Question

Consider an economy where at time t there are N=75 old individuals and population grows at 20% per period. Individuals are endowed with ω₁ =20 units when young and ω₂=12 when old. Assume that each individual's utility is given by U(c₁,c₂)=lnc₁+lnc₂ Finally, suppose that the old generation at time t have a total 500 units of fiat money.

a. What are the per period budget constraints for a young person born at time t ? Write down the real money supply function for period t. What is the real money demand function (NOTE: you need not solve for a consumer's savings function to do this!!)? Under what condition on prices will the money market clear (you need not solve for equilibrium)? Use this condition to find the real rate of return on money between periods t and t+1

Answer 1

The per period budget constraint for a young person born at time t can be determined by considering their consumption choices when young and when old. The real money supply and demand functions can be derived using the total money supply and the price level. The money market clears when the real money demand is equal to the real money supply.

Step-by-step explanation:

The per period budget constraint for a young person born at time t can be determined by considering their consumption choices when young and when old. Assuming that there are N=75 old individuals and the population grows at a rate of 20% per period, each young person will have a share of the total consumption when they are old. Let's denote the share as s=N/(N+1), where N is the number of old individuals. The per period budget constraint can be represented as c₁ = ω₁ + (s x ω₂). If we substitute the given values of ω₁=20 and ω₂=12, we can find the budget constraint for a young person. The real money supply function for period t can be determined by using the formula Mᵣ = (M/P), where M is the total money supply and P is the price level. The real money demand function can be derived by considering the utility function and solving for the optimal consumption when young and old. Finally, in order for the money market to clear, the real money demand should be equal to the real money supply. This condition can be used to find the real rate of return on money between periods t and t+1.