CORPORATIST AND DECENTRALISED LABOUR UNIONS IN A MACROECONOMIC MODEL WITH IMPERFECTLY

COMPETITIVE FIRMS*

NICHOLAS ROWE

Carleton University

I. INTRODUCTION

Some economists have noted that countries where wages are negotiated centrally by economy- wide federations of employers and labour unions tend to have lower rates of unemployment than countries where wages are negotiated in a decentralised manner by individual employers and their labour unions! And whereas cartels normally put pressure on their members to keep prices up, economy-wide federations of labour unions (or their political representatives when in power) instead often pressure their constituent labour unions to keep wage demands down. This paper provides a simple and general model which accounts for these observations.

In their seminal article, Calmfors and Driffill (1988) have formally modelled an economy where wages and employment are determined by bargaining between labour unions and employers' federations, and have derived the result of a U-shaped relation between level of employment and size of labour unions. When unions are very small they have little market power and so employment is high. When unions are medium-sized they have more market power, and each union is prepared to sacrifice some employment to gain higher real wages. But when one union increases its wages this also causes the price of output in its sector to rise, and this imposes an externality on other unions, because it reduces their real wages. When one big super-union covers the whole economy employment is again high, because the super- union internalises these externalities.

The model I present in this paper is in one respect a special case of the Calmfors and Driffill model, in that I only compare three cases: a competitive labour market; a labour market with medium-sized unions; and a labour market with one big super-union. But by simplifying the model in this dimension I am able to represent it diagramatically, which is a benefit not only in its own right but also because it lets us generalise the model beyond the special functional forms needed for a tractable mathematical solution. I also compare a monopolistically

* I thank Richard Carson, Ehsan Choudhri, Orlando Manti and participants at a Carleton University Macro Workshop for their comments. Errors and opinions are mine.

' See, for example, Bruno and Sachs (1985), Lash (1985), and Newel1 and Symons (1987).

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competitive with a perfectly competitive output market. I can thereby show that the super- union does not always have to accept lower real wages to increase employment, as it does in the Calmfors and Driffil model; it might be able to increase both. Also, the super-union may choose even higher employment than if the labour market were perfectly competitive.

I present a simple macroeconomic model with monopolistically competitive firms, each facing a monopoly union. All workers are unionised. Each union maximises the utility of a representative worker in its firm, setting a wage unilaterally to which the firm reacts by choosing employment? The ‘corporatist’ solution, in which all unions act collectively as a single unit, always results in higher employment and lower nominal wages than the decentralised solution. Surprisingly, for some not unreasonable parameter values, corporatism results in higher employment and higher real wages, and does so even in comparison to a competitive labour market!

11. THEMODEL

We imagine a world with two distinct classes of people: capitalists and workers. Capitalists get profit income only, and workers get wage income only. Each capitalist has the exclusive right to produce one particular good, which is an imperfect substitute for the good produced by any other capitalist. The number of goods is fixed, perhaps because all the flavours that the human palate enjoys have already been discovered and patented, or because nature only provided a fixed number of locations suitable for production, each of which is owned by a different capitalist.

All workers are identical. Each gets disutility from working, with increasing marginal disutility. Workers (and capitalists) have a taste for variety, preferring to consume a balanced diet of equal portions of all goods, though they are willing to substitute quantity for balance, by consuming relatively more of a good with a lower price.

Initially there is a free flow of labour between firms and so a competitive labour market. Then a change in the law permits the workers at each firm to form a union with the right to make their firm a closed shop. Subsequently, a further legal change permits the independent unions to form a super-union, with the right to make the whole economy a closed shop. I model the equilibrium under each of these three different institutional assumptions.

* For a defence of the monopoly union model, in which firms are on their labour demand curves, see Oswald (1987) and Pemberton (1987). The monopoly union model can be seen as a limiting case of the more general ’right to manage’ model (see Nickel (1982)) where the wage is determined bilaterally according to relative bargaining power of firm and union, but the firm sets employment unilaterally. Alternatively, the ’right to manage’ model can be seen as yielding outcomes midway between a monopoly union and a competitive labour market model. The monopoly union model is adopted here for simplicity. The conclusions would be qualitatively unchanged with the more general model.

