Consider a commodity money model economy like the one described in this chapter but with the following features: There are 100 identical people in every generation. Each person is endowed with 10 units of the consumption good when young and nothing when old. To keep things simple, let us assume that each young person wished to acquire money balances worth half of his endowment, regardless of the rate of return. The initial old own a total of 100 units of gold. Assume that people are indifferent between consuming 1 unit of gold and consuming 2 units of the consumption good.
a. Suppose the initial old choose to sell their gold for consumption goods rather than consume the gold. Write an equation that represents the equality of supply and demand for gold. Use it to find the number of units of gold purchased by each person, m^g_t, and the price of gold, v^g_t .
b. At this price of gold, will the initial old actually choose to consume any of their gold?
c. Would the initial old choose to consume any of their gold if the total initial stock of gold were 800? In this case, what would be the price of gold and the stock of gold after the initial old consumed some of their gold? Compare your answer in this part with your answer in part a. Does the quantity theory of money hold?