Consider an economy in which people wish to hold money balances worth a total of
ID: 2752567 • Letter: C
Question
Consider an economy in which people wish to hold money balances worth a total of 5 million goods. They are indifferent between money issued by the central bank andmoney issued by private banks (as long as both offer the same rate of return). In the initial period, the central bank issues $1 million and uses the proceeds to purchase capital. The central bank owns a stock of capital equal to its stock of money and usesthe return to pay interest on its money. Assume that x=1.2 and a dollar always buystwo goods. Intermediation, including the payment of interest on money, is costless.
a) What rate of interest must the central bank offer to induce people to accept its money? Does this satisfy the central bank’s budget constraint?
b) What is the real value of the total amount of money issued by private banks?
c) Is there an equilibrium in which a dollar always purchases three goods? In this case, what is the real value of money issued by private banks?
d) Argue that the people are indifferent between the equilibrium in which a dollar is worth three gods and the equilibrium in which a dollar is worth two goods.
e) Suppose the central bank pays no interest on its money but maintains a constant stock of capital, using the net return from the capital it owns to buy up and burn a fraction of its money. Find z, the rate of change of the nominalcentral bank money stock. Check that the government budget constraint ismet. (You should no longer assume that vt=2 in all periods.)
Explanation / Answer
Answer:
A consequence of the public’s indifference between the money of private banks and of the central bank is that the price level may be undetermined—a wide range of price levels may be an equilibrium. Look again at the market-clearing conditions for money:
Nh + vM = N(y – c1) .
This equation can be satisfied by a range of possible combinations of v and h. If people decide to hold exclusively central bank money, we find an equilibrium in which h = 0 and v = N(y c1)/M. If instead they decide to accept none of the central bank’s money, we find an equilibrium in which h = (y c1) and v = 0.
Any values of h and v that satisfy Equation and lie between these two extremes can also be an equilibrium.
Because people are indifferent between the two forms of money, given that each offers the same rate of return, it is impossible to guess which of the many equilibrium will occur. The central bank has a number of options to pin down the value of a unit of its money. It could set v equal to any number between 0 and N(y c1)/M.
With the public indifferent among the various possible equilibria, there would be no difficulty in enforcing any particular value of v within this range. Almost as straightfowardly, the central bank could choose the real value of central bank investments Kg. Because Kg = vM when money is fully backed, by picking Kg and M, the government can determine v. Another way to determine the value of central bank money involves setting reserve requirements.. The central bank can require that each private bank hold reserves of central bank money equal to a fraction ( ) of the value of the private bank’s deposits and bank notes. To ensure that banks or the public will not hold central bank money in excess of the required reserves, the central bank can promise to pay interest only on required reserves. Under this monetary regime, the market-clearing condition for money balances becomes Nh = N( y c1) , with the reserve requirement specified as Nh = vM.
Combining Equations, we obtain the result
vM = N ( y c1 ) v = N ( y c1) M .
It is easy to see from Equation that by choosing , the central bank may fix the price level.