Chapter 4: The Supply of Money PDF

Chapter 4 The supply of money 4.1 Introduction In Chapter 2 we discussed what constitutes money and in Chapter 3 we analysed the factors that determine how much money individuals, and economies as a whole, demand. In this chapter we will discuss how money, credit money in particular, is created an...

Chapter 4 The supply of money 4.1 Introduction In Chapter 2 we discussed what constitutes money and in Chapter 3 we analysed the factors that determine how much money individuals, and economies as a whole, demand. In this chapter we will discuss how money, credit money in particular, is created and what determines the supply of money. As we shall see in later chapters, the supply of money is hugely important since a change in the money supply can lead to changes in the price level and inflation but also to changes in real variables such as output and unemployment. By affecting the money supply, the monetary authorities can ‘control’ or at least help limit the fluctuations of these variables. Later in this chapter we will see how the authorities can implement monetary policy to help control the money supply. 4.2 Aims The aim of the chapter is to study the money supply as one of the building blocks of the money market equilibrium, the role of financial intermediaries in the credit supply process and how monetary policy makers can control money supply. 4.3 Learning outcomes By the end of this chapter, and having completed the Essential reading and activities, you should be able to: describe and discuss the different roles of financial intermediaries describe why maturity transformation is so important in financial markets define on which side of a bank’s balance sheet deposits and loans appear and explain why the balance sheet must indeed balance explain how the monetary authorities can influence the total money supply by changing the monetary base or by introducing mandatory reserve ratios or other regulation. 43 4. The supply of money 4.4 Reading advice Any monetary economics textbook will have a section on the supply of money but the book followed most closely in this chapter is Goodhart (1989). Chapter 5 covers the role of and need for financial intermediaries and Chapter 6 covers the ideas of the money multiplier and high-powered money. Unfortunately there is no good reference for the model of the banking sector at the end of the chapter so you are advised to work carefully through this section and through the Activities.1 4.5 Essential reading Artis, M.J. and M.K. Lewis Money in Britain: Monetary policy, innovation and Europe. (New York; London: Philip Allan, 1991). Goodhart, C.A.E. Money, Information and Uncertainty. (London: Macmillan, 1989) Chapters 5, 6 and 10. 4.6 Further reading Books Brunner, K. ‘High-powered money and the monetary base’, in Newman, P., M. Milgate and J. Eatwell (eds) The New Palgrave Dictionary of Money and Finance. (London: Macmillan, 1994). Goodhart, C.A.E. ‘The monetary base’, in Newman, P., M. Milgate and J. Eatwell (eds) The New Palgrave Dictionary of Money and Finance. (London: Macmillan, 1994). Laidler, D.E.W. Taking money seriously and other essays. (New York; London: Philip Allan, 1990) Chapters 4 and 5. McCallum, B. Monetary Economics. (New York; Macmillan; London: Collier Macmillan, 1989). Papademos, L. and F. Modigliani ‘The supply of money and the control of nominal income’, in Friedman, B. and F. Hahn (eds) Handbook of monetary economics. (Amsterdam: North-Holland, 1990). Journal articles Goodhart, C.A.E. ‘What should Central Banks do? What should be their macroeconomic objectives and operations?’, Economic Journal 104(427) 1994, pp.1424–36. 1 The survey article of Papademos and Modigliani is good but difficult. You should, however, be able to read and understand the basics of Section 3 of this article. 44 4.7. Financial intermediaries 4.7 Financial intermediaries Financial intermediaries, such as banks, are hugely important in activities such as the financing of investment projects and in the safekeeping of savings. At any point in time, there are agents who spend less than they earn, and so wish to save, and there are agents who spend more than they earn, and so need to borrow. The main service that a bank provides is the collection of funds from those who wish to save and the lending out of funds to those who wish to borrow. The reward for providing such services comes from the difference between the rate of interest paid on savings and that charged on loans. By charging a higher rate of interest rate on the funds they lend to firms and households than on the funds they accept from depositors, banks can make profits. This is also called credit spreads. If there are agents who want to save and others who want to borrow, why do those with funds to spare not just lend directly to those who want to borrow (i.e. why do we need a bank or financial institution at all)? There are a number of reasons to explain the existence of financial intermediaries, which include: 1. Economies of scale in transactions and information. In order to have a sufficiently diversified portfolio, agents with funds to save should hold a large number of different assets. If each agent only had limited funds available, this could only be done by ‘clubbing’ together. This is exactly the type of service unit trusts and pension funds provide. Also, if an agent wanted to borrow a large sum of money, to buy a house or factory for example, it is unlikely that they would find a single other agent willing to lend such a large sum. If a large number of agents deposited small quantities of savings at a bank, the bank could then lend a large amount to a single borrower. The financial intermediary may also be able to obtain better information about the creditworthiness of a prospective borrower than an individual agent can; and the intermediary may be more likely to retrieve assets from a borrower who defaulted on the loan after being made redundant. 