Question

can anyone help me with this question?

2. An review of intertemporal optimization: Suppose a consumer's utility function is given by U(c,2) where ci is consumption in period 1 and ca is consumption in perio You can assume that the price of consumption does not change between periods 1 and 2. The consumer has $100 at the beginning of period 1 and uses this money to fund consumption across the two periods (i.e. the consumer does not gain additional income in period 2 beyond the interest acerued on her savings). The consumer faces interest rate r. (a) Write down the consumer's (intertemporal) budget constraint. (Make sure you account for the interest accrued on savings between period 1 and period 2!) (b) Write down the consumer's optimization problem (Lagrangian). What is the objective function? What are the choice variables? What are the parameters? (c) what are the optimal values of ci and c2: ci and cr (d) Suppose now the consumer has $101 to spend instend of $100. How does this affect your answer to part (c) above? (e) How does the S1 increase in part (d) affect the consumer's utility? (There are two ays to answer this: a "brute force comparison and an explanation using the Lagrange r A. You must provide at least one of these answers, but it will improve your multiplier A'. You must provide at least one of these answers, but it will i undonet andine of constrained optimization if you are able to provide both.)

Answer 1

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