Consider an economy where 50 percent of the population is poor and 50 percent is rich. The poor have an income, which is a function of the interest rate r: yp = 8,000 ¥ r1/2, and the rich have an income with the following functional form: yr = 8,000 ¥ r1/2 + 1,500. Assume that both the rich and the poor have the same utility function: u(y) = -y2 + 8,000y + 2,000. A benevolent government wants to maximize the welfare of the society:

It must decide whether to give a subsidy to the bank in order to decrease the interest rate from 22 percent to 20 percent, to keep the interest rate at 22 percent without subsidy, or to raise the rate to 25 percent. What strategy would you suggest to this government to follow? Assume that the maximum income in this economy does not exceed $4,000.

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max W(r)=0.5u(yp)+0.5u(yr).