This directly contradicts Newel1 and Symons (1987) for instance, who state that the purpose of corporatism must be to reduce (presumably real) wages.

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a) The Model - a Special Case

A special case of the model assumes constant elasticities of output demand and labour supply, and constant returns to scale in production? This benchmark case illustrates the essentials most simply.

There is a large fixed number of firms in the economy. Each firm i faces the output demand function:

yi = (Pi/P)-B(M/P) B > 1 ( 1 )

where yi is the quantity demanded of firm i’s output, M is the nominal money supply per firm, and P is the average of all firms’ prices. (Since we consider only symmetric equilibria, it is immaterial exactly how the price index is constructed.)

Each firm has a production function

yi = ni

where ni is employment at firm i. This assumption enables us to talk about output and employment interchangeably.

The economy’s labour supply curve is given by

n = (W/P)r y > 0 (3)

where n is employment per firm, and W is the nominal wage.

(i) Competitive Labour Market

If the labour market were modelled competitively, each firm would choose output/employment to maximise profits taking the general price level and wage as given. The first order condition requires each firm to set (real) marginal revenue equal to (real) marginal cost:

(Pi/P)(l - l / B ) = W/P (4)

We solve for the symmetric macroeconomic equilibrium by setting the real price (Pi/P) equal to one (since all firms choose the same price) and by substituting the resulting solution for the real wage into labour supply:

( 5 ) j = n = (W/P)Y = (1 -l/B)Y

(ii) Decentralised Monopoly Unions

We now model the labour market as a Stackleberg equilibrium, in which a monopoly union picks a point on the firm’s labour demand curve, by setting the wage unilaterally and letting

Variants of this model are now increasingly common in the macroeconomic literature. See Blanchard and Kiyotaki (1987) for example.

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the firm choose output/employment to maximise profits taking the wage as given. The monopoly union can be thought of as a profit maximising firm, with the labour demand curve as its average revenue curve, and the labour supply curve as its marginal cost curve! In this simple model, where the firm’s average revenue curve has a constant elasticity of B, the firm’s marginal revenue curve (which is the union’s average revenue curve) also has a constant elasticity of B. Using the standard formula MR = (1 -1/B)AR to relate marginal to average revenue, we represent the union’s first order condition that marginal revenue equal marginal cost as:

(1 -l/B)( Wi/P) = ( f l i ) ’ / Y

Substituting in for the real wage from the firm’s first order condition (4)’ we get:

(1 -l/B)Z(P,/P) = ( n p (7)

Imposing symmetry on (7) yields the macroeconomic equilibrium as

3 = rf = (1-1/B)27 (8)

Since (1 -l/B) < 1, we see, unsurprisingly, that 3 < - that is the monopolisation of competitive labour markets will reduce output and employment. In the limit, however, as B approaches infinity, so that firms’ outputs become perfect substitutes and so firms become perfectly competitive, (1 -l/B) approaches one, and 3 approaches j . In this special case of the model, workers can only have monopoly power if firms have monopoly power. With constant marginal product of labour, if the demand curve facing the firm is flat then so is its marginal revenue product curve, which is the labour demand curve facing the union.

Let the representative worker’s indirect utility function be the real wage income minus the integral under the labour supply curve

u, = (W,/P)n,-(I/(l +I/y))n,l+”,

The individual worker in the competitive labour market takes the wage as given, so maximising U, with respect to n, yields the inverse labour supply curve:

au, = W,/P-n,l/r = o an, -

The monopoly union recognises the relation between wages and employment, given by (I), (2) and (4) as

(W, /P) = (n,/(M/P))-l/B (1 -l/B)

Substituting this expression for real wages into the worker’s utility function yields

