Consider the two period model discussed in class with no credit market imperfections. Suppose that a consumer has the following: Current income = y = 200 Future income = y'= 150 Current taxes = t = 40 Future taxes = t'=50 Real interest rate = r = 0.05 (5% per period) This consumer prefers to consume equal amounts of consumption in all time periods. (a) Find the consumer's optimal amount of current and future consumption as well as his saving to achieve this. (5 points) (b) Is this consumer a lender or a borrower? How can you tell? (2 points) (c) Graph the above equilibrium on a graph with c on the horizontal axis and c'on the vertical one. Be sure to show the optimal consumption point and the endowment point. (5 points) (d) Illustrate the new equilibrium for this consumer if the real interest rate falls to 0.03. Was the income or substitution effect larger for this consumer? Be sure to include the new intercepts, optimal consumption point, and label the substitution effect "B." (5 points) (e) If there was friction in the credit market such that the borrower and lender face different interest rates, explain, in words, what would happen to the lifetime budget constraint and why.