2. Insurance. Agents are, in general, risk-averse. If there are two states of the world, one where an agent received a high income and another where (s)he received a low income, the average of the utilities from both high and low incomes will be less than the utility of the average income. As such, the agent would be willing to pay a fraction of their income in order to smooth their income receipts and hence their consumption. This is exactly the service insurance firms provide. In a similar fashion, banks provide insurance services by guaranteeing a rate of return to depositors even if loans made to borrowers turn bad. Without the bank, the default risk would be faced entirely by the individual/depositor. By paying the bank, depositors accept a lower deposit rate than that they have to pay on loans, depositors can protect themselves from the default risk and obtain a higher utility.2 3. Maturity transformation. Arguably the most important service provided by banks is that of issuing one form of debt that is illiquid (of long maturity), while taking on another which is of short maturity. Individual lenders generally want to lend (to the bank) while still having quick access to their money, in order to make transactions or for precautionary motives. The liabilities of the bank (the deposits 2 Unless, however, the bank fails as a result of too many borrowers defaulting, for example! 45 4. The supply of money of savers) are then liquid and the bank will promise to convert the depositors’ assets on demand. The banks assets, on the other hand, will tend to be illiquid since private borrowers tend to want to hold long maturity liabilities (the loans/assets of the bank). For example, if a firm wanted to borrow money to build a factory, they would want to borrow long term. This would allow the steady income earned from the investment to gradually pay off the loan. Activity 4.1 If you had $1,000 in cash and you deposited this at a bank, on what side of the bank’s balance sheet would this appear? On what side of your own balance sheet would it appear? What could and should the bank do with this cash? Since banks hold short maturity liabilities, which they promise to pay to the depositors on demand, and hold long maturity assets in the form of loans to borrowers, a paramount concern of banks is therefore to ensure that they can honour demands for withdrawals by customers. To do this they must always hold an adequate supply of liquid assets. The problem is that the most profitable assets of a bank are those that possess least liquidity. Indeed, if the banks held only the most liquid assets in their portfolios they would not even cover their operating costs! The highest profits are earned on long-term loans and investments but these are comparatively illiquid assets in a bank’s balance sheet. Banks are therefore obliged to balance liquidity on the one hand against profitability on the other. Activity 4.2 Why are liquidity and profitability sometimes referred to as conflicting objectives? 4.8 The money multiplier and base money Base money, also known as high-powered money is the monetary liabilities of the Central Bank. This consists of notes and coins, and the deposits and reserves of banks with the Central Bank. If the monetary authorities increased the monetary base by printing money and giving it to private individuals, those individuals will, more likely than not, deposit a fraction of it with their bank. The bank will not want to keep all of these deposits in the form of liquid assets, as this strategy will not earn the bank the most money. Remember that liquid assets earn the lowest interest. Instead it will keep a fraction of it in liquid form but lend out the rest in order to earn a higher return. The funds given out as loans will be spent and subsequently deposited at the bank of whoever sold the goods to the initial borrower. Again the bank will lend out a fraction of these new deposits and the process continues. In equilibrium the total increase in the money stock, the liabilities of the government (notes and coins) and the liabilities of banks (deposits) will be a multiple of the increase in the high-powered money. This multiple will depend on the fraction of the money individuals wish to deposit with their bank, the currency-deposit ratio, and the fraction of the deposits the bank wishes to keep in cash reserves and not lend out, the reserve-deposit ratio. If these ratios are stable through time then by controlling the base money, the monetary authorities can control the total money supply in the economy.3 Let the total money supply in the 3 Controlling the money supply is not as simple as it sounds, however. See Goodhart (1989). 