Prof. Gustavo Indart Department of Economics University of Toronto ECO 100Y INTRODUCTION TO ECONOMICS Lecture 16. THE DEMAND FOR MONEY AND EQUILIBRIUM IN THE MONEY MARKET We will assume that there are only two types of assets in the economy: bonds and money. Therefore, individuals have to decide how much of their total wealth they will keep in the form of bonds, and how much in the form of money. We will further assume that there is no financial return (interest) on money holdings, but that there is a financial return (interest) on bond holdings. What determines this return on bond holdings? 16.1 THE DETERMINATION OF THE RATE OF INTEREST Consider the case of a perpetual bond, which is a promise to pay a fixed amount (coupon) to the holder of the bond every year and forever. For example, a bond that costs $100 may have a coupon of $5. We must first make a distinction between the face value of the bond and its market price. The face value of the bond is the amount of money that an individual must pay for the bond when it is issued ($100 in our example). The market price of the bond is the amount of money the individual will obtain in the market when she sells her bond. The face value of the bond is fixed, it does not depend on market forces (demand and supply). The market price of the bond, however, does depend on demand and supply.
2 When there is an excess supply of bonds in the market, the price of bonds decreases; when there is an excess demand for bonds in the market, the price of bonds increases. The return or yield on the bond is not equal to the coupon (Q C ) divided by its face value, but to the coupon divided by its market price (P C ): i = Q C / P C. The yield on bonds represents the interest rate or the opportunity cost of holding money. Suppose that there is an excess supply of bonds in the bond market. Therefore, the bond with a face value of $100 and a coupon of $5 will have a lower market price, say $80. Hence, at the present time the return or yield on this bond is: i = $5 / $80 = 6.25%. That is, the market nominal rate of interest is 6.25%. Therefore, when the money market is in disequilibrium (and thus the bond market is also in disequilibrium), adjustments in the rate of interest restore equilibrium in both markets. For instance, when M D > M S (excess demand for money) and thus B D < B S (excess supply of bonds), the price of bonds falls and the interest rate increases. As the price of bonds falls, the quantity demanded of bonds increases and equilibrium is restored in the bond market. As the rate of interest increases, the demand for money decreases and equilibrium is restored in the money market. 16.2 THE DEMAND FOR MONEY The amount of wealth that everyone in the economy wishes to hold in the form of money balances is called the demand for money. There are three major motives for holding money: 1) transaction motives; 2) precautionary motives; and
3 3) speculative motives. 16.2.1 The Transaction Demand for Money The transaction demand for money arises when money is used to make regular payments. That is, the use of money as a medium of exchange creates the transaction demand for money. The need for holding money for transaction purposes arises because revenues and payments do not coincide in time. Suppose that an individual receives $1,000 a month and spends the same amount every month. If he spends the $1,000 the same day that he receives it, then there is no need for him to hold cash balances. However, a problem arises when he receives $1,000 one day but spends it at different dates within the month. There are benefits and costs of holding money for transaction purposes. In deciding how much money to hold for transaction purposes, the individual has to weigh the costs of holding money balances against its benefits. Let's assume that no interest is paid on money balances. In this case, then, the cost of holding money is equal to the interest forgone. Indeed, instead of holding an asset in the form of money which does not earn any interest, the individual could hold a different asset, say a bond, on which he would earn a return. The benefits of holding cash balances can be measured by the costs or inconveniences that could arise from not holding them. That is, the benefits of holding money balances are equal to the costs of not holding them. Indeed, if there were no cost or inconvenience of holding small amounts of cash, the individual would keep all his wealth in the form of assets that give him a monetary return (e.g., bonds) and convert some assets into cash whenever he has to make a payment.
