Suppose wins (Q) are produced by units of playing talent (L) according to the following function,

Q = 20L - L2

a. Determine the marginal product of labor, (MPL), equation.

b. Suppose the marginal revenue for a win is constant and equal to 20 (i.e., MR = 20). Determine the demand for talent (L) equation and graph it.

c. If the price of a unit of talent (w) is 120, what is the optimal amount of playing talent to hire? Graph this result and compute the total economic rents collected by the employer.

d. The price of a unit of talent drops to 80. Determine the new optimal amount of talent to hire. Add this result to your graph. What is the change in the total amount of economic rents collected by the owner?

e. Suppose the owner is not concerned with profit maximization, but simply wants to maximize wins. How many units of talent would maximize wins? What would be the resulting maximized number of wins?

10 = L/100 + L/50

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