Assume an autocratically led country. The autocrat lives for 2 periods. In period 1, he can choose to tax income y₁ = 100 at rate t. In period 2, income that has not been taxed away yields period 2 income equal to 2[(1 - t)y₁^0.5. Assume no discount rate, but assume that there is a 20% chance that the autocrat will be toppled after period 1. Calculate the optimal period 1 tax rate for the autocrat, assuming that he will want to tax away all income in period 2. What is the optimal period 1 tax rate if there is a 60% chance that he will be toppled after period 1? What is the connection between the probability of losing power in period 2 and the period 1 tax rate?