Answer the following questions. Use graphs whenever applicable.

Q1. A common belief is that the destruction of capital through an unexpected event, such as a earth- quake or a weather storm, causes output (GDP) to fall. In the context of the real intertemporal model with investment, discuss the impact on the economy of a partial destruction of capital. Why might output actually increase following the unexpected destruction of capital? Briefly discuss an actual situation where output actually increased following a weather disaster.

Q2. Suppose we have a small country with 100 consumers whose preferences are given by:

u(C, C') = ln(C) + In(C')

This utility function has a marginal rate of substitution given by:

MRS = C'/C

where C and C' are current consumption and future consumption, respectively. Each consumer receives income of y = 1000 and y' = 1000. There is also a Government which spends C = 10000 and C' = 10000 in the current and future periods, respectively. The Government's budget constraint in the current period is:

G = T + B

while in the future period its budget constraint satisfies:

T' = G' + B(1 + r)

where B is government borrowing, T and T' are taxes in the current and future periods and 1 + r is the gross interest rate.

(a) Derive each consumer's lifetime budget constraint and state the consumer's problem? What are the conditions which define the consumer's optimal choice?

(b) Suppose all government spending is financed through borrowing so that T = 0 and B = 10000. What are each consumer's savings? What is T' and t', where t' is the amount of taxes paid by each consumer in the future period? What is the equilibrium gross interest rate 1 + r?

(c) Suppose all government spending is financed through a combination of borrowing and taxes so that T = 5000 and B = 5000. What are each consumer's savings? What is T' and t', where t' is the amount of taxes paid by each consumer in the future period? What is the equilibrium gross interest rate 1 + r?

(d) Suppose all government spending is financed through taxes so that T = 10000 and B = 0. What are each consumer's savings? What is T' and t', where t' is the amount of taxes paid by each consumer in the future period? What is the equilibrium gross interest rate 1 + r?

(e) Given your answers in parts (b), (c) and (d), does Ricardian equivalence hold?

(f) Suppose the government maintains financing through taxes as in part (d), but there are actually two types of individuals with differing incomes. The first type has incomes of y = 1500 and y' = 500, while the second type has incomes of y = 500 and y' = 1500. There are 50 type one individuals and 50 type two individuals. Who borrows, who saves and explain why? What is the equibrium interest rate?