U, = (1 - V B ) (M/P)1/Bn,cl-’/B)-(I/(l +I/y))n’+l/7

Maximising utility now yields

which can be rewritten in the form of marginal revenue equals marginal cost as

(1 -I/B)2 (Pj /P) = n’/r

1992 CORPORATIST AND DECENTRALISED LABOUR UNIONS IN A MACROECONOMIC MODEL 295

(iii) A single economy-wide union

Notice that although decentralised unions reduce employment conpared to the competitive labour market solution, they leave real wages unchanged. The individual union faces a trade- off between real wages and employment since its firm’s real price varies with employment, but in aggregate the average real price of all firms must be one, so that real wages are determined by imposing symmetry on (4) to yield

(W/P) = (1-l/B) (9)

Acting collectively, unions face a perfectly elastic demand curve for labour. The super-union will maximise its profits by setting employment where the given real wage equals the marginal cost or supply price of labour.

(10) (W/P) = (1 -l/B) = ii”?

But this yields exactly the same solution for output and employment as with a competitive labour market!

(11) 9 = ii = (l-l/B)?

(iv) Diagrammatic exposition

We can show these results with the aid of two diagrams. The top diagram shows the position of the individual firm and its union, taking aggregate variables as given. Because of the constant returns to scale assumption, the bottom axis can represent either output or employment, and most curves can be interpreted in two ways also. The curve labelled vmp depicts the value marginal product of labour (equals (Pi/P) times marginal product), but since the marginal product is everywhere one, it can also represent the firm’s demand curve. The curve labelled mrp is the marginal revenue product curve (equals marginal revenue times marginal product), or simply the marginal revenue curve. Since the firm sets real wage equal to (real) marginal revenue product, the mrp curve is the firm’s labour demand curve, and thus the monopoly union’s average revenue curve. The mwr curve depicts (real) marginal wage revenue, which the union sets equal to its marginal cost, as given by the labour supply curve s.

The individual firm’s value marginal product depends on its own output and on aggregate output. Whereas the vmp curve in the top diagram shows how value marginal product varies with its own output holding aggregate variables constant, the lower diagram’s VMP locus’ shows how value marginal product varies when all firms expand output proportionately. (Readers familiar with the Chamberlinian DD curve being steeper than the dd curve should stop here to adjust their intuitions. Our DD curve is horizontal! But Chamberlin was comparing the price of expanding firms within the industry to the price of firms outside the industry. We have all firms in the whole economy expanding together, so their prices will all vary together, and the real price at any firm will stay constant at one.) The VMP locus is horizontal because the real price is constant at one, as is the marginal product of labour. The assumption of constant elasticity of demand ensures that the MRP and MWR loci are horizontal too. Given our assumption of segmented labour markets, the two labour supply curves s and S are identical.

To ensure comparability, the bottom axis in the lower diagram shows aggregate output and employment per firm, Y and N. Points labelled A, B and C have the same location in both diagrams.

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B P, P FIGURE 1

Point B in the top diagram shows where the labour demand curve mrp is tangential to the worker’s indifference curve I,. Point B lies directly above point C, where the union’s marginal revenue curve mwr intersects the labour supply curve s (which must pass through the lowest point on each indifference curve, since it represents the employment choice of workers maximising utility taking wage as given). But whereas point B is a tangency point in the top diagram, we find I,, intersects MRP at B in the bottom diagram. The tangency in the bottom diagram is at D, which represents the optimal point for the super-union. In this simple model, with constant elasticity of demand and constant marginal product, the MRP locus happens to be horizontal, and so this corporatist solution coincides with the solution with a competitive labour market. (If the output market were perfectly competitive too, firms would set employment where the real wage equals (real) value marginal product, so equilibrium would be at point E).

1992 CORPORATIST AND DECENTRALISED LABOUR UNIONS IN A MACROECONOMIC MODEL 297

b) The Model - the General Case6

The diagram shows us that the assumptions of constant elasticity of demand and constant marginal product create a very special case in which the VMP, MRP, and MWR loci are all horizontal. With diminishing marginal product of labour, for instance, these three loci would be downward-sloping. With increasing marginal product, they would be upward-sloping. Similarly, if the elasticity of demand fell as all firms expanded output together, MRP and MWR loci would be downward-sloping, though VMP would remain horizontal. An interesting case is where elasticity of demand increases with higher output by all firms, so that the MRP and MWR loci are upward-sloping. This case is shown in Figure 2.

