(30 points) Consider an economy with two types of consumers labeled h and I. Consumers have preferences for current and future consumption given by:...

Some consumers are very patient and have a high βh, others are impatient and have a low βl (βl < βh). Note that β 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 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.

Find the equilibrium if y = y' = y-bar.

1. First, solve the problem of a type h consumer. This is to find ch, ch' and sh.
2. Second, solve the problem of a type l consumer. This is to find cl, cl' and sl.
3. Finally, using the market clearing condition to solve for R as a function of exogenous variables.

(30 points) Consider an economy with two types of consumers labeled h and I. Consumers havepreferences for current and future consumption given by:UhCh; Ch )= In ch + Bh In chul(c. ci) =Ing+Biinc