should be compared with a fixed pay case where trade unions

23

would like to hold the first-period rates and gain from technological change. However, a fixed pay contract establishes not only the pay rate but also the level of effort thereby keeping the participation constraint binding. Consequently, fixed pay workers would not gain from keeping the same rates of the first period, because it is implicit that effort cannot be adjusted (unlike the piece rate system).13

Therefore, in order not to replicate the results of the previous section, we grant fixed pay workers the power to get the same pay rate (α1) and to profit from technological change through reduced workload; namely in the second period workers would like to deliver the same output as in the first period and get the whole surplus from technological change in terms of lower effort levels. As a consequence, only a contract that grants this increased utility would be accepted. This last bargaining structure considers stronger trade unions, which are able to gain from technological change without limiting their bargaining power to the status quo of the first period. Analytically, since y1 = e1 + θ, the introduction of new technology would change the production function such that y2 = ke2 + θ. If workers want to profit fully from technological change by getting the same salary, they should set

e2 equal to k

e1 such that 11

2 yk

eky =+= θ ; in other words, workers reduce effort but

deliver the same output. If we grant this type of power to workers, the participation

constraint of the second period must take the form 2

11

222 2

1

2

1

−≥−k

ee αα .14

The last case under examination is when trade unions exert their power in such a way to make rates sticky (SR). Trade unions may want to hold the old rates and profit from technological change by forcing the long-term manager to write only one rate for both periods or, alternatively, by imposing on a short-term manager no rates re-negotiation in the second period such that only the first period rate is applied.15 This is an unwelcome outcome for the employer who cannot maximise his second period profits because workers prohibit negotiation. As a result, the employer can only marginally profit from the introduction of new technology. Piece rate workers have the possibility of gaining from the improved technology over the entire second period. By contrast, fixed pay workers do not gain any surplus because their rates remain unchanged; however, they could considerably constrain the profits of fixed pay firms. This last circumstance may seem paradoxical because workers would not gain anything by forcing firms to hold the rates. However, it is not uncommon to see fixed pay workers defend their old pay and effort rates simply

13 From the viewpoint of fixed pay workers, this case would be the same as the NTU case. It would also be the same for the employer as well, who can propose a contract that in the second period would give to workers the same utility of the first period (i.e., zero in our case). Indeed, eventually workers’ participation constraint would be binding in both periods; thus, asking the same utility of the first period would bring about no effect. 14 As one can see from the appendix, eventually the worker is going to work more in the second period contrarily to what his initial intentions were. In effect, this contract must be seen as the outcome stemming from a possible threat that trade unions can put into effect in the second period if rates are not changed by accounting for the different production rates. As a consequence, by maximising the programme, the principal simply anticipates this threat and includes the relevant cost in the programme. 15 This solution may also occur when employers fear that re-negotiation costs are going to be high once technological change will take place. High cost of re-negotiations may be due to several reasons. For example, the new contractual terms may be too favourable to workers because they have strong bargaining power; workers’ retaliation may be very costly by causing strikes, stoppages, etc.

24

because of their consolidated habits, which may also lead them to resist the introduction of new technology.

In Table 3, by comparing the three different contractual structures, which correspond to three distinct trade union bargaining powers, we realise that employers are seriously damaged by sticky rates.

Table 3. DDIIFFFFEERREENNTT BBAARRGGAAIINNIINNGG SSTTRRUUCCTTUURREESS BBYY DDIIFFFFEERREENNTT TTYYPPEESS OOFF MMAANNAAGGEERRSS

NTU NR SR

Fixed Pay

( )0

12

1 2

=

+=Π

S

k

2

2

2

4

2

1

2

1

k

kS

k

k

−=

+=Π

0=

=Π

S

k

Short-Term Manager

Piece Rate Pay

( )0

2)1(2

12

4

=

++

+=Π

S

k

k

εε ( ) ( )

( )22

2

4

2

2

12

1

212

2

ε

εεε

+

−=

++

+

−+=Π

kS

k

kk

( )

( )22

2

2

12

1

1

1

ε

ε

ε

+

−=

+

+=Π

kS

k

Fixed Pay

( )0

12

1 2

=

+=Π

S

k

( )22

24

2

4

122

12

−

−=

−=Π

k

kkS

k

k

( )