S

mwr mwr

n” n

A iv N

FIGURE 2

In Rowe (1987) and Rowe (1989) I give a more complete discussion of modelling monopolistic economies with general (i.e. non-constant elasticity) demand functions.

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In Figure 2, with constant marginal product but increasing elasticity, the solution with a super-union has higher employment and higher real wages than with a competitive labour market, which in turn has higher real wages and employment than with decentralised unions. We must note, however, the solution with a super-union, as depicted in the top diagram, requires workers to be off their supply curves to the right. This could only be possible if the super- union can force workers to sell more labour than they wish at the going wage.

It is relatively easy to find consumer preferences to generate such cases. One simply posits that the marginal rate of substitution between consumption of firm i’s output and other firms’ outputs is some function DCVY) of firm i’s output consumed, y, and (average) other firms’ outputs consumed, Y. A marginal rate of substitution function, defined over the consumption space (other firms all set the same price in equilibrium so their output is a composite commodity) is no less primitive than a utility function. Utility maximising consumers set marginal rate of substitution equal to relative price, so Pi/P = DO,Y), which can thus be interpreted as an inverse demand function. The restrictions D, < 0, D, > 0 are sufficient (but not necessary) for convexity, but place no restrictions on how elasticity of demand (= D/D,y) varies with individual firm and aggregate output.

In the example shown in Figure 2, with an upward-sloping MRP locus, if the union or unions set temporarily fixed nominal wages, fluctuations in nominal aggregate demand will trace out a downward-sloping aggregate supply curve in price level-real output space, and generate procyclical fluctuations in real wages. Stability requires that the aggregate demand curve be steeper than the aggregate supply CUNC which ensures that the super-union sets lower nominal wages than decentralised unions, even if real wages are higher.

Suppose in this example that initially we have decentralised union wage-setting. The unions then all join together into a super-union. The super-union will reduce nominal wages. With lower nominal wages, individual firms now find that marginal revenue exceeds marginal cost, or equivalently that marginal revenue product exceeds the real wage, and so each wishes to cut its relative price to move down along its demand curve. Now it is not possible for all firms to cut their relative prices, of course, but the attempt by each firm to do so causes a fall in the nominal price level, a movement along the aggregate demand curve, and an outward shift in each individual firm’s demand curve. If the MRP locus is upward-sloping, the eventual fall in the nominal price level exceeds the fall in nominal wages that brought it about, and so real wages will increase.

Within the framework of this simple model: a super-union can always do at least as well as decentralised unions, since the former could always choose to impose the same wage as the latter chose. Similarly the super-union could never do worse than the competitive labour market. More surprisingly, the competitive labour market will typically give the representative worker higher utility than will decentralised unions. Figure three shows the rarer case where the competitive labour market does give the worker lower utility than decentralised unions, but shows that this requires a steeply downward-sloping MRP locus, which occurs only when there is strongly diminishing marginal product of labour, or when elasticity of demand is strongly decreased by a boom in aggregate output.

’ This simple model, of course, ignores many important issues which could cause a single central union to do worse than decentralised unions, such as the problem of negotiating and enforcing an economy- wide agreement between heterogenous workers in heterogenous jobs under imperfect information.

1992 CORPORATIST AND DECENTRALISED LABOUR UNIONS IN A MACROECONOMIC MODEL 299

N

FIGURE 3

111. PERFECT COMPETITION I N THE OUTPUT MARKET

The model so far has assumed that each firm is monopolistically competitive, but it is a simple matter to reinterpret the model so that the output market is perfectly competitive. Under monopolistic competition each distinct good is produced by only one firm, which thus sees itself as facing a downward-sloping demand curve; under perfect competition each distinct good is instead produced by many firms within that sector, and each firm takes prices as given and so sets employment where wage equals value marginal product. If each sector contains many competitive firms but only one labour union, the union will still face a downward-sloping labour demand curve, but it is now the value marginal product curve vmp instead of the marginal revenue product curve mrp. And if all these sectoral unions join one big super-union, it now faces the value marginal product locus VMP instead of the marginal revenue locus MRR