46 4.9. A simple model of the banking sector economy, M , be made up of deposits, D, and the liabilities of the government, notes and coins, C. Therefore: M = D + C. (4.1) Also, let high-powered money, H, be made up of the notes and coins in the general public, C, and the remainder of the government’s liabilities held by banks in the form of reserves, R: H = C + R. (4.2) Dividing (4.1) and (4.2) by D and then dividing one by the other, we can write:   1 + (C/D) M =H . (C/D) + (R/D) (4.3) The bracketed term is the money multiplier: the factor which, when multiplied by the base money, gives the total money supply in the economy. As can be seen, it is a function of the currency-deposit ratio (C/D), and the reserve-deposit ratio (R/D). The monetary authorities should be able to directly control the stock of high-powered money, H, but the determination of the total stock of money, M , ultimately depends on the banking sector and the preferences of private individuals. It is the workings of the banking sector to which we now turn. 4.9 A simple model of the banking sector Assume a banking industry whose market is described by: D = d0 − d1 (i − iD ) L = d0 + l1 (i − iL ) (4.4) (4.5) where L is the (demand for) bank loans, D is the (supply of) bank deposits, iL the rate charged on loans, iD the interest paid on deposits and i the ‘market’ interest rate. Note that the supply of deposits is a positive function of the interest rate paid on deposits and a negative function of the market interest rate – the interest rate one could earn elsewhere. If iD was large relative to i, that would encourage individuals to deposit more funds with the bank. Equivalently, the demand for loans is a negative function of the interest rate charged on loans. If the interest rate you had to pay on a loan was high relative to the market rate, you would borrow, not from the bank, but from elsewhere. Assume the banks have no operating costs and have no other assets or liabilities. Finally, d0 captures an arbitrary banking relationship constant. It represents the minimum an individual would deposit to the bank and the minimum a firm receives from the bank to hold a bank relationship. Competitive equilibrium The profits made by the bank will equal the quantity of loans, L, multiplied by the interest earned on those loans, iL (which is the bank’s revenues)4 minus the costs faced 4 Assume there are no borrowers defaulting on their debts. 47 4. The supply of money by the bank. Costs will equal the interest paid to depositors in order to encourage them to hand over their funds to the bank. Costs then equal the quantity of deposits, D, times the interest rate paid on deposits, iD . Denoting bank profits by Π and noting that in a competitive equilibrium, profits equal zero: Π = L · iL − D · iD Π = 0 (competitive equilibrium). (4.6) (4.7) When making the additional assumption that the bank holds no reserves, in order for the bank’s balance sheet to balance, loans (assets) must equal deposits (liabilities), L = D. Substituting into (4.6) and using (4.7) implies that in equilibrium: iD = iL . (4.8) Substituting into (4.5) and equating L with D gives: d0 − d1 (i − iD ) = d0 + l1 (i − iL ). (4.9) Solving for the interest rate on deposits, which equals the interest rate charged on loans from (4.8), gives: iD = iL = i. (4.10) This implies total deposits, D, which equals total loans, L, equals d0 from either (4.4) or (4.5). This is shown in Figure 4.1 below. In equilibrium, the interest rate paid on deposits equals the interest rate charged on loans, which equals the market interest rate, i. The level of deposits, which in this model is equal to the level of the money stock, equals the amount of loans. Figure 4.1: 48 4.9. A simple model of the banking sector Government regulation of the deposit rate One way that the government could reduce or control the money supply is by setting a limit on the interest rate paid on deposits. If the maximum interest rate banks can pay on deposits is less than i in the above example, then the amount of funds savers are willing to deposit with the bank will fall, resulting in a lower money supply. Note that this will also be associated with a lower quantity of loans that, despite the lower money supply, may be harmful to the economy if it means some investment opportunities are not undertaken. Consider the case where the government sets the interest rate on deposits equal to zero. From (4.4), the quantity of deposits is fixed at D = d0 − d1 i. Diagrammatically, this is shown in Figure 4.2. Figure 4.2: The level of deposits, and hence of the money supply, has fallen from d0 to d0 − d1 i because of the government regulation. Since deposits must equal loans in order for the bank’s balance sheet to balance, the lower level of deposits means a lower level of loans, which is associated with a higher interest rate charged, iL > i. Also, since there is a difference between the interest rate charged on loans and that paid on deposits (which has been set at zero), the government regulation has allowed the banks to make positive profits. Activity 4.3 1. By equating deposits with loans, and noting that iD = 0, find an expression for iL in terms of the market interest rate, i. 2. Using (4.6) find an expression for the profits made by the banks in terms of the market interest rate. 49 4. The supply of money Reserves As discussed above, banks will try to keep a fraction of their assets in liquid form in order to meet the day-to-day needs of depositors who withdraw their funds. Assume that the government introduces a mandatory reserve ratio, r∗ (i.e. total reserves of the bank, R, equals r∗ × D). The bank’s assets now comprise loans, as before, but now include these reserves. Its liabilities are just the deposits of its customers. Assets = Liabilities ⇒ r∗ · D + L = D ⇒ L = (1 − r∗ )D. (4.11) Substituting (4.11) into the zero profit condition, (4.6) and (4.7), and rearranging will give the interest rate charged on loans to be: iL = iD > iD . 