ch_5_classical_theory.pdf

Chapter 5 Classical theory 5.1 Introduction The classical model is hugely important for the analysis of monetary theory. If one commodity has been introduced into the economy to serve the functions of money and has no other use or value, what determines the value of such a commodity, or the prices...

Chapter 5 Classical theory 5.1 Introduction The classical model is hugely important for the analysis of monetary theory. If one commodity has been introduced into the economy to serve the functions of money and has no other use or value, what determines the value of such a commodity, or the prices of other goods and services in relation to that money commodity? These are essentially the questions we will be answering in this chapter. We will analyse the general equilibrium framework of Walras and use it to explain what is meant by the ‘Classical dichotomy’, namely the separation of the real side of the economy from the monetary side. Finally, we will give an explicit example of Walras’ law by introducing money in a general equilibrium framework; a set-up we will use extensively in later chapters. 5.2 Aims In this chapter we aim to study a general equilibrium environment with money. 5.3 Learning outcomes By the end of this chapter, and having completed the Essential reading and activities, you should be able to: define and explain the term ‘neutrality of money’ describe the essential features and predictions of the quantity theory of money describe the main features of the classical system and the classical dichotomy discuss the implications of Walras’ law in the determination of general equilibrium state the nature and importance of Patinkin’s real balance effect for the internal consistency of the classical dichotomy. 5.4 Reading advice You are recommended to read the appropriate chapters or sections in one or more of the basic monetary economics textbooks before tackling the material presented here. All will discuss, to greater or lesser extents, classical theory and issues surrounding 57 5. Classical theory monetary neutrality. The book followed most closely here is Lewis and Mizen, Chapters 3 and 4, but see also Harris, Chapters 4 and 5. You are also strongly advised to read the entries on ‘Neutrality of money’ and ‘Quantity theory of money’ in The New Palgrave Dictionary of Money and Finance. The latter chapter is quite long but covers material relevant not only for this, but for other chapters in the guide. 5.5 Essential reading Friedman, M. ‘The quantity theory of money’, in Newman, P., M. Milgate and J. Eatwell (eds) The New Palgrave Dictionary of Money and Finance. (London: Macmillan, 1994). Harris, L. Monetary Theory. (New York; London: McGraw-Hill, 1985) Chapters 4 and 5. Lewis, M.K. and P.D. Mizen Monetary Economics. (Oxford; New York: Oxford University Press, 2000) Chapters 3 and 4. Patinkin, D., ‘Neutrality of money’, in Newman, P., M. Milgate and J. Eatwell (eds) The New Palgrave Dictionary of Money and Finance. (London: Macmillan, 1994). 5.6 Further reading Cagan, P. ‘Monetarism’, in Newman, P., M. Milgate and J. Eatwell (eds) The New Palgrave Dictionary of Money and Finance. (London: Macmillan, 1994). Laidler, D. ‘The quantity theory is always and everywhere controversial – why?’, Economic Record 67(199) 1991, p.289. Patinkin, D. Money, interest and prices: an integration of monetary and value theory. (New York: Harper and Row, 1965). 5.7 The quantity theory of money The value of money can be established through the well-known ‘equation of exchange’, which is at the centre of the classical quantity theory of money. The equation of exchange, MV ≡ P T (5.1) is an identity since the two sides of the equation are simply different ways of measuring the same thing, namely the total value of all monetary transactions in the economy. M is the stock of money, the number of units of the money commodity, V is the velocity of circulation, the number of times each unit of money is used in transactions per period, T is the number of transactions in a period and P is the average monetary value of each transaction.1 Essentially, the value of the money paid out, M V , must be equal to the value of goods and services it buys, P T . 1 Note that the ‘stock’ of any variable refers to the total accumulated value of a variable over years, whereas ‘flow’ refers to a change in the variable within a given time period. 