04

1 2

=

+=Π

S

k

Long-Term Manager

Piece Rate Pay

( )0

2)1(2

12

4

=

++

+=Π

S

k

k

εε ( )

( )22

2

2

4

2

1

2

1

ε

ε

+

−=

+

+=Π

k

kS

k

k

( )( )

( ) ( )( )22

222

2

22

8

11

4

1

ε

ε

+

−+=

+

+=Π

k

kkS

k

k

All profits in the last column are lower than all corresponding profits of the NR case.16 Evidently, the NR profits are lower than the corresponding profits of the no-trade-unions case. Sticky rates do not allow employers to profit from the implementation of new technologies, and this, of course, becomes a serious impediment when technology has a considerable impact on the production process. Sticky rates are not advantageous to fixed pay workers either. Consequently, under fixed pay contracts, moving from sticky rates to negotiated rates would represent a Pareto improvement.

The same observation is valid for piece rate contracts with short-term managers. Indeed, piece rate workers already get their maximum surplus by negotiating the rates; forcing the short-term manager to hold the rates would not grant workers any additional surplus. Conversely, with long-term managers, piece rate workers gain more by holding the rates fixed rather than negotiating a higher reservation utility before signing the

16 Short and long-term managers offering fixed pay are the only exception to this pattern, but only for very low levels of k. This means that a reasonable technological enhancement is enough to make all the NR cases preferable with respect to all SR cases.

25

contract as in the NR case. Excluding the latter case, when technological change occurs, it is beneficial to negotiate apposite rates such that both parties can profit from the improved technologies. However, by holding the rates fixed, a piece rate worker would immediately gain from the introduction of the technology and this is an important difference in the attitude of trade unions to negotiating piece rate contracts compared to fixed pay contracts.

In summary, when trade unions are able to influence the outcome of workers’ contracts (especially piece rate contracts) a new technology must not be introduced abruptly but should be discussed with trade unions and its benefits negotiated. Even those firms that offer fixed payments would find it beneficial to negotiate new rates (i.e., wages and effort) and grant some surplus to the workers. It is worthwhile noticing that a long-term manager reduces workers’ surplus in all instances when compared with a short-term manager. Lower surplus for workers is translated into higher profits. Hence, a manager who has preventive knowledge of the amount of technological change and incorporates this knowledge into the contract is better off.

DIFFERENCE IN PROFITS WITH AND WITHOUT TECHNOLOGICAL CHANGE

The comparison of the profit levels for each contractual scheme is important because it explains which payment scheme is the most profitable according to different degrees of workers’ power when technology is introduced as a parameter. However, we may also want to understand which type of contract achieves the highest profit gains when an output-enhancing technology is introduced. This analysis is important because we can compare the impact that the same technological shock has on competing firms applying different compensation schemes. Indeed, there may be payment schemes that ceteris paribus are more beneficial than others when new technologies or techniques are introduced in the production process. In order to carry out this analysis we need to calculate the difference between profits with technological change and profits without technological change (see the Appendix and Table 3). As mentioned above, by calculating this difference, monitoring costs for fixed pay are cancelled out. This allows a more precise comparison between the two compensation schemes.17

The simulations carried out within the three different bargaining structures suggest that when trade unions do not possess any bargaining power (i.e., NTU case), the impact of technological change is basically equivalent for both compensation schemes, to wit, two firms, one adopting piece rates and the other fixed pay, will approximately gain equally from technological change. Small differences arise when the risk component becomes important and technological improvements become significant; in such a case, fixed pay is slightly more favourable than piece rate pay.

Marked differences arise when trade unions secure certain levels of surplus from technological change through their bargaining power. Figure 7 on the following page shows the NR and SR cases for different types of manager. These graphs depict the difference between the profit gains from technological change under fixed pay and the gains from technological change under piece rate pay for a large set of risk/technological change combinations. Thus, positive values signal that technological shocks increase profits for fixed pay firms more than they do for piece rate firms and vice versa for negative values.

17 Suppose the gains from technological change for fixed pay are the following: ΠFP

k–ΠFP. Where ΠFPk is

equal to the two-period profits with technological change k(>1) in the second period, whereas ΠFP is equal to the two-period profits when there is no technological change, namely k=1 in both periods. It is easy to show that difference between profits cancel out monitoring costs that apply to both cases.

