Quantity-cum-Quality Contests - J. Atsu Amegashie (Center for Economic Studies and ifo Institute (CESifo), 2018)
I consider a contest in which the quantity of output is rewarded and another in which the quality of output is rewarded. The output in the quality contest plays a dual role. It counts in the quality contest but it is also converted into quantity-equivalent output to obtain total output in the quantity contest. This latter feature implies that the two contests are interlinked. Examples abound. There are contests in which there is a prize for the number (quantity) of publications by a scholar, a politician's accomplishments, an athlete's number of Olympic medals, etc and there is also a prize for a scholar's publications in top journals, a politician's major accomplishments, or an athlete's number of Olympic gold medals . I find that when the unit cost of producing quality is sufficiently high, then treating quality and quantity as the same has a disincentive effect on the production of quality. In contrast, when the unit cost of producing quality is sufficiently low, treating quality and quantity as the same has no disincentive effect on the production of quality. There is an equilibrium in which high-ability and low-ability contestants, in spite of being non-identical, have the same probability of winning the quantity contest. When contestants are budget-constrained, I find that whether an increase in the budget will increase effort in the quality contest depends on the size of the initial budget.
Keywords: D72; 330; Bayesian Nash equilibrium; contests; quality; quantity