Question

Individuals in the economy live for three periods and in each period Nt = nNt−1 young individuals are born. That is, the number of young born in each period grows at the rate n > 1. Denote the stock of fiat money in the economy in period t by Mt and suppose that the supply of fiat money grows at the rate z > 1 such that Mt = zMt−1. The young are endowed with y units of time and use all of this time to work. Each unit of labor produces one unit of the consumption good so that each young individual is endowed with y units of the consumption good when young. The individual is endowed with nothing when they are in middle-age and old. The consumption good cannot be stored across periods. Individuals care about consuming in each period of their life and have two assets they can acquire. First, they can sell the consumption good to acquire fiat money at the price in period t. Second, the individual can convert the consumption good into units of capital, where each unit of the consumption good can create one unit of capital. Capital is illiquid. That is, if an individual creates a unit of capital when young, it does not mature until the individual is old. Denote the two-period return on capital by X and the one period return on capital by x = X0.5. Individuals cannot directly trade unmatured capital with each other. 1. First consider an economy without banks so that a young individual can consume, acquire money or invest in capital.Suppose a young individual uses one consumption good to acquire money when young. How many consumption goods does the individual receive in middle-age from the acquired money?

Answer 1

The amount of consumption goods a young individual receives in middle-age for one good invested in money when young, in an economy without banks, depends on inflation and typically results in fewer goods due to the reduced purchasing power of money.

Step-by-step explanation:

In an economy without banks, if a young individual uses one consumption good to acquire money when young (at time t), the number of consumption goods they receive in middle age from the acquired money will depend on the rate at which the price level changes due to inflation (which is often tied to the growth rate of money supply).

If the money supply grows at a rate z, while the number of goods produced (y units of the consumption good) does not increase at the same rate, the individual will likely receive fewer consumption goods in exchange for the money because of the decreased purchasing power of money.

Assuming the price of the consumption goods increases at the same rate as the money supply, the individual would receive 1/z units of the consumption good in the next period.