4 But there are certain costs and inconveniences involved (e.g., bank charges for withdrawals, the inconvenience of going to the bank very often, etc.). Therefore, as indicated above, when deciding how much money to hold for transaction purposes, the individual has to weigh the costs and benefits of holding small balances. The transaction demand for money depends on the level of the rate of interest and the level of income. The transaction demand for money decreases with the rate of interest and increases with the level of income. Since the opportunity cost of holding money is the interest forgone, as the interest rate increases the transaction demand for money decreases. Also, as income rises the number of transactions increases and thus there is a need for more cash balances. 16.2.2 The Precautionary Demand for Money In discussing the transaction demand for money we have seen that an individual does not know exactly what income he will be receiving in the next few weeks and what payments he will have to make. Therefore, the individual will hold some money for precautionary purposes, that is, to be able to cover some unexpected payments he might have to make. If he has to make a payment and does not have the cash he incurs a loss that we may call the cost of illiquidity. The more money an individual holds, the less likely he is to incur the costs of illiquidity but the more interest he is giving up. Therefore, we are once again in a tradeoff situation. As before, there must also be an optimal amount of precautionary money balances to hold determined by the balancing of interest costs against the advantages of not being
5 caught illiquid. As in the case of the transaction demand for money, the precautionary demand for money also depends on both the rate of interest and the level of income. 16.2.3 The Speculative Demand for Money The transaction demand and the precautionary demand for money emphasize the medium of exchange function of money, that is, the need to have money on hand to make payments. The speculative demand for money emphasizes the store of value function of money, that is, the role of money in the investment portfolio of an individual. Wealth is hold in specific assets, and these assets make up a portfolio. Since the return in most assets is uncertain, investors try to minimize risk by diversifying the portfolio investment. A risk-averse investor will want to hold some amount of a safe asset as insurance against capital losses on assets whose prices change in an uncertain manner. The safe asset is held precisely because it is safe, even though the return on this asset is lower than the expected return on other riskier assets. Given the rate of inflation, money is a safe asset because its real value is known with certainty. When the rate of inflation is unknown, the real value of money is also uncertain. However, money is still a relatively safe asset since the uncertainty about the values of equity is even larger. The demand for money (the safest asset) depends on the expected yields and the riskiness of the yields on other assets, where riskiness of the return on other assets is measured by the variability of the return. An increase in the expected return on other assets increases the opportunity cost of
6 holding money and thus reduces the demand for money. An increase in the riskiness of the return on other assets has the opposite effect. The implications of the speculative demand for money are similar to those of the transactional and precautionary demands. An increase in the interest rate of non-money assets (e.g., long-term bonds yields) reduces the demand for money. The level of wealth is relevant to the speculative demand for money. The level of wealth determines the size of the total portfolio investment, and thus increases in wealth will lead to increases in the demand for money (the safest asset). If we assume that, in the long-run, wealth increases proportionally to income, then the speculative demand for money also increases with the level of income. 16.3 THE DETERMINATION OF THE EQUILIBRIUM RATE OF INTEREST We indicated that the demand for money depends on the rate of interest and the level of income. That is, M D = ky hi. Diagram 16.1: The Demand for Money i M S i 2 i 0 i 1 M D M
7 Since the demand for money increases as the rate of interest decreases, we can draw a downward-sloping demand for money curve (M D ) with the interest rate on the vertical axis and the quantity of money on the horizontal axis. In the same diagram, we can also draw the supply of money (M S ) which is assumed to be fixed, that is, M S does not change with the rate of interest. If the rate of interest is i 2 (see Diagram 16.1 above), the quantity supplied of money is greater than the quantity demanded of money (there is an excess supply of money), and thus the interest rate falls. If the rate of interest is i 1, the quantity supplied of money is less than the quantity demanded of money (there is an excess demand for money), and thus the interest rate rises. When the rate of interest is i 0, however, the quantity supplied and the quantity demanded of money are equal and thus i 0 is the equilibrium rate of interest. 16.3.1 The Effect of a Change in the Level of Income We said that the demand for money depends on the level of income. That is, as income increases the demand for money increases. Diagram 16.2: The Effect of an Increase in Income i S M i 1 i 0 M D 1 (Y 1 ) M D 0 (Y 0 ) M
8 This suggests that there is one demand for money curve for each level of income. The curve M D 0 corresponds to the level of income Y 0. As Y increases to Y 1, the demand for money curve shifts up to M D 1. Since the supply of money remains fixed, there is now an excess demand for money at the level of interest rate i 0. Therefore, the rate of interest increases to i 1 when the demand for money increases to M D 1. 16.3.2 The Effect of a Change in the Supply of Money Suppose now that the demand for money remains constant but the stock of money increases from M S 0 to M S 1. Diagram 16.3: The Effect of an Increase in the Supply of Money i M S 0 M S 1 i 0 i 1 M D M At the level of interest rate i 0 there is now an excess supply. Therefore, the rate of interest decreases to i 1 when the supply of money increases to M S 1.