1 − r∗ (4.12) The interest rate charged on loans is now higher than the interest rate paid on deposits. This is in order to compensate the banks for holding reserves, on which it earns no interest. Total loans are now less than total deposits so each dollar lent out must earn a higher return than that paid on each dollar deposited with the bank. iL then needs to be greater than iD . Activity 4.4 Substitute out L and D from (4.4) and (4.5) into (4.11). Then substituting out iL from (4.12), show that the rate of interest paid on deposits is equal to:   l1 r∗ r∗ (1 − r∗ )d0 . (4.13) iD = 1 − i + l1 + d1 (1 − r∗ )2 l1 + d1 (1 − r∗ )2 Substitute this out into the supply of deposits equation, (4.4), and show that total deposits are given by: D= d1 l1 r∗ l1 + d1 (1 − r∗ ) d − i. 0 l1 + d1 (1 − r∗ )2 l1 + d1 (1 − r∗ )2 (4.14) Although (4.13) and (4.14) appear complicated, they simply relate the deposit rate and total deposits (money supply) to the market interest rate and to the reserve ratio. By changing the mandatory reserve ratio, the government can change the total money supply through the activities of the banking sector. However, the way in which D varies with r∗ is uncertain and depends on the parameters of the model. With no reserve requirements we equate L to D in order for the bank’s balance sheet to balance. In this situation we equate L to (1 − r∗ )D from (4.11). Therefore the new intersection results in a lower value of L but a higher interest rate charged, iL . Total revenues for the bank, L × iL , could then increase or decrease depending on the elasticity of the demand for loans function. 50 4.9. A simple model of the banking sector If the demand for loans is elastic then, if L falls, revenue will fall. Banks will be forced to cut the interest paid on deposits, so iD falls, resulting in fewer deposits and hence causing the money supply to fall. If the demand for loans is inelastic, a fall in L, caused by the reserve ratio, will increase revenues. The banks will increase iD and so total deposits will increase. Monetary base control As seen above, the government can control the money supply by directly controlling the rate of interest paid on deposits and it can also affect it through imposing a mandatory reserve ratio. However, by forcing the banks to hold a certain level of reserves, not just a reserve ratio, it can directly control the monetary base. Note that high-powered money equals reserves plus cash held by the general public (see (4.2)) and the government directly controls the amount of cash in the economy since it is the monopoly supplier. The government fixes the amount of bank reserves, R, at R∗ . Together with the reserve ratio, r∗ , this explicitly determines the amount of deposits in the economy since R∗ = r∗ D. Inverting (4.14) will give an expression for the market interest rate in terms of r∗ and R∗ . l1 + d1 (1 − r∗ )2 l1 + d1 (1 − r∗ ) d − D (4.15) i= 0 d1 l1 r∗ d1 l1 r∗ where: D= R∗ . r∗ (4.16) This is shown in Figure 4.3. Figure 4.3: 51 4. The supply of money The level of total deposits, and hence the supply of money, is determined by the mandatory requirement that the banks hold a fixed level of reserves, R∗ , and have a fixed reserve ratio, r∗ . Changing R∗ will directly affect the money supply, shifting the vertical D = R∗ /r∗ schedule left or right. However, doing so will necessitate a change in the market interest rate in order to achieve equilibrium in the banking sector. Activity 4.5 Assume an economy in which the demand for bank loans is given by: L = 1000 + 25(i − iL ) and in which the portfolio preferences of the public generate a supply of bank deposits given by: D = 1000 − 50(i − iD ) where iL is the interest rate charged on bank loans, iD the interest rate paid on bank deposits and i the ‘market’ interest rate (and interest rates are measured in percentage points so that a rate of two per cent is given as 2, not 0.02). The banks hold no reserves and have no other assets and liabilities and incur operating costs of £60 a year for every £1,000 of deposits. 1. Assuming the banking system is competitive, solve for the loan rate and the deposit rate as functions of the market interest rate and determine the stock of money in equilibrium. 2. Imagine that the banks were now to collude and reach an agreement to set loan and deposit rates which maximise the profits of the industry. What loan and deposit rates will they set, what will be the profits of the industry and what will be the effects of this cartel on the stock of money? 3. Assume the banking industry is described as in the first part of the question (i.e. competitive and unregulated). The government can influence the ‘market’ interest rate through its dealings in the gilt-edged money markets. What is the effect of a change in the market interest rate on deposit and loan rates and on the stock of money? Explain. Is monetary policy impotent in this economy? (For Feedback, see the end of this chapter.) 4.10 A reminder of your learning outcomes By the end of this chapter, and having completed the Essential reading and activities, you should be able to: describe and discuss the different roles of financial intermediaries describe why maturity transformation is so important in financial markets define on which side of a bank’s balance sheet deposits and loans appear and explain why the balance sheet must indeed balance 52