Consider a consumer with preferences for consumption today versus tomorrow represented by the utility function U(C,C') = C^2/5C'^3/5. Let income today is 50, income tomorrow is 20, taxes today are 10, and taxes tomorrow are 15.

A. Assume that there is a different borrowing versus lending rate, so that the lending rate is only 5% but the borrowing rate is 10%. Calculate the optimal consumption bundle. (hint: the consumer will be a saver)

B.On a (C,C') graph that is properly labeled, please show the optimal consumption bundle obtained in part (a).

C. Given the consumer still faces this 5% lending rate, but the government now faces a 10% lending rate. Assuming the government wishes to maximize the consumer's level of utility and taxes can be negative, what change would the government make? What would be the consumer's new consumption bundle given this change?