How does assuming perfect rather than monopolistic competition affect the conclusions of the model? The most important conclusion survives intact. The corporatist super-union will still choose higher employment than decentralised unions, because the aggregate VMP locus facing the super-union is flatter than the sectoral vmp curve facing the individual sectoral union. To see this, remember that real value marginal product equals real price times marginal product. When the individual union reduces employment it reduces output in its sector relative to other sectors and so raises its sector’s real price; but when all unions together reduce employment and output real prices stay the same. Figure 4 superimposes the vmp curve on the VMP locus to show the conflict between individual union and super-union, assuming constant marginal product and hence a horizontal VMP locus for simplicity. The super-union chooses the tangency point A on the VMP locus, but each individual union would prefer

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to defect from this cooperative solution by demanding higher money wages, raising its sector’s real price and real wage, by moving up along vmp, to its tangency point D. But if all unions try to do this the rise in the general level of money wages and prices will reduce real money balances, reducing aggregate demand and aggregate employment and so shifting the vmp curve leftwards to vmp,, where it is tangent to the union’s indifference curve at a point N, the non- cooperative solution, on the VMP locus.

Other conclusions of the model however, are changed when we go from monopolistic to perfect competition. Perfectly competitive firms must have constant or diminishing marginal product to satisfy the second-order conditions for maximisation of profits. This means that the VMP locus must be flat or downward-sloping, unlike under monopolistic competition where the MRP locus might slope up, either because marginal product increases or because elasticity of demand increases when all firms expand output together (even though the mrp curve slopes down). And without an upward-sloping VMP locus we cannot get the surprising result of the super-union choosing higher employment than a competitive labour market.

I\; m N

FIGURE 4

IV. THE SOURCE OF THE INTER-UNION EXTERNALITY

The usual defence of labour unionism is that workers do better by acting cooperatively than if each worker pursues his own self-interest. In this model we see that unions do better by acting cooperatively than if each union pursues its own self-interest, and indeed that the latter is typically worse for workers than if each worker pursued his own self-interest. Partial cooperation is here typically worse than none at all. What ttan is the source of the externality that each union imposes on other unions? There are two ways of thinking of this externality, depending on whether one wishes to think of unions as setting employment or as setting wages.

1992 CORPORATIST AND DECENTRALISED LABOUR UNIONS IN A MACROECONOMIC MODEL 301

First, think of unions as setting employment. In the special case of the model, with constant elasticity and marginal product, a firm’s profit maximising condition that wage equal marginal revenue product pins down the real product wage as:

(12)

If other unions cut their employment, this causes the real price of output of their firms to rise, which entails a fall in the real price Pj /P in our firm, which in turn entails a fall in our union’s real consumption wage Wj/P = (Wi/Pi) x (Pi/P), which reduces our workers’ utilities.

Wi/P, = (1 - 1/B)

Second, think of unions as setting nominal wages. If other unions raise their wages, their firms’ nominal prices will rise. This will have three effects on our workers’ utilities. First, our real wages will fall with the rise in the nominal price level. Second, the fall in our relative price will tend to increase employment in our sector. Third, the rise in the general nominal price level will reduce real aggregate demand and tend to reduce our employment. Will our employment then rise or fall? We cannot tell, for it depends on the elasticities of relative and aggregate demand. But suppose we responded to their increased nominal wages by raising our wages by the same amount. This would keep our real wage and relative price the same, thus eliminating the first and second effects, but the third effect - the ‘aggregate demand externality’ caused by the higher general price level - would reduce our employment and utilities.

V. CONCLUSION

Decentralised labour unions always do worse for their members than a single centralised union, and typically do worse than if there were no unions at all. Decentralised unions cause employment to be lower than they would wish, and sometimes real wages to be lower too.