26

One can immediately appreciate that applying fixed pay is preferable for the large majority of bargaining structures and levels of technological change. In particular, short-term managers applying piece rates, who must re-negotiate rates in the second period (i.e., NR case), are very vulnerable to workers’ requests as workers can claim a large share of technological gain. Most probably this was the long-term outcome that could be applied to the emerging American iron and steel industry. Managers updated the rates only when the urge for a change due to the innovations became significant. This imposed increasingly high reservation wages to skilled workers, who did not accept worse conditions than those acquired through the technological innovations. However, applying output-related pay, like the contract system, was inefficient vis-à-vis a fixed payment scheme that could ensure larger profits even by allowing for some surplus to be shared with the workers. Under the NR bargaining structure, long-term managers still gain more by applying fixed pay rather than piece rate pay but without the marked difference experienced by short-term managers.

12

34

5

k

00.5

11.5

2 Risk

-2

-1

0

1

2

Difference between Gains

23

45

00.5

11.5

12

34

5

k

00.5

11.5

2 Risk

-2

-1

0

1

2

Difference between Gains

23

45

00.5

11.5

NNRR -- SSHHOORRTT--TTEERRMM MMAANNAAGGEERR ((AA)) NNRR -- LLOONNGG--TTEERRMM MMAANNAAGGEERR ((BB))

12

34

5

k

00.5

11.5

2 Risk

-2

-1

0

1

2

Difference between Gains

23

45

00.5

11.5

12

34

5

k

00.5

11.5

2 Risk

-2

-1

0

1

2

Difference between Gains

23

45

00.5

11.5

SSRR -- SSHHOORRTT--TTEERRMM MMAANNAAGGEERR ((CC)) SSRR -- LLOONNGG--TTEERRMM MMAANNAAGGEERR ((DD))

FFiigguurree 77.. DDii ff ffeerreennccee bbeettwweeeenn GGaaiinnss ffrroomm TTeecchhnnoollooggiiccaall CChhaannggee iinn tthhee NNRR aanndd SSRR ccaasseess

The SR case with long-term managers also shows unequivocally that fixed pay offers higher incremental profits than piece rate pay. By contrast, with a short-term

27

manager, piece rate pay may prevail for very large levels of k. This pattern is mostly explained by the utility functions of the CARA type. Under piece rates and short-term managers, as rates are held fixed, workers increase their effort for increasingly larger levels of k because there is no substitution of effort for leisure due to income effects. Conversely, fixed-pay profits suffer much from the cost of keeping the rates (and therefore the effort level) to their first period level. Yet, fixed pay with a long-term manager can internalise technological change into the single rate which is going to be applied for both periods.

Even if not reported in the graphs, which depict the difference between the profit gains from technological change of fixed pay and piece-rate pay, the level of the gains are higher when rates are negotiated rather than preserved to their first period level. In other words, regardless of the payment system, sticky rates do not allow to take full advantage of technological change. This corroborates the conclusion of the previous section, to wit, overall profits under sticky rates are always lower than negotiated rates. Again, trying to bargain over the rates is extremely important for employers if they want to profit from improved technologies; if this is not possible employers may be induced to get rid of trade unions, these attempting to preserve old rates and seize the surplus from employers’ investments.

66.. CCOONNCCLL UUSSII OONN This investigation has highlighted the limitations of the use of a specific incentive scheme -– the contract system – that played a very important role in the history of industrial relations in the iron and steel industry of the United States. A growing industry, such as that of iron and steel in the second half of the nineteenth-century, could not indefinitely sustain a piece rate system that was originally born within an industrial organisation that did not experience the rates of production and technological change and the dynamics of the industrial relations that marked that sector in that specific historical epoch.

The investigation has shown how costly applying piece rate pay can be when high rates of technological innovation are coupled with strong trade unions. By using agency theory, it has shed some light on the conflicting nature of piece rate pay compared to fixed pay as new technology is introduced. Piece rate workers can immediately (i.e., without rate changes) profit from new technology both by the higher output brought about by the improved technology and by adjusting their effort levels, since the latter are not contractually stated. If we accept that in reality the expiration date of labour contracts usually differs from the date of introduction of new technology, then piece rate workers have the time to earn additional surplus until the new contract is discussed and subsequently signed. This makes rates negotiation very difficult. Workers could stake their advantage in the confrontation with their employer when second-period rates must be negotiated. If employers attempt to limit this advantage, workers could threaten to go on strike. Therefore, rates are likely to be sticky because rates updating will not be as easy as implementing new technology. Conversely, fixed pay workers, given the nature of their contract, do not in general gain any benefit from technological change because, on the one hand, a higher production does not affect their pay, and on the other hand, their effort level is contractually stated and monitored. Thus, fixed pay workers cannot exert lower effort levels unless they re-negotiate rates. This makes their bargaining power weaker compared to piece rate workers.

