Consider a version of the model economy presented in this chapter with fiat and private money. Assume that population is constant with 400 people born each period. Each young person is endowed with 10 units of consumption good when young and nothing when old. Let the central bank issue $10,000. A bank can issue up to $1,000 but has to hold reserves backing every dollar of private money.
a. Solve for the equilibrium price level in this model economy.
b. Suppose the backing rule is modified so that the bank can issue $2,000 backed by only $1,000 of reserves. Compute the price level in this new setting. Explain the difference between the two price levels.