Question 2 (30 points)

Subject:EconomicsPrice: Bought3

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Question 2 (30 points). Consider an economy with two types of consumers labeled h and l. Consumers have preferences for current and future consumption given by: un (en ca) = In cu + Ba Inch en (a, ci) = Ina + Bi Inch Some consumers are very patient and have a high Bh, others are impatient and have a low B, (B1 <B1. Note that B is the weight in the future consumption, or the discount rate. Consumers are equal in their income and there are no taxes (that is, t = t = 0). The government does not have to finance any spending. There are N consumers of each type in this economy. That is, in total there are 2N consumers, N of them are type h and N are type l. I recommend that you make a change of variable to solve this problem: instead of working with the net interest rate (r), work with the gross interest rate R=1+r. 1 (a) Carefully define an equilibrium for this economy. (b) Find the equilibrium if y=ý = 7. (a) First, solve the problem of a type h consumer. This is to find Cha ch and shi (6) Second, solve the problem of a type I consumer. This is to find q, cand si. 7 (c) Finally, using the market clearing condition to solve for R as a function of exogenous variables. (c) Solve for the equilibrium interest rate R if Bi= Bh. What are c, cand s in this case?