Reference no: EM133273783
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 labour 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 Pt = 1/vt 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.
(a) 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?
(b) How many consumption goods does the individual receive when old if they decide to hold the money for two periods until they are old?
(c) Suppose a young individual uses one consumption good to create capital when young. How many consumption goods does this capital provide to the individual in middle age?
(d) How many consumption goods do the individuals receive from the capital when they are old?
(e) Using the answers to the previous parts, explain why fiat money and capital can co-exist in this economy in equilibrium.
(f) Referring to the above parts, explain what is meant when we say that individuals have a liquidity mismatch problem in this economy.