16.4 INVESTMENT AND THE RATE OF INTEREST 9 Up to now we have been assuming that the level of investment was fixed. That is, we have assumed that I = I. However, we indicated earlier that, in reality, investment depended on various variables, particularly on the level of the rate of interest and on the level of output (income): I = I bi + fy. This equation implies that investment increases as the level of income increases, and decreases as the rate of interest increases. Let s assume, for simplicity, that investment is a function of the rate of interest only: I = I bi. This investment function is also known as the marginal efficiency of investment function or MEI. Diagram 16.4: Investment and the Rate of Interest i I i 0 i 1 I I 0 I 1 I
16.4.1 The Aggregate Expenditure Curve 10 We have seen before that, in a closed economy, when I = I, aggregate expenditure (AE) was equal to: AE = C + I + G = AE + c (1 t) Y, where AE = C + I + G, assuming TA = ty. Assuming now that I = I bi, then our expression for aggregate expenditure becomes AE = AE bi + c(1 t)y. This expression for aggregate expenditure suggests that there is one AE curve for each level of the rate of interest, and that the AE curve shifts up when the rate of interest decreases. 16.4.2 Equilibrium Income In equilibrium, Y = AE, that is Therefore, equilibrium income is equal to: Y = AE bi + c(1 t)y [1 c(1 t)]y = AE bi. 1 Y* = ( AE bi). 1 c(1 t) When investment depends on the rate of interest, there is a particular AE curve for each level of the rate of interest. Therefore, we are going to obtain a different equilibrium income for each level of the rate of interest. This can be observed in Diagram 16.5 below.
11 Diagram 16.5: Equilibrium Income and the Rate of Interest i AE AE 1 i 0 AE 0 i 1 AE bi 1 b i AE bi 0 I 0 I 1 I Y* 0 Y* 1 Y When the rate of interest is i 0, investment is I 0 : The corresponding AE curve is AE 0 : I 0 = I bi 0. AE 0 = AE bi 0 + c(1 t)y. And the corresponding equilibrium income is Y* 0 : 1 Y* 0 = ( AE bi 0 ). 1 c(1 t) Note that the change in the rate of interest affects equilibrium income through its effect on the investment component of AE. 16.5 THE EFFECT OF MONETARY POLICY Suppose that the government increases the supply of money in the economy. That is, the Bank of Canada increases the money supply through an open market purchase of Government Bonds.
12 How will this increase in money supply affect the equilibrium level of income? The first effect of the shift of the M S curve from M S 0 to M S 1 is to decrease the rate of interest to i 1. Diagram 16.6: The Effect of Expansionary Monetary Policy i i AE M S 0 M S 1 AE 1 i 0 i 0 AE 2 i 2 i 2 AE 0 M D 2 (Y 2 ) i 1 i 1 M D 0 (Y 0) I M I 0 I 2 I 1 I Y 0 Y 2 Y 1 Y The decrease in the rate of interest increases investment from I 0 to I 1, where I 0 = I - bi 0 and I 1 = I bi 1. The increase in investment shifts the AE curve up to AE 1 and the equilibrium level of income increases to Y 1. However, there is now a feedback. The increase in Y also increases the demand for money. Therefore, the rate of interest only falls to i 2, the level of investment only increases to I 2, the AE curve only increases to AE 2, and equilibrium income only increases to Y 2. 15.8 THE EFFECT OF MONETARY POLICY WITH PRICE FLEXIBILITY Suppose, as before, that the Bank of Canada increases the money supply through an open market purchase of Government Bonds.
13 Diagram 16.7: The Effect of Expansionary Monetary Policy i M S 0 M S 1 i i 0 i 0 i 1 i 1 i 2 M D 1 (Y 1 ) i 2 M D 2 (Y 2 ) M D 0 (Y 0 ) I AE M P I AE 1 (P 0 ) SRAS AE 2 (P 2 ) AE 0 (P 0 ) P 2 P 0 AD 1 45 AD 0 Y 0 Y 2 Y 1 Y Y 0 Y 2 Y 1 Y How is this increase in money supply going to affect the equilibrium level of income? We already know that the increase in the supply of money is going to have an expansionary effect in the economy through its effect on investment. Thus both the AE curve and the AD curve will shift to the right. With no change in the price level, the rate of interest would settle at i 1, the AE curve would shift to AE 1, the AD curve would shift to AD 1, and income would increase to Y 1.
14 However, if price is allowed to change, P would increase to P 2 and income would increase only to Y 2. Indeed, the increase in P would allow the AE curve to shift only to AE 2. Note that at this equilibrium income, the demand for money would be lower than at Y 1 and thus the interest rate would be i 2. Thus the increase in price causes a reduction in consumption and net exports, but a further increase in investment to I 2.