58 5.7. The quantity theory of money The quantity theory determines the price level on the basis of the assumptions made about the variables in the equation. V is taken as exogenous, being determined by various institutional features of the economy, such as the frequency with which workers get paid. T , the number of transactions, is determined by real variables such as preferences, endowments and technology, and M is, in a fiat money economy, determined by the government.2 On these assumptions the price level, P , is proportional to the stock of money, M , in the sense that changes in the stock of money lead to equi-proportional changes in the price level. Taking logs of (5.1) gives: ln Mt + ln Vt = ln Pt + ln Tt (5.2) where we have introduced a time subscript to all variables. Differentiating this with respect to time gives: 1 dMt 1 dVt 1 dPt 1 dTt · + · ≡ · + · . (5.3) Mt dt Vt dt Pt dt Tt dt If velocity and transactions are considered exogenous, meaning these are not changing through time, then their derivatives with respect to time are simply zero. For the remaining terms, noting that (1/Xt ) · (dXt /dt) is simply the growth rate of Xt , then (5.3) implies that the growth rate of the money supply is equal to the growth rate of the price level (i.e. inflation). In this sense, inflation cannot occur without a commensurate increase in the supply of money. The Cambridge view of the quantity theory Whereas the equation of exchange is a flow equation, relating the number of transactions made per period to the flow of money per period handed over to facilitate these transactions, the Cambridge school, under Marshall, transformed it to a stock equation. As such, the Cambridge school transformed the quantity theory to a demand function of the form:3 M = kP Y. (5.4) In its simplest form, velocity was assumed constant, in which case k = 1/V and the amount of money one held was equal to a proportion of the number of transactions, or alternatively, income, Y . The velocity of money The velocity of money measures how many times a unit of money is used to purchase goods and services per period. It is also a measure of the stability of the money demand. Consider now a situation where the velocity of money doubles (i.e. every individual spends their money twice as fast as before). What is the implication of this on the equation of exchange? Assume initially that Joanna gets paid £800 a month and spends a quarter of this at the beginning of each week. Her money balances are then £600 during the first week, £400 during the second week, £200 during the third and £0 during the final week of the month when she is waiting to receive her next salary. This is depicted in Figure 5.1a below. 2 ‘Transactions’, T , are often proxied by income, Y , to give a quantity theory of M V = P Y . Notice the similarity between this equation and the macroeconomic money demand equations in Chapter 2 of the subject guide. 3 59 5. Classical theory Figure 5.1: Joanna’s average money holdings over the month are then: £600 · 1 1 1 1 + £400 · + £200 · + £0 · = £300. 4 4 4 4 (5.5) Now consider the case where Joanna gets paid twice per month, receiving £400 at the beginning of week 1 and £400 at the beginning of week 3. Again she spends a quarter of her income in each quarter of the payment period, so that her money balances are £300 in the first half of week 1, £200 in the second half, £100 in the first half of the second week and zero in the last half of that week. Similarly, for the second half of the month. Notice that her transactions remain unchanged at £800 per month but the velocity of money has doubled; any money balance is spent twice as quickly. Her money holdings are now shown in Figure 5.1b. Joanna’s average money holdings over the month are therefore given by:   1 1 1 1 × 2 = £150. (5.6) £300 · + £200 · + £100 · + £0 · 8 8 8 8 As a result of the velocity of money doubling, caused by a change in the way people are paid, the average money holdings over the period have halved from £300 to £150. Other determinants of the velocity of money include individual habits and spending patterns, social conditions, the efficiency of the payments system and possibly also the interest rate. As discussed in Chapter 2, if the interest rate remains high for some time, this may cause individuals to try to find more efficient ways of holding their wealth in order to avoid the high opportunity cost of holding money. One consequence of high interest rates may then be that any money balances are spent more quickly, implying an increase in velocity. The classical dichotomy and monetary neutrality The classical economists assumed that, although money was essential for the efficient functioning of the economy, the quantity of money units had no impact on real 60 5.7. The quantity theory of money variables. According to the ‘Classical Dichotomy’ only real variables (preferences, endowments and technology) determined real outcomes (quantities and relative prices).4 The quantity of money, on the other hand, determined the absolute price level or the value of goods in terms of monetary units, from the equation of exchange. According to the classical economists, money was neutral, in the sense that the quantity of it has no effect on any real variable in the economy. In order to explain these ideas more fully, we first consider the notions of Say’s law and Walras’ law. Say’s law and Walras’ law Say’s law essentially states that supply creates its own demand. In a barter economy in which there are n − 1 goods, each supplier has an endowment of some good. They each exchange these goods for those they desire and it is the