Roving bandit vs. stationary bandit Assume that there are two periods, 0 and 1. The first period output from the economy is 1, an autocrat can tax it with a tax rate, 0 ≤ t ≤ 1.
a. Denote the tax revenue as c0. How much is it in terms of t? How much of the output is left after tax, i.e., how much is 1 − c0 in terms of t?
b. Assume that the second-period output from the economy is 2(1 − c0), which is increasing in how much of the first-period output is left after tax. Assume that the autocrat will tax all of the second-period output. Denote the second-period tax revenue as c1. How much is it in terms of t?
c. Now assume that the autocrat can choose the first-period tax rate, t, to maximize the net present value of tax revenues from the two periods, with a discount factor, 0 ≤ β ≤ 1. In which case the autocrat is more patient and has a longer horizon, β = 0, or β = 0.5, or β = 1?
d. What is the net present value of tax revenues from the two periods in terms of t and β?
e. What is the optimal tax rate for the autocrat, in terms of β?
