Economics Letters 55 (1997) 139–143

Input contracts, market structure and the empirical specification ofprice cost margins

*Peter LukacsSchool of Business and Economic Studies, ESS Building, University of Leeds, Leeds, LS2 9JT, UK

Received 23 September 1996; accepted 5 February 1997

Abstract

We examine the implications for the empirical specification of the margins-concentration relationship of different forms ofcontracting for intermediate inputs. We offer an alternative explanation why the results of profit margin regressions dependon whether the margin is deflated by gross output or net output. 1997 Elsevier Science S.A. 1997 Elsevier ScienceS.A.

Keywords: Intermediate inputs; Market structure; Price cost margins

JEL classification: L11; L14

1. Introduction

In recent years it has become common when specifying empirical price cost margins to use net1output as opposed to the more usual gross output in the denominator. Conyon and Machin (1991b),

point out that with gross output as the denominator the point estimate on concentration from aregression of margins on concentration is lower than with net output as the denominator and the

2estimate is frequently insignificant. Dickson (1994) argued that the use of net output in thedenominator was necessary to control for ‘‘stage of production’’ effects. We analyse contractualrelations in markets for intermediate inputs and argue instead that it is more appropriate to control forthese factors by adding an additional independent variable to the specification rather than by changingthe dependent variable.

*Tel.: 144 113 233 6866; fax: 144 113 233 4465; e-mail: P.Z.Lukacs@bes.leeds.ac.uk1Examples of this include Conyon and Machin (1991a); Haskel and Martin (1994); Conyon (1995) for studies of the UK andDickson (1991) using Canadian data.2Within an alternative methodology for attempting to infer market power the issue of the use of net versus gross output hasbeen raised in a similar way. Hall (1988) has been criticised by Domowitz et al. (1988); Norrbin (1993) for the use of valueadded as the basis for measuring of market power.

0165-1765/97/$17.00 1997 Elsevier Science S.A. All rights reserved.PII S0165-1765( 97 )00056-6

140 P. Lukacs / Economics Letters 55 (1997) 139 –143

2. The oligopoly model with input contracts

In analysing the relations between input supplier and purchaser we assume a downstreamproduction function where there are two generic inputs to the production process intermediate inputs

3(m) and labour (l). The production function for firm i is of a form y 5 f(l , m ) and which is assumedi i i

to be homogeneous of degree g. The profit function for firm i is

p 5 py 2 p m 2 wl , (1)i i m i i

where p is the price of intermediate inputs and w is the wage. If firms are price takers in inputm

markets the firm chooses m and l to maximise profits. Using Euler’s theorem the first order conditionsyield,

py 2 p m 2 wl s (1 1 l )i m i i i i]]]]] ]]]5 (1 2 g ) 1 g , (2)py hi

where s is the market share of firm i, l is the conjectural parameter, h is the absolute value of thei i

industry price elasticity of demand. This is the conventional specification from Cowling and Waterson(1976) and the left hand side is the standard empirical measure of the price cost margin. Below weconsider three alternative forms of contracting for intermediate inputs that alter this specification.

Assuming that the firm possesses some monopsony power over the price paid to the upstream firm,the price of inputs p depends upon the quantity demanded by the firm, so the profit function is of them

form p 5py 2wl 2p (m)m . Maximising this with respect to m and l and rearranging yields ani i i m i

alternative relation,

py 2 wl 2 p m s (1 1 l ) p mm i i m]]]]] ]]] ]]5 (1 2 g ) 1 g 1 ´ , (3)py h py

where ´5(dp /dm)(m /p ) is the reciprocal of the elasticity of derived demand for bought in inputs. Ifm m

bought in inputs are purchased on long term contracts which control both the volume and price ofdeliveries the value of material inputs is converted into a fixed cost. Introducing a short runproduction function which depends only upon the labour input y 5g(l ) and maximising with respecti i

to labour input yields.

py 2 wl s (1 1 l )i i i i]]] ]]]5 (1 2 g ) 1 g , (4)py hi

where g is the degree of homogeneity of the production function g(l). (4) can clearly be rearrangedas,

py 2 wl 2 p m s (1 1 l ) p mi i m i i i m i]]]]] ]]] ]]5 (1 2 g ) 1 g 2 , (4a)py h pyi i

Introducing efficient bargaining of intermediate input prices using the Nash bargaining framework, we

3Including capital in the production function does not change any of the qualitative predictions of the paper and it istherefore excluded for reasons of clarity.

