Consider an agent with the stage utility function vi (xi) = 2 xi , where xi is the amount of the good that he consumes in period i. This agent lives for two periods. He is endowed with 14e of income at the start of the first period and 1e at the start of the second period. The price of the good is 1e in either period, the discount rate of the agent is = 1 2 , and the interest rate is r =50%.

1. Write down the life-time utility of this agent as a function of his consumption levels in the two periods.

2. For this part of the exercise, assume that there are no financial markets. Nevertheless the agent can save a part of his endowment of 14e from the first period and consume it in the second period (without earning any interest). Represent the intertemporal budget constraint of the agent in this case. What are the optimal consumption choices in the two periods? For the rest of the exercise, suppose that the agent has access to financial markets and can borrow or lend money at the market interest rate.

3. Write down the intertemporal budget constraint of the agent.

4. What is the optimal choice of the agent? Will he be borrowing money or lending money? 5. Represent on the graph the two situations we considered in questions 2 and 4. 6. Examine how would the agents consumption in the first period change with the access to financial markets. Which effect is stronger? The income effect or the substitution effect?