Consider an economy in which people wish to hold money balances worth a total of 4,000 goods. They are indifferent between money issued by the central bank and money issued by private banks (so long as both offer the same rate of return). The central bank owns a constant stock of capital equal to its stock of money and uses the net return to pay interest on its money. Assume that x = 1.15 and a dollar always buys two goods. Intermediation, including the payment of interest on money, is costless.
a. What net rate of interest must the central bank offer to induce people to accept its money? What is the total net return from assets owned by the central bank? Prove that this satisfies the central bank's budget constraint.
b. What is the range of dollars that may be issued by the central bank so that a dollar always buys two goods? If the central bank issues $500, what is the total nominal value of money that will be issued by private banks?
c. Assume again that the central bank has issued $500. If the central bank doubles the nominal stock of central bank money, for what central bank policy will a dollar still buy two goods? For what central bank policy will the value of a dollar fall to one good? Explain why your answer depends on what the central bank does with the new money.