In ‘Insider-Outsider’ models: unions can sometimes worsen the average lot of workers when those inside the union benefit themselves by imposing a greater harm on non-member outsiders, like the unemployed? In this model, either all or else no workers are union members, and all are treated alike. Perhaps, though, we can think of members in other unions as being treated like outsiders by our union, just as we are so treated by them.

One source of inter-union externality that has been wholly ignored here is that when one union raises wages it reduces the profits of its employer, which is likely a firm owned largely by workers and ex-workers through their pension plans and private savings, who are mostly members or ex-members of other unions. I have instead assumed an economy with two mutually exclusive classes - workers and capitalists - which is perhaps how some union leaders view the world. The centralised union solution is not Pareto Optimal, for it ignores the interests

Such as Lindbeck and Snower (1988).

An alternative explanation of lower unemployment rates under corporatism might be that each union cares mostly for its own employed members, but partly for the unemployed. Individual unions will then moderate their own wage demands very little, since any single union’s wage increase has only a very small effect on the economy-wide unemployment rate, but when all unions are taken together, the welfare of the unemployed becomes a public good, for which each union is prepared to pay with lower wages provided all other unions make matching contributions.

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of the capitalists. The only efficient level of employment is where the labour supply intersects the VMP locus, maximising the total surplus which is the area between labour supply and VMI? Equally challengeable is my assumption that a union accurately and faithfully pursues the interests of its members, and that a super-union would likewise pursue the interests of its member-unions!O

In the long run, firms must make profits or they will shut down. If the need to keep the employer in business puts a sharp kink in the constraint facing the union, as when labour demand suddenly falls to zero if wages increase a penny more, there will likely be a continuum of macroeconomic equilibria. (Start in one zero profit equilibrium, then increase the number of firms. Unions will likely cut wages exactly enough to keep firms at zero profits again.) If on the other hand the kink in the constraint facing the union gets smoothed out by, for instance, some uncertainty over whether a penny increase in wages will cause the firm to fold, the present analysis will probably remain qualitatively correct.

REFERENCES

Blanchad, O.J. and Kiyotaki, N. (1987), “Monopolistic Competition and the Effects of Aggregate Demand”, American Economic Review, vol. 75, no. 5, December.

Bruno, M. and Sachs, J. (1985), The Economics of Worldwide Stagflation (Oxford: Blackwell).

Calmfors, L. and Driffill, J. (1988), “Bargaining Structure, Corporatism and Macroeconomic Performance”, Economic h l icy , vol. 3, April.

Lash, S. (1985), ‘The End of Neo-Corporatism?: The Breakdown of Centralised Bargaining in Sweden”,

Lindbeck, A. and Snower, D. (1988), “Cooperation, Harassment, and Involuntary Unemployment: An

Newell, A., and Symons, J. (1987), “Corporatism, The Laissez-Faire and the Rise in Unemployment”,

British Journal of Industrial Relations, vol. XXIII, no. 2.

Insider-Outsider Approach”, American Economic Review, 78, no. 1.

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Discussion Paper no. 130.

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Nickel, S.J. (1982), “A Bargaining Model of the Phillips Curve”, London School of Economics CLE

Oswald, A.J. (1987), “Efficient Bargains are on the Labour Demand Curve; Theory and Facts”, London

Pemberton, J. (1987), “A Defence of Models with Pareto Inefficient Wage and Employment Determination”,

Rowe, N. (1987), “A Simple Macroeconomic Model with Monopolistic Firms’’, Economic Inquiry, vol.

Rowe, N. (1989), “Do Small Menu Costs Cause Bigger and Badder Business Cycles in Monopolistic

University of Reading Discussion Paper no. 190.

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Macroeconomies?”. Journal of Macroeconomics, vol. 11, no. 1.

lo For instance, if workers or firms are heterogenous, how can the central union tell whether one union is justified in demanding higher pay because of special conditions like (possibly temporary) higher labour demand or lower supply? Ehsan Choudhri has suggested that a central union might be forced through this ignorance to impose uniform pay scales, and the costs of this undesirable uniformity should be set against the benefits to workers that this paper elucidates.