Question: erences over two periods, Consider an agent (Anna) with pref- U(x1, x2) = u(x1) + Bu(x2) Anna is endowed with 1 unit of x1,

erences over two periods, Consider an agent (Anna) with pref- U(x1, x2) = u(x1) + Bu(x2) Anna is endowed with 1 unit of x1,

erences over two periods, Consider an agent (Anna) with pref- U(x1, x2) = u(x1) + Bu(x2) Anna is endowed with 1 unit of x1, and 0 units of x2. Anna faces some interest rate, r, which she takes as given. 1. What is Anna's budget constraint in period 1, given that she may save or borrow? What is her budget constraint in period 2, given that she may save or borrow? 2. Combine these two budget constraints: what is Anna's lifetime budget constraint? 3. Specify the problem that Anna will solve to maximize lifetime utility? What are the first order conditions? 4. What is her Euler Equation? Please offer a short interpretation of this Euler Equation. Now, suppose that Anna lives for T > 2 periods. She is endowed with 1 unit of the good in period 1, and 0 units of the good in all other periods. Her preferences are described as T U(x1,...,x2) = t u(x) t=1 Activate W Go to Settings 5. State Anna's budget constraint. If you are stuck, consider using the same method that you used for the two period model, and extend that to 3 periods. Do you notice a pattern? 6. Derive a first order condition. Show the Euler Equation. Is it any different than the two period case? What if we considered the relationship of consumption that was two periods apart? Is there an analogy to the Euler Equation for this relationship? 1 . 7. Define = We call p the discount rate. Suppose p > r. Does Anna's consumption of the good increase over time or decrease? What if p < r?

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