Homework Answers Chapters 23, 3, and 27 Chapter 23 Questions 1, 3, and 6 1. Money refers to any asset that can be used in making purchases (examples are cash and checking account balances). People hold money despite its lower return precisely because of its usefulness in transactions; a person who held no money and wanted to make a purchase would either have to resort to time-consuming barter or else incur the costs of selling other assets to obtain money. 3. The Fed’s three tools to reduce the money supply are to conduct an open-market sale of bonds, to reduce lending to banks at the discount window, or to increase legal reserve requirements. If the Fed sells $1 million in government bonds to the public, it will receive $1 million in checks drawn against banks in return. By presenting these checks to banks, the Fed can take $1 million in bank reserves out of the system, which results in a decline in deposits (by $1 million divided by the reserve/deposit ratio) and hence a decline in the money supply. Similarly, if the Fed reduces its lending to banks at the discount window by $1 million, bank reserves again fall by $1 million, and deposits fall by $1 million divided by the reserve-deposit ratio. Raising legal reserve requirements does not reduce bank reserves; however, by raising the reserve/deposit ratio this action reduces the amount of deposits that banks can hold, given the amount of reserves they have. So again deposits and the money supply decline. 6. The quantity equation is written as M × V = P × Y. If we assume that velocity and output are constant during the period of time we are considering, then changes in M, the money stock, are directly proportional to changes in P, the price level. For example, a 10% increase in the money stock will lead to a 10% increase in the price level; i.e. a 10% inflation rate. Larger percentage increases in the money stock will lead to higher inflation rates while lower percentage increases in the money stock will lead to lower inflation rates, according to the quantity equation (again, assuming that velocity and output are constant). This conceptual relationship is generally supported by empirical evidence over long periods of time, as illustrated in Figure 23.1. Exercises 1, 4, 5, 8 p. 614-615 1 a. Cigarettes were passed hand to hand in exchange for goods and services, hence they were a medium of exchange. Prices were quoted in terms of cigarettes so they were a unit of account. Finally, as prisoners held hoards of cigarettes for future use they functioned as a store of value. b. Cigarettes are relatively durable (chocolate, for example, can melt) and low enough in value to be useful in small transactions (with highly valuable bootsthere is no way to purchase a small item or “make change”). Other advantages of cigarettes include their portability and their relative uniformity in value (one pair of boots might be worth much more than another pair). c. Yes, because he could trade them for something else that he wanted. In the same way, we have no direct use for dollar bills (they are not very good wallpaper, for example), but we accept them because we can trade them for things that we do want. 4 a. Deposits equal bank reserves/(desired reserve-deposit ratio) = 100/0.25 = 400. The money supply equals currency held by the public + deposits = 200 + 400 = 600. b. Let X = currency held by the public = bank reserves. Then the money supply equals X + X/(reserve/deposit ratio), or 500 = X + X/0.25 = 5X and X = 100 So currency and bank reserves both equal 100. c. As the money supply is 1250 and the public holds 250 in currency, bank deposits must equal 1000. If bank reserves are 100, the desired reserve/deposit ratio equals 100/1000 = 0.10. 1250 = 250 + 100/r 1000 = 100/r so r = 0.10 5 a In a fractional-reserve banking system (where the reserve/deposit ratio is less than one), banks loan out part of their deposits. The process of banks making loans and the public redepositing their funds in banks increases deposits and the money supply, until the point that the banking system has reached its desired ratio of reserves to deposits. Because each dollar of reserves ultimately “supports” several dollars of deposits, one extra dollar of bank reserves results in an increase in the money supply of several dollars (the money multiplier is greater than one). The money multiplier equals one only in the case of 100% reserve banking. In that case reserves are equal to deposits, so that an extra dollar of bank reserves increases deposits and the money supply by only one dollar. b. Initially the money supply is $1000 and currency held by the public is $500, hence deposits are $500. As the desired ratio of reserves to deposits is 0.2, initial bank reserves must be $100. An increase of $1 in bank reserves expands deposits from $500 to $101/0.2 = $505, increasing deposits and the money supply by $5. Similarly, an increase of $5 in reserves increases deposits and the money supply by $5/0.2 = $25, and an increase of $10 raises deposits and the money supply by $10/0.2 = $50. As the money supply rises by 5 times the increase in bank reserves, the money multiplier in this economy is 5.c. As the example in part b illustrates, in general the increase in deposits and the money supply equals the change in bank reserves times 1/(desired reserve/deposit ratio). Hence the money multiplier equals 1/(desired reserve/deposit ratio). In the example of this problem the money multiplier equals 1/0.2 = 5. d. The Fed could raise legal reserve requirements. If this action forced banks to raise their ratio of reserves to deposits, the result would be a smaller money multiplier (since the money multiplier is the inverse of the reserve/deposit ratio). 8. a. The price level for 2004 and 2005, along with the inflation rate between the two years is given below. 2004 2005 M 1000.0 1050.0 V 8.0 8.0 Y 12000.0 12000.0 P = MV/Y 0.667 0.700 Inflation Rate = 4.94% b. As the following table illustrates, when the money supply increases the inflation rate also rises, holding output at its previous level. 2004 2005 M 1000.0 1100.0 V 8.0 8.0 Y 12000.0 12000.0 P = MV/Y 0.667 0.733 Inflation Rate = 10% c. As the following table illustrates, if the money supply rises at nearly the same rate that real output rises, the inflation rate