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___________________________________________________CHAPTER 13______________ THE DEMAND FOR MONEY ____________________________________________________________________________ The introduction of money into an economy makes households better off, and in many ways it is like an improvement in technology. Once the "invention" arrived, and it arrives early in the development process, households must decide how much money they want to hold. In this chapter we study this decision. But, before we begin, we need to agree on the meaning of the word money. In ordinary conversation the word money can have several different meanings. If you ask someone how much money you make in a particular job, money means income. When you see a large house with fancy cars in the driveway you might say that those people have a lot of money. In this case money means wealth. If someone points a gun at you and asks for your money, you will give him, or her, your cash. When we talk about money we have the same meaning in mind as the mugger - currency and coin. Later, in chapter 20, we will discuss some different definitions of money that are in common use. Average Money Balances The amount or quantity of money that you hold fluctuates each day. On the weekends you may hold large money balances while in the middle of week you may only have lunch money. Right after payday your wallet may be full, but near the end of the pay period you may be short of cash. Fluctuations in daily money balances depend on the idiosyncrasies of individual tastes, the weather, pay periods, and so forth. To avoid dealing with the erratic behavior of daily money balances, economists focus on the demand for and behavior of average money balances. money demand 2 Let's look at a simple example to see what we mean by average money balances. Suppose at 5:00 P.M. on each of the next seven days you count the money (coins and bills) that you have on you. After the week you could make a table something like Table 13.1. Table 13.1 M T W R F S SN money $65 $90 $85 $75 $100 $15 $60 balances Your money holdings fluctuate substantially as we expected. To calculate your average money holdings, we add up the balance for each day. This gives $490. Since there were 7 days in this experiment, the average money balances are $490/7 = $70. We say that over this week your demand for (average) money balances was $70. If this was a typical week, then $70 equals your demand for money balances or demand for money for short. The quantity of average money balances results from a choice, implicit or explicit, that you make. For example, on Monday you could have spent $10 more or put $10 in your savings account. This would have reduced your money holdings by $10 on Monday and on each succeeding day. Your average money balances would have fallen to $60. On the other hand, a reduction of spending by $10 on Monday would have increased your average money balances to $80. By doing neither, you reveal a preference to hold $70 in average money balances. Real Money Balances Households use money to purchase goods and services, and they are therefore interested in the quantity of goods that their money balances will buy. It is one thing to have $200 in money balances when the price level is $2 per bundle and quite another to have $200 in money balances when the price level is $2000 per bundle. In the first instance money balances represent 100 bundles of goods, while in the second case money balances represent only 1/10th of a bundle. The number of bundles of goods that a household's nominal balances will buy is called the household's real money balances. In symbols real money balances are written as 3 chapter 13 real money balances = M/P. For a given price level, nominal money balances and real money balances behave in the same way. As a matter of fact, if the price level is fixed, we don't have to worry much about the distinction between real and nominal money balances. It is when the price level is allowed to change that it becomes important to differentiate between the two. For now we keep the price level fixed so that we do not have to worry about the distinction. Money Demand It is costly to hold money balances since they represent bundles of goods that could be consumed. Therefore, no one will voluntarily hold money unless they receive some benefits. One possible motive for carrying money from one period to another is savings. However, money is a poor vehicle in which to save because it bears no interest. We will have to look for a reason to hold money somewhere else. Money is the medium of exchange and the final payment in most transactions involves the transfer of money. But this alone is not enough to generate a demand for money. To see why, suppose that there are two assets in the economy: bonds that pay risk free interest and money that bears no interest, but is used in all transactions. Also assume that it is free to exchange money for bonds and vice versa. In this world it would be optimal to hold bonds until the moment you were ready to make a purchase. Right at the instant of purchase you would sell just enough bonds to make payment. The seller would take the cash and immediately buy bonds. No one would hold money for more than a moment. The crucial assumption in the above example is that it is free to swap bonds for money and money for bonds. When we drop this assumption and assume instead that it involves a transactions cost to convert assets from one form to another things change. Transactions costs may be fees paid to brokers when you buy or sell stocks and bonds, so-called brokerage costs, or they may be the time and inconvenience of going to and from the bank or ATM machine, so-called shoe leather costs. Once we recognize transactions costs, it is no longer optimal to hold only bonds. The transactions costs would be too high. Every time you wanted to buy a drink from a machine or pay for lunch, you would have to go to the bank; and this would grow old rapidly. money demand 4 For most households it will also not be optimal to hold only money. When you hold money it means that you are not holding bonds, and are thus foregoing the interest income that bonds yield. The interest income given up because of holding money balances