level of their endowment, that determines how much they can buy. Supply funds demand. It must therefore be true that the sum of expenditures over all goods i = 1, . . . , n − 1 must equal the sum of the supplies of all goods, denoted Si . n−1 X pi Di ≡ i=1 n−1 X pi S i (5.7) i=1 where pi is the relative price of one good in terms of another. Remember we are considering a barter economy here, which therefore has no monetary prices. Alternatively, defining the excess demand for good i, EDi , as Di − Si , then: n−1 X pi EDi ≡ 0. (5.8) i=1 In Say’s view, market laws imply that there cannot be a ‘general glut’. If there exists an excess demand for one good then there must be an excess supply of another. However, there cannot be a general excess demand or general excess supply at the aggregate level (in a closed economy). Each household has endowments of one or more goods, and a utility function defined over all goods, from which we can derive the demand of each household for each good as a function of relative prices. Adding up the demand for each good across households, and given the total endowment of that good, we can write down a market clearing equation for each good as a function of relative prices. Since all households must balance their budgets, the sum of all market clearing equations must add up to zero. Therefore in a market for n − 1 goods, if there is equilibrium in n − 2 goods, there must be equilibrium in the final market. This is Walras’ law. The n − 1 market clearing equations are not independent; if all markets except one clear, the last market must clear also. Only n − 2 equations are independent, but this is sufficient to solve for n − 2 relative prices, for example the prices of all goods in terms of good 1. To establish the equilibrium of an economy of n − 1 goods we may solve for n − 2 relative prices and this will in turn determine the demand from each household for each good. 4 Relative prices being the exchange ratios of one good for another, for example one kilogram of tomatoes equals two loaves of bread. 61 5. Classical theory Money in general equilibrium Now consider a monetary economy (i.e. we introduce fiat money as the n-th good). The price of this good is pn , usually normalised to unity for simplicity. From Walras’ law: n X pi Di ≡ i=1 n X pi S i (5.9) i=1 and separating out good n, money: n−1 X pi D i + pn D n ≡ i=1 n−1 X pi Si + pn Sn . (5.10) i=1 Dn and Sn are the demand and supply of nominal money balances, respectively, and from Walras’ law we can see that if there is equilibrium in the n − 1 goods markets then there must be equilibrium in the money market. However, Say’s law may not hold. There can exist a general excess supply in the n − 1 goods markets; (5.7) may not hold, but only if this is offset by excess demand in the money market. The demand for good i will depend on all relative prices and income, implying excess demand for good i, EDi , of:5   Pn−1 P1 P 2 , ,..., , Y − Si∗ (5.11) EDi = fi Pn P n Pn where Y is the total output. However, the absolute price level, the price of money, pn , will have no effect on excess demand. If the price of money, pn , doubles, caused by a doubling of the money supply from the equation of exchange, since pn is an average of all other prices, then p1 , . . . , pn−1 must all double also. The relative prices, p1 /pn , . . . , pn−1 /pn , will not change, resulting in no change in (excess) demands for any goods. In this way, a changing of the money supply will have no repercussions in the real economy. Hence money is neutral. Patinkin and the real balance effect There were found to be a number of criticisms of the dichotomy the classical economists had proposed.6 One problem was that the model was internally inconsistent. On the one hand, the excess demand for each commodity, i = 1, . . . , n − 1, was only dependent on relative prices, not the absolute price level, pn , and from Walras’ law, the excess demand for money is then determined. The excess demand for money is then only a function of relative prices. However, from the quantity theory, which is needed to solve the entire system of equations, the demand for money explicitly depended on the absolute price level. On one side, money market equilibrium depends only on relative prices while on the other side, it depends only on the absolute price level. An attempt to resolve this problem was made by Patinkin who included the value of real money balances, Sn /pn , as a determinant of the demand for each good; in other words the excess demand for each good i is given by:   Pn−1 Sn P1 P2 , ,..., , Y, − Si∗ . (5.12) EDi = fi Pn Pn Pn Pn 5 6 Assume for simplicity that the supply is fixed at Si∗ . See Lewis and Mizen (2000) Chapter 4 for an excellent description of these criticisms. 