Question

Consider an overlapping generations model with the following characteristics: Each generation is composed of 100 individuals. The fiat money supply changes according to Mt = 1.25Mt-1. The initial old own a total of 50 units of fiat money (M0 = $50). Each period, the newly printed money is given to the young of that period as a lump-sum transfer (subsidy). Each person is endowed with 10 units of the consumption good when born and nothing when old. Preferences are such that individuals wish to save 5 units when young at the equilibrium rate of return on fiat money.

(a) What is the real rate of return on fiat money in this economy?

(b) How many goods does a young individual receive as a subsidy in period 1?

(c) What is the price of the consumption good in period 1, p1, in dollars?

Answer 1

Answer:
(a)
The real rate of return on fiat money in the economy is given by below equation:

Money supply equation given in the question
     M_t = 1.25M_t-1
=> M_t+1 = 1.25M_t
=>

(b)
The volume of money printed each period is given by:

Assuming amount of goods received by individual to be x,
As we have 100 individuals in each period, which implies
    
=>
Now considering money growth question,

Now, demand for supply of the money is given by

=>
As we know, y - c_1,t is the saving of the old, which is = 5,
N_t = 100
M_t = 100
so,

Hence, individual will receive 4 units of subsidy.

(c)
The price of the consumption good in period 1, p1, in dollars is given by:

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