1. (25 marks) Consider the following version of the two-period endowment economy: There are two periods and two different consumers, each who lives for two periods. The two consumers have identical utility functions U(c,c') = Inc + βlnc'. The two consumers have different endowments of y and y' however: Consumer l's endowment is (y,y') = (0,10), and consumer 2's endowment is (y,3') = (10,0). There is no
labour, no government (and hence no taxes) and no endogenous production. The two consumers can trade with each other by buying or selling bonds S in the current period that promise to pay 1 + r units of consumption in the future period.
(a) (2 marks) Write down each consumer's budget constraints in the present and future.
(b) (2 marks) Derive and provide an intuitive interpretation of the Euler-equation for consumer 1.
(c) (2 marks) Now write down the Euler equation for consumer 2 (it is not necessary to derive it if you can write it directly).
(d) (3 marks) Use consumers 1 and 2's Euler equations to find an expression that relates consumer l's choice of current and future consumption to consumer 2's choice of current and future consumption in equilibrium. Provide an interpretation.
(e) (4 marks) Find the optimal level of consumption for each consumer in the current and future periods.
(f) (2 marks) Show who is the lender, and who is the borrower.
(g) (4 marks) Plot each consumer's choice on a c' - C diagram, clearly showing each consumer's endowment.
(h) (3 marks) What is aggregate savings equal to in this economy?
(i) (3 marks) What role does (individual or aggregate) savings play in this economy?

2. (5 marks) In the two-period endowment economy in Chapter 8, find an expression for aggregate savings. Interpret the meaning of your answer.

3. (10 marks) In the two-period production economy of Chapter 11, find an expression for aggregate savings. Is this expression the same as the expression for aggregating savings in question 2? Why or why not?

4. (30 marks) Consider an economy which is identical to the Chapter 9 two-period endowment economy except that there are three periods instead of two, and only a single consumer. The consumer has preferences U(C1, C2, C3) = In C1 + βIn C2 + β²In C3, and is endowed with exogenous income Y1, Y2 and Y3, where subscripts denote variables in periods 1, 2 or 3. The consumer and the government can buy and sell bonds S1 in period 1 at interest rate T1, and as well buy and sell bonds S2 in period 2 at interest rate T2- The government has spending G1, G2, G3 and lump-sum taxes T1, T2, I3 in each of periods 1, 2 and 3 respectively. The initial and terminal conditions are otherwise the same as the two-period economy (ie consumers begin period 1 with no assets, finish period 3 with no assets).
(a) (2 marks) Write down the consumer's budget constraint for each period.
(b) (6 marks) Now derive the consumer's lifetime budget constraint
(c) (4 marks) Write down the government's budget constraint for each period.
(d) (6 marks) Now derive the government's lifetime budget constraint
(e) (2 marks) Show| the consumer's problem.
(f) (5 marks) Find an Euler-equation the describes the trade-off between period 1 and period 2 consumption.
(g) (5 marks) Find and Euler-equation that describes the trade-off between period 1 and period 3 consumption. Interpret this equation.

1. (25 marks) Consider the following version of the two-period endo...