P. Lukacs / Economics Letters 55 (1997) 139 –143 141

can explicitly model the relative bargaining strengths of the upstream and downstream firm. We takethe profits of the upstream material input producer to equal p 5( p 2c )m, assuming a constantu m m

marginal cost of input production, and the profits of the downstream firm are as in (1). Setting thes 12soutside option to zero, the Nash bargain is of the form N5p p , where s is the bargaining poweru d

of the input producer. Maximising the Nash bargain with respect to m and p with respect to l, thend

substituting, yields the relation,

py 2 p m 2 wl s (1 1 l )i m i i i i]]]]] ]]]5 (1 2 s)(1 2 g ) 1 (1 2 s)g (5)py hi

It is readily apparent that if s 50, i.e. the input supplier has no bargaining power, then (5) collapses to(2). If s 51, i.e. the end producer has no bargaining power, the input supplier is able to extract thefull surplus, hence the price cost margin is equal to zero.

An alternative way in which the ratio of intermediate inputs to sales may influence the theoreticalrelation between margin and market structure is if firms are using a fixed proportions technology. Ifintermediate inputs are used in fixed proportions to the other inputs and we assume material input

4used in a constant proportion of s 5m /y we can obtain a Leontief production function of the formm

y 5min[( g(l ) /12s ), (m /s )].i i m i m

Assuming efficient use of inputs and maximising profits the first order condition becomes,

py 2 wl 2 p m py 2 p m s (1 1 l )i i m i i m i i i]]]]] ]]]] ]]]5 (1 2 g ) 1 g . (6)py py hi i

3. Consequences for the empirical specification

In each of the cases considered above a modification is implied to the conventional specification ofthe margins market structure relationship. In three cases the conventional price cost margin ispreferred but with the addition of the ratio of intermediate input costs to sales as an independentvariable. In these cases we can obtain specific predictions for the coefficient on such an includedvariable in an empirical regression. In the monopsony model the coefficient should be ´, in the longterm contract model the predicted coefficient should be 21, and in the fixed proportions technologycase the coefficient is predicted to be 2(12g ). In the bargaining model a measure of bargaining

5strength is required as a right hand side variable to prevent mispecification. In each case theconventional specification is mispecifed by omitting a relevant variable to control for inputcontracting.

These relations therefore offer a plausible explanation for the observed empirical disparity betweenmargins deflated by net output and gross output if, as is presented in Conyon and Machin (1991b),there is a correlation between market structure and vertical integration, measured as one minus the

4This particular functional form is taken from the discussion in Rotemberg and Woodford (1995).5It has been observed that this is empirically important in bargaining over labour (e.g. Conyon, 1992) but to our knowledge ithas not been investigated with respect to intermediate inputs.

142 P. Lukacs / Economics Letters 55 (1997) 139 –143

ratio of intermediate input costs to sales. However contrary to the arguments presented in Conyon andMachin (1991b); Dickson (1994) we would therefore argue that adjustment should not be made to themeasured price cost margin. Adjusting the price cost margin by using net output instead of grossoutput imposes an assumed model onto the data and abstracts from the issue of the role ofintermediate inputs in price formation. Adding independent variables enables an explicit test of therole of intermediate inputs and can also control for the potential omitted variable bias.

It is interesting to note in this regard the focus in Conyon and Machin (1991b); Dickson (1994) onthe food processing industries as important in the use of the net output denominator margin. We wouldexpect food processing firms to make relatively extensive use of long term contracting in the form offutures contracts that will specify both price and quantity in purchasing agricultural inputs. However areasonable case could also be made for expecting some degree of monopsony power or bargaining forcertain types of food products. The relations presented here offer a way forward for testing betweenthe hypotheses.

4. Conclusion

We have illustrated the implications of a variety of input contract relations for the specification ofmargin-market structure relations. We have argued that the correct response to the potential existenceof these contractual relations is not to redefine the price cost margin but is instead to include furtherindependent variables that permit testing of the different models.

Acknowledgments

I would like to thank Keith Cowling and Mike Waterson for valuable discussions. Any errorsremain my own.

References

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