62 5.8. A simple general equilibrium framework Real money balances are the ratio between nominal money balances and the price level. A change in either of these nominal variables will change the value of the real variable and thereby change the demand for commodities. Thus, starting from a position of equilibrium in all markets including the money market, assume that there is an increase in the supply of money. This increases real money balances which in turn increases the demand for commodities, even though there has been no change in relative prices. But the increase in demand, having started from a position of equilibrium, must mean that there is now excess demand, a situation which denies Say’s law. The increased demand for commodities will then bring about an increase in the general level of prices that will reduce real balances. Eventually real balances will return to their equilibrium level, as will the demand for commodities. Real balances provide a bridge between the real and monetary sectors of the classical system and dispose of the classical dichotomy, that is factors influencing nominal variables are separated from factors influencing real variables, while retaining the neutrality of money, that is monetary changes do not change real variables. 5.8 A simple general equilibrium framework Whereas in the previous analysis, individuals’ utility was defined over goods, we now assume it depends also on the level of real money balances. The justification, according to Patinkin, is that even if households plan to balance their budgets so that planned purchases are equal in value to planned sales, it may be convenient to buy and sell goods at different times. The more money they hold, the greater the extent to which they can purchase goods ahead of making sales. Money holdings stand as a proxy for the more convenient sequence of transactions they make possible. Thus, money is in the utility function. Assume a household’s utility depends on the quantity of goods consumed, X, and on real money balances, M/P . Let the household have initial endowments X0 of goods and M0 of nominal money balances. The budget constraint faced by the household is then, in nominal terms: P X + M ≤ P X0 + M0 . (5.13) So that the nominal expenditure on goods, P X, plus the holdings of nominal money balances, M , must not be greater than the nominal value of the endowments of goods and money. Writing the budget constraint in real terms (dividing by the price level) gives: M0 M ≤ X0 + . (5.14) X+ P P The household’s utility function takes the specific form U = X 1/2 (M/P )1/2 . In order to determine the demands for goods and real money balances, we maximise the utility function subject to the budget constraint. To do this we form the Lagrangian:7 L=X 7 1/2  M P 1/2   M0 M + λ X0 + −X − . P P (5.15) We also impose an equality in the budget constraint as this implies no wastage of goods or money. 63 5. Classical theory Differentiating with respect to the two choice variables, X and M/P , gives the first order conditions of:  1/2 ∂L 1 −1/2 M = X −λ=0 (5.16) ∂X 2 P  −1/2 ∂L 1 1/2 M = X − λ = 0, (5.17) ∂(M/P ) 2 P from which we obtain M (5.18) P Substituting into the budget constraint will give solutions for the demands for goods and nominal money balances of: X= X= X0 + M0 /P 2 and M = P X0 + M0 . 2 (5.19) Assume now that the economy consists of n households each identical to the one described above. The market clearing condition in the goods market then becomes:   X0 + M0 /P n = nX0 . (5.20) 2 In other words, total demand equals total supply. Solving for the price level gives: P = M0 . X0 (5.21) Alternatively, we can write down the market clearing condition for the money market:   P X0 + M0 n = nM0 . (5.22) 2 If we solve for the price level here, we obtain: P = M0 . X0 (5.23) In this economy, money is neutral. Real output per household is fixed at X0 as it depends on endowments. From the solution of the price level, a change in the money supply will only lead to a proportional increase in prices. Real money balances and ‘production’ of goods do not change. An increase in money, M0 , will shift the demand function for good X outwards in Figure 5.2 but this simply causes the price level to increase. Activity 5.1 Why is the solution for the price level the same when we solve for the goods market equilibrium as for when we solve for the money market equilibrium? (Hint: Consider Walras’ law and the fact we are considering only two markets: those for goods and money!) 64 5.9. A reminder of your learning outcomes Figure 5.2: 5.9 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: define and explain the term ‘neutrality of money’ describe the essential features and predictions of the quantity theory of money describe the main features of the classical system and the classical dichotomy discuss the implications of Walras’ law in the determination of general equilibrium state the nature and importance of Patinkin’s real balance effect for the internal consistency of the classical dichotomy. 5.10 Sample examination questions Section A Specify whether the following statement is true, false or uncertain. Explain your answer in a short paragraph. 1. ‘A doubling of the velocity of circulation results in the price level doubling.’ 65