Rank Order Tournamentslazear & Rosen

An extension of tournament theory to include the case of market power gives additional insight into the factors that influence the firm’s choice of labor contracts. When the firm has market power it can extract the full surplus from workers by paying them tournament wages. The only way to achieve the same result with ordinary labor contracts is to make workers pay for a higher wage. When there is randomness in the production process, nonlinear pricing even of this sort becomes problematic. Transactions costs make tournament wages the more likely choice for the firm when it attempts to exploit market power. Introduction Tournament theory has gained a solid place in the lexicon of labor markets. Since the seminal paper by Lazear and Rosen (1981) we have become aware of the ubiquitous circumstance of tournament wages as a component of worker compensation. Indeed, the more we look, the more we find. Even so, tournament theory is nagged by the problem originally addressed by Lazear and Rosen. Since tournament wages possess the same efficiency characteristic as piece-rate pay, what "breaks the tie in practical situations. " Lazear and Rosen appeal to measurement cost. For instance, they say, "Salesmen, whose output is easily observed, typically are paid by piece rates, whereas corporate executives, whose output is more difficult to observe, engage in contests. " But even here the sands shift beneath the theory. It is very common for salesmen to be paid by contests as well. This puzzle pops up again and again. Consider, for example, the labor market described by Knoeber and Thurman (1994). They report data taken from the records of a major chicken processing company in its dealings with farmers contracted to raise birds. Over the course of the sample period, the processor changed its labor contracts from tournament-based wages to meanadjusted piece-rate pay. What caused this change in regime? Measurement costs alone do not seem to be the explanation. * Thanks go to Dan Benjamin and Jiangxia Wang for helpful comments. Additionally, a debt is owed to Benjamin and Bob Tollison for encouraging me to work on this topic. Contact information at end. 12 Lazear and Rosen, p. 848, (paraphrased). 13 Id. 14 Personal experience yields two examples of firms using tournament wages in addition to sales commissions. United Healthcare circa 1990 held contests among its sales staff offering expense paid trips to Paris for the top performers. Brunswick as far back as the 1980s has sent the top sales people to Hawaii. Revised: December 1, 2003; M.T. Maloney 16 901 Notes28.doc Department of Economics Clemson University Another example echoes the same riddle. It has been observed that from time to time in some southern textile firms, production-line waste material is 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 these 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 uses a simple extension of the Lazear-Rosen model to help explain these phenomena. The extension involves the effect of market power in the organization of labor markets. 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. Workers perform identically in an efficiently structured tournament compared to piecerate pay. Even though Lazear and Rosen set up the model using the assumption of competitive tournament organizers, this is not necessary to derive their results. Their model implicitly embodies a surplus between the value of output and the worker's cost of effort to produce that output. In the competitive setting, firms are forced to pay out this surplus to the workers. In the Lazear-Rosen framework, optimal effort is implied by the following equation: W W g C m 1 2 − = ′( ) 7 where W1 and W2 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 by the worker, m, is an implicit function of the prize spread and variance of winning, but not a function of expected earnings. Expected earnings enter worker decision-making through the participation constraint. The worker will only play if the expected payout is at least as large as the cost of effort. That is, 2 1 2 0 W W C m + − ≥ ( ) * 8 where one-half the purse is the expected prize. In competition, the purse equals the value of output, V, times expected production, i.e., 9 W W m V 1 2 2 + = * 15 The notation here is nearly identical to Lazear and Rosen; see p. 846. Production is characterized by a noisy relation between labor effort supplied, m, and output, q; q=m+ε, where ε has zero mean and constant variance. 16 Given homogeneous workers and the assumed Nash-Cournot equilibrium. Revised: December 1, 2003; M.T. Maloney 17 901 Notes28.doc Department of Economics Clemson University and the expected prize to each player is mV. In order to be competitive the firm maximizes the difference between the expected prize and the cost of effort by the optimal choice of prize spread. This gives the condition that: 10 V C m = ′( ) which is the same result found for competitive piece-rate pay. However, the distribution of the surplus between mV and C(m) in equations (2) and (3) 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: