The consumer's problem Logarithmic preferences This question appeared (verbatim) on the 2016 final exam Question III (40 points) The consumer's problem in a dynamic model Consider a two period consumption saving model from Chapter 9 A consumer's income in the current period is exogenous The incomes in the current and in the future periods are denoted by y and y' There are no taxes The consumer's utility function is giv en by U(c,c') Inc Inc', 0 1, where denotes the discount factor To answer questions a) to e), assume that the credit market is perfect The real interest rate on borrowing and lending is denoted by r a) (5 points) State in details the consumer's optimization problem b) (5 points) Derive and interpret the two conditions that define the optimal choice of consumption in the current and in the future periods c) (5 points) Find the analytical expressions for the optimal values of consumption in both periods, and optimal savings s d) (5 points) Suppose y 480, y' 500 and 0 9 Consider the real interest rate r 0 1 What are the optimal values of consumption in both periods Is the consumer a lender or a borrower Explain Represent the consumer's choice of c, c' and s on a graph Make sure to label the axes and the points of the intercepts of the budget constraint with the horizontal and vertical axes Indicate the value of the slope of the budget constraint, the endowment point, and the point of optimality e) (10 points) Keep the values y 480, y' 500 and 0 9 Suppose the real interest rate increases to r 0 2 Find the new optimal values of consumption Is the consumer a lender or a borrower Explain How is the consumer's welfare affected by the increase in the real interest rate Compare with the case of r 0 1 Explain your response Draw a new graph to illustrate the impact of a higher real interest rate on the consumer's choice On this diagram, show the optimal consumption choice for the old and the new interest rates Comment on the relative strength of the income and substitution effects of the real interest rate changes

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Question: The consumer's problem: Logarithmic preferences This question appeared (verbatim) on the 2016 final exam. Question III (40 points): The consumer's problem in a dynamic

The consumer's problem: Logarithmic preferences This question appeared (verbatim) on the 2016 final exam. Question III (40 points): The consumer's problem in a dynamic model Consider a two-period consumption-saving model from Chapter 9. A consumer's income in the current period is exogenous. The incomes in the current and in the future periods are denoted by y and y'. There are no taxes. The consumer's utility function is giv en by = U(c,c') Inc Inc', 0 <

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