1. Two consumers (call them A and B) have utility functions over consumption in period 1...

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1. Two consumers (call them A and B) have utility functions over consumption in period 1 and consumption in period 2 given by U(c1, c2) In(c1)+ In(c2) In period 1, consumer A receives income of = 80 and consumer B receives y = 120. In period 2, the endowments are reversed, consumer A gets y=120 and consumer B gets y = 80 a. First assume consumers are not allowed to save (so they just consume their income each period). Calculate each consumers' MRS at these consumption values. b. Now let consumers save. They receive an interest rate r on their savings. Write out the budget constraint for each consumer in each period and the combined two-period budget constraint. c. Find the optimal consumption for each consumer in each period as a function of the interest rate. d. If r=0.2, calculate how much each consumer wants to save (or borrow if optimal saving is negative) and consumption in each period. Is this allocation feasible (i.e. does the market clear)? e. Find the equilibrium interest rate. f. Now assume consumer B's income in period 2 increases to y=100 (everything else stays the same). Find the new equilibrium interest rate and consumption in each period. Is the interest rate higher or lower than the interest rate in part e? Explain the economic intuition of this result. g. Now assume consumers discount consumption in period 2 relative to period 1 so that their utility function becomes U(c1, c2) In(c) +In(c2) Where is a discount factor between 0 and 1. Keeping the values from question f, what is the equilibrium interest rate and consumption in each period if = 0.9? Explain the economic intuition. 1. Two consumers (call them A and B) have utility functions over consumption in period 1 and consumption in period 2 given by U(c1, c2) In(c1)+ In(c2) In period 1, consumer A receives income of = 80 and consumer B receives y = 120. In period 2, the endowments are reversed, consumer A gets y=120 and consumer B gets y = 80 a. First assume consumers are not allowed to save (so they just consume their income each period). Calculate each consumers' MRS at these consumption values. b. Now let consumers save. They receive an interest rate r on their savings. Write out the budget constraint for each consumer in each period and the combined two-period budget constraint. c. Find the optimal consumption for each consumer in each period as a function of the interest rate. d. If r=0.2, calculate how much each consumer wants to save (or borrow if optimal saving is negative) and consumption in each period. Is this allocation feasible (i.e. does the market clear)? e. Find the equilibrium interest rate. f. Now assume consumer B's income in period 2 increases to y=100 (everything else stays the same). Find the new equilibrium interest rate and consumption in each period. Is the interest rate higher or lower than the interest rate in part e? Explain the economic intuition of this result. g. Now assume consumers discount consumption in period 2 relative to period 1 so that their utility function becomes U(c1, c2) In(c) +In(c2) Where is a discount factor between 0 and 1. Keeping the values from question f, what is the equilibrium interest rate and consumption in each period if = 0.9? Explain the economic intuition.