is called interest opportunity cost. The decision on how much money to hold involves a trade-off between transactions costs and interest opportunity costs. If you hold a large quantity of money balances, you only go to the bank infrequently. But, you also have little interest income. On the other hand, if you hold low money balances in favor of more bonds, you enjoy a higher interest income. But, you must make frequent trips to the bank. An Example of the Trade-Off A simple example helps to illustrate the nature of the trade-off between the two types of costs. Consider a household that receives $700 each Monday morning for the previous week's work. All purchases are made with cash and the household spends $100 each day. The house hold has a savings account at a bank that is open 7 days a week, but it is costly in terms of shoe leather cost to go to and from the bank. Table 13.2 Balances with Seven Trips to the Bank M T W R F S SN money balances $100 $100 $100 $100 $100 $100 $100 savings balances $600 $500 $400 $300 $200 $100 $0 spending $100 $100 $100 $100 $100 $100 $100 Begin by assuming that the household chooses to go to the bank each morning to withdraw $100 for the day's purchases. In this case the household makes 7 trips to the bank and holds $100 in (average) money balances. The average balance in their savings account is $300 (just sum the daily balances in savings and divide by 7). Table 13.2 reports the data for daily spend ing, money balances, and savings account balances. 5 chapter 13 Now suppose that the household makes just 3 trips to the bank. On Monday they withdraw $200, on Tuesday $200, and on Friday $300. Table 13.3 summarizes the balances for this case. Table 13.3 Balances with Three Trips to the Bank M T W R F S SN money balances $200 $100 $200 $100 $300 $100 $100 savings balances $500 $500 $300 $300 $0 $0 $0 spending $100 $100 $100 $100 $100 $100 $100 The household's average money balances have increased to $171.43, while average balances in the savings account have fallen to $228.57. Making fewer trips to the bank increases average money balances because the household must make a larger withdrawal on each trip to the bank. Transactions costs decrease because of the fewer number of trips, but, since savings balances are smaller, interest income is also smaller. Lower transactions costs are enjoyed only at the expense of higher interest opportunity costs. The Determinants of Money Demand In the face of transactions costs, money is held to finance spending and an increase in trans actions costs raises money demand. To see why, suppose, for instance, that your bank reduces the number of tellers or closes down an ATM machine so it takes longer to make withdrawals. This increase in transaction costs encourages you to make fewer trips to the bank. But, if you make fewer trips to the bank, on each trip you have to take out more money, and this increases your holdings of average money balances, just as in the example. Higher spending also increases the demand for money since more money is required to carry out more expenditures. On the other hand, a higher interest rate makes it more attractive to hold bonds. Bond holdings, the savings balance in the earlier example, increase, and the demand for money falls. money demand 6 Because the price level has been held constant, our analysis applies to both the demand for real money balances and the demand for nominal money balances. It is convenient to summarize our discussion in terms of the demand for real money balances, and we write Md/P = L(r, Y, γ), - + + where Md/P is the demand for real money balances, r is the rate of interest, Y is real income and represents total spending, and the Greek letter γ (gamma) is the transactions cost of swapping money and savings balances (bonds). The negative sign under r means that an increase in r lowers the demand for real money balances. The positive sign under Y means that an increase in income raises the demand for real money balances. Finally, the positive sign under γ means that an increase in transactions costs raises the demand for real money balances. The Cost of Holding Nominal Money Balances It is now time to let the price level vary and consider the demand for nominal money balances. To see how changes in the price level affect the demand for nominal money balances, we need to find out how much current consumption is given up when you hold $1. Suppose that the price of a bundle of goods is $.50. In this case each dollar of money balances that you hold represents 2 bundles. This is an easy calculation and can be written down in symbols as $1/$.50 per bundle = 2 bundles. This means that the opportunity cost of holding $1 in average money balances is two bundles of goods. Now suppose that the price of a bundle increases to $2.00. The cost of holding $1 in money balances falls to 1/2 a bundle. In symbols $1/$2 per bundle = 1/2 bundle. 7 chapter 13 The cost of holding the $1 has fallen because the $1 represents fewer bundles than it did before prices rose. In general, the cost of holding $1 in money balances is $1/P = cost of holding $1 in money balances in terms of bundles of goods An increase in the current price level lowers the cost of holding $1 in money balances because holding the $1 represents fewer bundles of goods foregone. It is easy to get confused here if a sharp distinction isn't drawn between the current price level and the future price level. If you expect prices to rise in the future, you would try to spend your money today before prices went up. This would lower your demand for money. On the other hand, if the current price level increases, and no subsequent changes are expected, it is too late to spend your money. It has already lost some of its value. Instead, you will hold more money because the dollar value of your spending willincrease. Our conclusions are: 1) An increase in the current price level lowers the cost of holding money balances and thus increases money demand. 