The Aggregate Le Chatelier Samuelson Principle with Cournot Competition

In a market in which firms have market power, the impact of a change in wages on labour demand is not easily determined. Indeed, if after a decrease in wages one firm chooses to increase labour demand for producing more, this reduces the output price; this in turn may lead other firms to decrease their production and their demand for labour. We show that this ambiguity at the firm level is likely to be resolved at the aggregate level of the industry: under some empirically testable restrictions an increase in wages is likely to trigger a decrease in labour demand. The Le Chatelier principle states that the sensitivity of input demands with respect to own price variations is smaller when the output level is held constant than when it is adjusted. It holds whether competition on the output market is perfect or imperfect, provided the production level of competitors is held constant. A first aim of this paper is to extend the Le Chatelier principle to the case where the production levels of competitors are allowed to vary. For a given level of production, a cost minimizing firm has an incentive to use more intensively the factors of production whose price decreases and to substitute the other factors by the cheaper one (substitution effect). When the firm is able to set its production level in order to maximize profit, it benefits from the factor price reduction even further (expansion effect). With a competitive output market this expansion effect leads to a further increase in the demand for the factor that becomes cheaper. With imperfect competitive output markets the direction of the effect is less clear: if all competing firms increase production to exploit the reduction in factor price, the output price must fall, and this reduces each firm’s incentives to expand its level of production and factor demand. We study whether aggregate factor demands are decreasing in markets with a particular type of imperfect competition, termed Cournot competition. Despite the ambiguous result at the firm level, we show that under some conditions the aggregate expansion effect is likely to be negative. We complete this paper with an empirical investigation of its theoretical results. In order to identify the Le Chatelier principle with aggregate data, and for decomposing the impact of input price changes on input demands into a substitution and an expansion effect, it is necessary to propose an adequate empirical specification compatible with heterogeneous firms. Instead of relying on a representative firm setup which implies estimation biases when firms are too heterogeneous, we define the aggregate cost function as the conditional expectation of the microeconomic cost function, given the available aggregate information. In this context, we show that it is possible to identify the conditional expectation of the substitution and expansion effects using aggregate data only. We propose a simple test for the validity of the representative firm model. The empirical application relies on a panel for 18 two-digit US manufacturing industries over the period 1949 to 2001. We obtain several results relative to the rate of returns to scale, the price-cost margin, the short and long run adjustment of input demand to input price change, and the impact of input price changes on output adjustment and inflation. The empirical findings confirm the validity of the Le Chatelier principle. We also find evidence for both increasing and constant returns to scale.

Koebel, Bertrand and François Laisney (2010), The Aggregate Le Chatelier Samuelson Principle with Cournot Competition, ZEW Discussion Paper No. 10-009, Mannheim.