Assume a consumer has current-period income y = 0, future-period income y = 200, and faces a market real interest of r = 0.05. There is no government and no taxes. The consumer would always want to consume equal amounts in both periods, if possible.

a.Write down the consumer's lifetime budget constraint and draw this constraint in a well-labelled diagram.

b.Calculate the consumer's current and future period consumption levels and optimal borrowing, and show this in the diagram above. Remember to draw the indifference curve that passes through the optimal bundle.

c.Suppose that everything remains unchanged, except that now the consumer can borrow up to 80 units, i.e., s-80. Calculate the consumer's current and future period consumption levels and optimal borrowing under this borrowing constraint, and show this in a new diagram. Remember to draw the indifference curve that passes through the optimal bundle.

d.Now, suppose that the individual can borrow any amount in a black market (an illegal underground market) for loans. Suppose that the "loan shark" charges 30% interest rate, i.e., r = 0.30. Calculate the consumer's current and future period consumption levels and optimal borrowing when he takes this loan from the loan shark. Assume that he cannot obtain the loan from the bank in part c. Show this in the diagram above in part (c). Remember to draw the indifference curve that passes through the optimal bundle.

e.What is the interest rate the loan shark could charge to make this individual indifferent between the black market loan and the bank loan as in part c- issued at r = 0.05 but capped at 80 units? Assume the individual can borrow either from the bank or from the loan shark but not from both of them at the same time.