2) An expected increase in the future price level raises the cost of holding money and thus reduces the demand money. A change in the future price level would mean that inflation is expected, so we may rephrase the second conclusion to read that an increase in the expected rate of inflation lowers the demand for real money balances. The first conclusion is represented graphically in Figure 13.1. In this figure the cost of holding each dollar, $1/P, is measured on the vertical axis and the quantity of nominal money balances, M, is measured on the horizontal axis. The initial price level is $10 per bundle, so the cost of holding $1 is 1/10th of a bundle. At this price level households want to hold $200 in nominal money balances. If the price level increases to $20 per bundle (and afterwards is expected to remain at $20), the cost of holding nominal money declines to 1/20th bundle per dollar. This decline leads households to increase their demand for nominal money balances to $400. We could do this for all price levels and this would trace out the nominal money demand money demand 8 curve. The demand curve for nominal money balances has a negative slope and can be thought of in the same way as a 1/P demand curve for any good. The demand for nominal money 1/10 balances is just Md and can be written in symbols as 1/20 Md = P*L(r, Y, γ, πexpected ) - + + - $200 where we have now added the expected rate of inflation as a determinant of money $400 M Figure 13.1 The Demand for Nominal Money Balances demand. On the Md curve the quantity of nominal money balances demanded and the price level, P, are the only variables that are changing. This means that the real rate of interest, r, the real income stream, Y, transactions costs, γ, and the expected rate of inflation, πexpected, are held constant along the Md curve. A change in the price level causes a movement along the Md curve, while changes in the remaining variables that determine money demand cause shifts in the Md curve. We analyze how the Md curve shifts in the same way that we studied shifts in consumption demand, investment demand, and in labor demand. The effect of a change in the income will be taken up first. The first order of business is to find a benchmark. In Figure 13.2 the Md curve is drawn so that at the price level P 0 the demand for nominal money balances is M d0 . Now assume that there is an increase in income. If the price level stays the same, what will happen to the demand for nominal money balances? Since income is higher, expenditures are higher as well, and house holds will want to hold larger nominal money balances. The demand for nominal money ∏ balances will increase, say, to M d0 . This means that an increase in (real) income shifts the Md ∏ curve upwards and to the right. The new curve is labeled M d . The same thought experiment reveals how the Md curve shifts when the interest rate increases. In Figure 13.3 we start with the same benchmark. Instead of changing income, we now let the interest rate increase. If the price level stays the same, what happens to the demand 9 chapter 13 for nominal money balances? The higher interest rate raises interest opportunity cost. Households substitute towards bonds and 1/P lower their demand for nominal money ∏ balances to, say, M d0 . The money demand curve shifts down and to the left. An increase in expected inflation also increases the cost of holding money because 1/P 0 money is losing its purchasing power at a more rapid rate. In response to this higher cost, households will reduce their average money holdings. A picture of this result would look just like Figure 13.3. Md ' Md Md M d' M 0 0 Figure 13.2 The Effect on Money Demand of an Increase in Income Now consider an increase in the transactions cost, γ. It is now more costly to go to the bank, and households will make fewer trips. Since fewer trips are made, withdrawals each time are larger, and average money balances increase. A picture of this result would look just like Figure 13.2. Extensions 1/P The above analysis emphasizes the relationship between money demand and the price level. Many economists prefer to emphasize the influence of money on the interest rate, and plot the demand for real money balances against the interest rate r. To see the shape of this money demand curve suppose at the interest rate r 1 the demand for real money balances is (Md/P)1. This is shown in Figure 13.4. As r falls, in 1/P 0 Md Md ' Md' Md M 0 0 Figure 13.3 The Effect on Money Demand of an Increase in the Interest Rate money demand 10 the figure from r1 to r2, households shift away from bonds into money, and the demand for real money balances increases to r (Md/P)2This gives us the downward sloping curve labeled L. The economics of money r demand are the same, no changes have been 1 made. Indeed, if we so chose, we could plot the demand for money against real income, r 2 L Y. We show this picture here because it turns out to be useful later when we study sticky wage models. Summary d M/P (M /P) (Md/P) 1 2 Figure 13.4 The Demand for Real Money Balances Plotted Against the Interest Rate In this chapter we studied the demand for money. In this context money means currency and coin, and the demand for money is the demand for average money balances. It is important to be clear on the distinction between real and nominal money balances. The demand for real money balances depends positively on income and transactions costs, and negatively on the real interest rate and the expected rate of inflation. _____________________________________________________________________________ _____________________________________________________________________________ Review Questions 1) How would you expect the introduction of credit cards into an economy to affect the money demand curve? 2) Plot the money demand curve against real income Y. What is the slope of this curve? How would it shift if interest rates fall? 11 chapter 13 3) Germany experienced a so-called hyperinflation from August of 1922 to November of 1923. Something that cost 1 mark in August of 1922 cost 10,000,000,000 marks by November of 1923. The average rate of inflation was 322% per month. What do you think happened to the demand for real money balances over this period? 4) Consider the path of daily money balances given below. money balances M T W R F S SN $100 $65 $80 $85 $140 $30 $60 What are average money balances? If the price level is $5, what are real money balances? 5) If the demand for real money balances is 20 bundles and the price level is $130, what is the demand for nominal money balances?