From the theoretical investigation we draw further conclusions. Firstly, the employer would be extremely tempted to get rid of trade unions when new technology is introduced. Indeed, trade unions can considerably reduce profits either by asking for a

28

share of the gains stemming from technology or by holding rates at sub-optimal levels. For example, ironmasters continually appealed to strike breakers coming from the South and from Europe as they were non-unionised and asked for lower rates (Krause 1992). This had the twofold effect of not only reducing union control in the plants but also of aligning the participation constraint to lower levels. In other words, the surplus that skilled workers wanted to claim was sustainable only by virtue of the strength of their trade unions and not because of the market conditions. The mechanisation brought about by the change in technologies and the resulting specialisation of labour reduced the professionalism and the skills previously required; this increased workers substitutability thereby reducing the actual reservation utility. Secondly, the choice of the payment system has an important impact on industrial relations and the production process. Where the payment system introduces several negotiations over the surplus stemming from technological change, the consequences are either stop-and-go production processes or employers’ reluctance to introduce new technology. Emblematic examples are the U.S. iron and steel industry for the former, and the well-known case of Lincoln Electrics for the latter (Milgrom and Roberts 1992). In particular, an extension to the model would be the endogenisation of technology, where one may expect that piece rate pay would result in a lower level of investment. However, in the iron and steel industry, strong trade unions coupled with piece rate pay did not severely undermine investments in innovative technologies. On the contrary, both the growing demand of iron and steel and the necessity to de-skill jobs, which would have reduced workers’ bargaining power, required increasingly higher investments on production and process innovations.18 Thirdly, according to the theoretical investigation, the employer should predict in advance the amount of technological change that will be introduced in the production process, and consequently should make all possible efforts to negotiate the corresponding new rates with the trade unions and try to anticipate their claims in advance.

The historical account offers additional insights about the collapse of the contract system as such, and consequently the decline of a certain system of industrial relations, than the theoretical investigation itself can predict. For example, the theoretical investigation did not account for an important feature of the contract system: the sliding scale system. Piece rates depended on the price of the bar iron, and, most importantly, they could not fall below a certain minimum base. Regardless of the introduction of new technology, the market conditions of the bar iron, which were marked by very low price levels, contributed to the decline of the contract system because they made more compelling the re-negotiation of the rates. The effects of technological change itself on the reference prices of the sliding scale system remain unclear. Presumably, not only did technological change make the production rates quickly obsolete but it also affected the product markets by pushing down the reference prices such that the re-negotiations of the minimum base rates compelled more frequent updating.

18 In turn, explicit incentive pay continued to survive because it was nonetheless considered the most efficient way to control moral hazard.

29

RREEFFEERREENNCCEESS

Allen, Robert C. (1979) ‘International Competition in Iron and Steel, 1850–1913’, The Journal of Economic History, 39(4): 911–937.

BITA (1902) American Industrial Condition and Competition, London: British Iron Trade Association.

Bridge, James H. (1903) The Inside History of the Carnegie Steel Company, New York: The Aldine Book Company.

Clark , Victor S. (1929) History of Manufactures in the United States, Volume II 1860–1893 and Volume III 1893–1928, New York: McGraw-Hill Book Company.

Doeringer, Peter B. (1968) ‘Piece Rate Wage Structure in the Pittsburgh Iron and Steel Industry – 1880–1900’, Labor History, 8: 262–274.

Elbaum, Bernard and Wilkinson , Frank (1979) ‘Industrial relations and uneven development: a comparative study of the American and British steel industries’, Cambridge Journal of Economics, 3: 275–303.

Fitch, John A. (1911) The Steelworkers, New York: Russell Sage Foundation.

Gold, Bela, Peirce, William S. and Rosegger, Gerhard (1970) ‘Diffusion of Major Technological Innovations in U.S. Iron and Steel Manufacturing’, The Journal of Industrial Economics, 18(3): 218–241.

