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Increasing the size of a team that creates a joint product may dull incentives, as this problem will illustrate.11 Suppose n partners together produce a revenue of R = e1++ en; here eiis partner is effort, which costs him c(ei) = e2i/2 to exert.a. Compute the equilibrium effort and surplus (revenue minus effort cost) if each partner receives an equal share of the revenue.b. Compute the equilibrium effort and average surplus if only one partner gets a share. Is it better to concentrate the share or to disperse it?c. Return to part (a) and take the derivative of surplus per partner with respect to n. Is surplus per partner increasing or decreasing in n? What is the limit as n increases?d. Some commentators say that ESOPs (employee stock ownership plans, whereby part of the firms shares are distributed among all its workers) are beneficial because they provide incentives for employees to work hard. What does your answer to part (c) say about the incentive properties of ESOPs for modern corporations, which may have thousands of workers?
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