Question

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4. Two consumers (call them A and B) have utility functions over consumption in period 1 and consumption in period 2 given by U (1,C2)n(c)ln(c2) In period 1, consumer A receives income of y 2, the endowments are reversed, consumer A gets y= 120 and consumer B gets y = 80 80 and consumer B receives y? = 120. In period (so they just a. First assume consumers are not allowed to save consume their income each period). Calculate utility for each consumer 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 (as in the notes) Find the optimal consumption for each consumer in each period function of the interest C. as a 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? In other words, given the amount of total income in the economy in each period, is it possible to consume as much as this allocation would suggest? Find the market clearing interest rate (the interest rate where total consumption adds to total income in each period) e. 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. Is it higher or lower than the interest rate in part e? Explain the economic intuition of this result (hint: think about what has happened to the relative scarcity of total income in each period and how that affects desired saving by each consumer). g. Now assume consumers discount consumption in period 2 relative to period 1 so that their utility function becomes U (C1, c2)n(ci + B ln(c2) Where Bis a discount factor between 0 and 1. Keeping the values from question f, what is the equilibrium interest rate if B= 0.9? Explain the economic intuition

Answer 1

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