Superstars and Mediocrities: A Simple Example

Marko Terviö, Helsinki School of Economics This example was part of an earlier version of what became “Superstars and Mediocrities: Market Failure in the Discovery of Talent,” Review of Economic Studies, 2009, 76(2), p. 829-850. Consider a competitive industry that combines workers with capital. There is free entry by …rms, which each need one worker to operate one machine that has a rental cost of $4 million.1 All units of output are identical, and the amount of output that a …rm produces depends solely on the talent of its worker. There is an unlimited supply of potential workers with an outside wage of zero (outside meaning outside this industry). A novice is equally likely to produce anywhere between zero and one hundred units.2 The talent of a novice worker is unknown (including to himself) but becomes public knowledge after one period of work. Careers are …nite and last at most 16 periods. Workers cannot commit to decline higher outside wage o¤ers in the future. Industry output faces a downward-sloping demand curve, and the number of …rms is “large,”so that …rms take the market price as given and there is no aggregate uncertainty. Finally, for simplicity, there is no discounting. How does this market for talent work? That depends crucially on whether aspiring workers can pay for the opportunity to work. There are two extreme cases to consider. In the …rst, individuals are constrained to take a non-negative wage. This is the ine¢ cient, but at the same time also the more straightforward case. In the second case, individuals are risk neutral and not credit-constrained. Due to the absence of imperfections, this is, not surprisingly, the e¢ cient benchmark. The purpose of the example is to compare the distribution of talent and wages in the industry under these two cases. Only the steady state is considered, where the number of entering and exiting workers is constant over time. 1All numbers in this example are chosen for convenience. 2For example, the machine could have a capacity for one hundred units per period, and talent could determine the proportion of successfully completed units.