A firm has the same revenue and cost function as in Spreadsheet Exercise 7.1

a. The shareholders of the firm hire a manager on a profit-sharing basis whose payment, M, is 25% of the firm’s profit: M = 0.25(R − C). The shareholders receive the remaining 75%, so their income is S = 0.75(R − C). Add columns for M and S to the spreadsheet in part a of Spreadsheet Exercise 7.1 and calculate the manager’s payment and the shareholders’ income for q=0, 1, 2, …, 20. Determine the amount of output that the manager will produce if the manager’s objective is to maximize his or her own compensation. Is this outcome consistent with the shareholders’ profit-maximizing objective?

b. Now suppose that the manager receives compensation equal to 10% of revenue, so that the return to the owners is S = 0.9R − C. Use Excel to determine the return to the manager and the return to the owners for q = 0, 1, 2, …, 20. Are the incentives of the shareholders and the manager aligned in this case?