1 Intertemporal choice An agent lives for two periods t = 1, 2, and consumes a single good in each period, which has price $1 per unit. Her perperiod utility function is u(ct) = \\/c_t, and her discount rate is 5. She earns labor income M1 = $100,000 in period 1, which rises to 102 = $190, 000 in period 2. She may save or borrow at interest rate 7', subject to the constraint that she repay any outstanding loan by the end of period 2. 1. Write down the agent's budget set for consumption in the two periods. 2. Write down the agent's intertemporal Euler equation (i.e. the tangency condition for optimality). What is the optimal ratio of consumption in period 2 compared to period 1? 3. Suppose 6 = 0.8 and a\" = 25%. What is the agent's optimal consumption plan? How much does she save / borrow at the end of period 1? 4. Redo the analysis of the previous part supposing instead that the interest rate has risen to 7' = 100%. 5. Redo the analysis of part 3 supposing instead that the interest rate has dropped to 7' = 0%. (The answers to these questions aren't all round numbers. Feel free to express your answers in decimal form if convenient.)