Market Power and the Organization of Tournaments

MARKET POWER AND THE ORGANIZATION OF TOURNAMENTS BY M.T. MALONEY CLEMSON UNIVERSITY

Tournament theory has gained a solid place in the lexicon of labor markets. Researchers are quick to label nuances of labor market contracts as tournament based. Proponents of tournament theory following the seminal paper by Lazear and Rosen (1981) tick off the various situations in which tournament wages are superior to more traditional forms of performance pay. Nonetheless these arguments are sometimes less than completely compelling especially when there is a change in the institutional regime. Consider, for example, the labor market described by Knoeber and Thurman. They report data on production of chickens over a period of ??? years. The data are taken from the records of a major chicken processing company and comprise the dealings between this company and the chicken farmers with whom it contracted. Over the course of the sample period, the processor changed its labor contracts from tournament based wages to mean-adjusted piece-rate pay. The obvious question is, Why did the firm switch? Another example echoes the same puzzle. It is commonplace in southern textile firms to have production line waste material collected by forklift operators on a periodic, intermittent basis. Once a week or so, forklift operators set about the plant picking up bundles of waste and depositing it at a common site. The pay for this chore comes from a pool that is split among these workers based on the rank order of their performance. In other words, for this particular chore, these workers are paid tournament wages. Interestingly, they are paid tournament wages when they could just as easily be paid by the piece. That is, the scores used to rank them ordinally could be used to pay them directly. This paper shows that a simple extension of the Lazear-Rosen model can be used to explain these phenomena. That extension involves the effect of market power in the organization of tournaments.

Market Power in the Tournament Model

The simple Lazear-Rosen model is familiar: two risk neutral, equally matched player/workers are paid from a purse comprised of a high and low prize. The high prize is paid to the top performer; the loser gets the low prize. These tournament wages are paid by a competitive firm and all surplus goes to the workers. The results of the model are equally familiar. The effort of the workers is determined by the spread of the prizes. The purse affects their willingness to work for one firm versus another. If the expected prize is insufficient to cover the cost of their effort, the workers stay home. The value of output directly affects the expected prize. As the value of output goes up, the firm also increases the spread of prizes and induces workers to exert more effort. Even though Lazear and Rosen set up the model using the assumption of competitive tournament organizers, this is not necessary to derive their results. From the perspective of the workers, it does not matter whether the firm is competitive or possesses market power. The prize structure and purse determine behavior parametrically. Workers choose the optimal amount of

Revised: November 19, 2002 Monopsony Tournaments work based on the spread of the prizes, and given this amount of effort, they will choose to participate if the purse is large enough. In the Lazear-Rosen framework, effort is implied by the following equation:

W1 W2 g  C(m*) 1

where Wi, i=1,2, are the high and low prices, g is the height of the density of luck in determining the winner, m is effort, and C is the cost of effort to the worker. Thus, optimal effort, m*, is an implicit function of the prize spread and variance of winning. The participation constraint is:

1 * 2 W1 W2  C(m )  0, 2 where one-half the purse is the expected prize given homogeneous workers and the assumed Nash-Cournot equilibrium. The expected prize must cover the cost of effort. In competition, the purse equals the value of output, V, times expected production, i.e.,

* W1 W2  2m V

However, the distribution of the surplus between m*V and C(m*) has no implications in the model. Consider the model derived in the context of a monopsonist contracting with the two workers. The monopsonist will maximize expected profits:

  2m*V  R

* where R = [W1 + W2] is the purse and m is the behavior of the workers in the response to the prize spread set by the firm as given in equation (1). The monopsonist maximizes profit by the optimal choice of purse and prize spread. However, profits are maximized subject to the participation constraint identified in equation (2). The monopolist must pay the workers enough to get them to play. The constrained objective function of the firm can then be written as:

* FR * I max{S,P}   2m (S)V  R   G C(m (S))J H2 K

where S is the prize spread, [W1 – W2]. The first order conditions reduce to two equations in purse and prize spread: ~ V  C(m* (S )) ~ R ~  C(m* (S )) 2

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The important result is the first of these. It says that the monopsonist firm does just like its competitive brother. The optimal spread is set such that the marginal cost of worker effort is equal to the value of output. That is, the firm sets the prize spread so that the workers’ response in effort creates a marginal cost to the worker that is equal to the value of output. Given this spread, the firm will pay no more than necessary to induce the workers to participate. The only difference between the monopsonist and the competitive firm is that the residual in the participation constraint for the workers is kept by the monopsonist instead of being paid out to the workers in the competitive market. In competition, the expected prize is mV. In monopsony, it is ½R. In monopsony, the firm keeps the residual, mV – ½R. However, the prize spread and, thus, the effort level is the same.

Market Power in Piece-Rate Pay

While it appears that extending the tournament model to account for monopsony yields very little that is new, one intriguing result comes from comparing the behavior of the monopsonist’s profitability from organizing production with a tournament to that of organizing production using piece-rate pay. If production is monopsonized and organized by piece-rate pay, the monopsonist maximizes profit by choosing the optimal gap between the price it pays the workers and the price that it gets for the workers’ output. In other words, the piece-rate monopsonist drives a wedge between the value of output and the payment for effort, (V – r). The implication of this result is striking. In a monopsony labor market, tournament wages generate higher profits than piece-rate pay. Formally, the piece-rate monopsonist maximizes profits given by:

E()  m* (r) (V  r)

The FOC for the monopsonist is:

E() m*  (V  r)  m*  0 r r or, in elasticity terms: m* r r  r m* V  r

This says that the monopsonist lowers r until the ratio of r to the profit spread is equal to the responsiveness of the worker to r.1 As the monopsonist in a piece-rate pay setting lowers r relative to V, it lowers the amount of effort that the worker exerts. It is clear that m* (r V )  m* (V ) . Thus, total expected output which is determined by the worker equating the marginal cost of effort to the pay for marginal effort is lower for monopsonized piece-rate compared to monopsonized tournament pay. Monopsony profits are lower under piece-rate pay than tournament wages. Hence, the model predicts that monopsonists will use tournament pay structures.

1 A simple example is useful. Assume that the cost of effort is given by m2. For this function the optimal r is one-half V.

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Conclusions

Thus, we have an explanation for the conundrums noted in the beginning. Market power can be added to the list of reasons for the existence of tournament wages. A possible explanation of why the pay scheme for trash collection in textile mills is tournament based is that in this setting the workers are monopsonized. For this minor task, the firm faces a fixed labor market.2 Thus, the firm is able to exercise monopsony power over the workers. If it were to pay based on the amount of refuse the workers collected, the profit maximizing piece rate would induce workers to exert less than the optimal amount of effort. By organizing production in the form of a tournament, it is able to induce optimal effort [ C(m* )  V ] and exploit its monopsony power to the fullest.

References

Knoeber, Charles R. and Thurman, Walter N., “Testing the Theory of Tournaments: An Empirical Analysis of Broiler Production,” Journal of Labor Economics, Vol. 12, 1994, pp: 155-179.

Lazear, Edward P. and Rosen, Sherwin . "Rank and Order Tournament: An Optimal Labor Contract" Journal of Political Economy vol. 89. 1981, p 841-864.

2 Assume that the workers cannot cartelize against the firm.