14. taxes and incentives Consider a setting where the manager’s input can be L or H and the output can be x1 = 10, 000 or x2 = 50, 000. The manager’s preferences are described in the usual fashion, i.e., (13.2). Let ρ = .0001 along with cH = cL = 5, 000 and also set the manager’s opportunity cost of working for this firm at M = 0. The owner is risk neutral. The output probabilities are noted below and input H is desired throughout the exercise.

x1 x2 input H .1 .9 input L .8 .2

(a) Determine and interpret an optimal contract.

(b) Suppose the owner is subject to a 20% income tax (i.e., a tax equal to 20% of the net of x−Ix), while the manager faces a zero marginal tax rate. Determine and interpret an optimal contract.

(c) Repeat

(b) above for the case where the owner is subject to a 20% income tax on income in excess of 20,000.

(d) Repeat

(c) above for the case cL = 4, 000.

(e) Repeat

(c) above for the case cL = 0.