Krause, Paul (1992) The Battle for Homestead, 1880–1892: politics, culture, and steel, Pittsburgh: University of Pittsburgh Press.

Milgrom , Paul and Roberts, John (1992) Economics, Organization and Management, Upper Saddle River, NJ: Prentice-Hall.

Novack, David E. and Perlman, Richard (1962) ‘The Structure of Wages in the American Iron and Steel Industry, 1860–1890’, The Journal of Economic History, 22(3): 334–347.

Popplewell, Frank (1906) Iron and Steel Production in America, Manchester: Victoria University of Manchester.

Stone, Katherine (1974) ‘The Origins of Job Structures in the Steel Industry’, in Fitzgerald Robert and Rowley Christopher (eds), Human Resources and the Firm International Perspective, Volume II, Chapter 2, Cheltenham: Edward Elgar.

Temin, Peter (1964) Iron and Steel in Nineteenth-Century America, Cambridge, MA: M.I.T. Press.

30

AAPPPPEENNDDII XX

The case of no technological change leads to the same profits levels for each type of

manager and for each degree of involvement of the trade unions in the bargaining process.

FFIIXXEEDD PPAAYY

12

1,1

2

1,1

21

22

11

=Π

==

==

+

α

α

e

e

PPIIEECCEE RRAATTEE PPAAYY

ε

εβ

εε

αε

εβ

εε

αε

+=Π

+=

+

−=

+=

+=

+

−=

+=

+ 1

1

1

1,

1

1

2

1,

1

1

1

1,

1

1

2

1,

1

1

21

2

2

22

1

2

11

e

e

The case with technological change leads to the following results.

NNTTUU

FFIIXXEEDD PPAAYY 2

22

11

2

1,

2

1,1

kke

e

==

==

α

α

SSHHOORRTT-- AANNDD LL OONNGG--TTEERRMM MM AANNAAGGEERR

PPIIEECCEE RRAATTEE

PPAAYY ( )( )22

24

22

2

22

3

2

2

111

2,,

1

1

2

1,

1

1,

1

1

ε

εα

εβ

ε

εε

αε

βε

+

−=

+=

+=

+

−=

+=

+=

k

kk

k

k

k

ke

e

SSRR

FFIIXXEEDD PPAAYY 2

1,1 == αe

SSHHOORRTT--TTEERRMM

MM AANNAAGGEERR PPIIEECCEE RRAATTEE

PPAAYY εβ

εε

αεε +

=

+

−=

+=

+=

1

1,

1

1

2

1,

1,

1

12

21

kee

FFIIXXEEDD PPAAYY 2

2

1

2

1,

2

1

+=

+=

kke α

LL OONNGG--TTEERRMM

MM AANNAAGGEERR PPIIEECCEE RRAATTEE

PPAAYY

( )( )( )

( ) ( )εβε

εα

εε

+

+=

+

+−=

+

+=

+

+=

2

22

2

2

2

2

22

2

1

2

1,

2

1

2

1

,2

1,

2

1

k

k

k

k

k

kke

k

ke

31

NNRR

FFIIXXEEDD PPAAYY

2

24

22

11

2

1,

2

1,1

k

kkke

e

−+==

==

α

α

SSHHOORRTT--TTEERRMM

MM AANNAAGGEERR

PPIIEECCEE RRAATTEE

PPAAYY

( ) ( ) εβ

εε

εα

ε

εβ

εε

αε

+=

+

−+

+

−=

+=

+=

+

−=

+=

2

2

22

2

22

64

22

3

2

1

2

11

,12

1

2,

1

1,

1

1

2

1,

1

1

k

kk

k

kk

k

ke

e

FFIIXXEEDD PPAAYY

22

46

22

2

2

2

12

2

1

)12(2

34,

122

1,

12

−−

==

−=

−=

k

kkke

k

k

k

ke

α

α

LL OONNGG--TTEERRMM

MM AANNAAGGEERR

PPIIEECCEE RRAATTEE

PPAAYY

εβ

εε

αε

εβ

εε

αε

+=

+−−−

=+

=

+=

+−

=+

=

2

2

222

242

22

3

2

2122121

,)(2

)(1,

1

,)(2

1,

1

k

k

k

kkk

k

ke

kkke