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Macroeconomic Theory II Bowen University College of Social and Management Sciences Economics Programme ECN 420: Macroeconomic Theory II MODULE V MONEY DEMAND FUNCTIONS Note that Money Supply is exogeneous while Money Demand is a derived function a) The Fischerian Equation: This is also regarded as the quantity theory of money. It states that the quantity of money M times the velocity of turnover of money in the repurchase of newly produced goods and services V must equal the value of money income PY where P is an index of prices and Y is the level of real income measured in base period prices. The equation therefore is: MV = PT Where M = M1 and M1 = Cash + DD Deposit McV = PT – The original equation Where Mc = Money in Circulation V = Velocity which is fixed T = Proxy for full employment output and it is fixed P = Price level Mc = 1/V PT – Too much money can be inflationary Assuming M*V* = PT, where M* = Mc + Md (Md = DD Deposit) Then V* = Vc + Vd 푃푇 :- M* = 푉∗ 푀∗푉∗ M* = 푉∗ 푉∗[푀푐+푀푑] M* = 푉푐+푉푑 1 b) Cambridge Equation As an alternative to Fisher’s quantity theory of money, Cambridge Economists such as Alfred Marshall, Pigou A.C, Robertson and Keynes formulated the cash balance approach. According to them the value of money is Determined by two important factors: (i) The condition of Demand for money, and (ii) the quantity of money available. The Cambridge equation therefore shows that given the supply of money at a point in time the value of money is Determined by the Demand for cash balances. When the Demand for money increase people will reduce their expenditures on goods and services in order to have and raise the value of money. The equation is discussed as follow: M = KPY Where M = exogenously determined supply of money. K = fraction of the real money income which people wish to hold in cash and Demand Deposit P = Price level Y = Aggregate real income 푀 Thus, the price level, P = 퐾푌 which is the value of money The reciprocal of price level is 1 퐾푌 = 푃 푀 1 퐾푅 Where = purchasing power of money according to Pigon, P = 푃 푀 1 Where P = 푃 K = proportion of total real resources or income R = Resources or income which people wish to hold in the form of titles to legal tender money. 2 In order to include bank notes and bank balances to the Demand for money. Pigon modifies the equation as: 퐾푅 P = (C + R(1 - C) 푀 Where C = proportion of total real income actually held by people and legal tender including token coins. (1 – C) = Proportion kept in bank notes and bank balances. In his own equation, Keynes stressed that the amount of purchasing power (or Demand of money) Depends partly on their taste and habits and partly on their wealth. Given the tastes, habits and wealth of the people, their Desire to hold money is given as N = PK Where K = number of Consumption in form of cash N = total currency in circulation (quantity of money) P = Price of consumption unit By taking into account bank Deposit, the equation becomes N = P(K + K1) If K, K1 and P are constant, P will change in exact proportion to the change in N. KEYNES TREATISE ON MONEY Keynes treatise on money is an autonomous theory of the price level in which money does not have a role to play. This is a radical departure from the classical quantity theory of money. This money which Determine the general price level in seemingly direct manner in Fisher’s rendering of the equation for the Determination of the general price level which emerges Keynes treatise on money. The Keynes equation for the Determination of the price level has its formations in two fundamental equations. 1. In the first equation the total normal income Y is split without overlap between the renumeration for factors of production on one hand (i.e. E) and windfall profit (Q) on the other hand such that: Y = E + Q – All expressed in nominal terms ---------- (1) 3 2. The second equation postulates a linear relationship between real output, real consumption and real capital goods such that: O = R + C --------------------- (2) Where O = output in real term R = Real Consumption C = Capital goods in real terms If the price level of consumption is P and the price level of Capital goods is P’, The general price level will be given by 푃푅+푃′퐶 푃푅 푃′퐶 3. π = = + ---------------------------------------------------------------- (3)\ 푅+퐶 푂 푂 Keynes then takes the important step of recasting eqn(3) in terms of investment such that i. I = P’C (I = Investment and I = S) ii. S = E – PR (Income less consumprion) PR = E – S Substituting (i & ii) into (3) we have: 퐸−푆 퐼 퐸−푆+퐼 퐸 1−푆 π = + – This can be rearranged as [π = ] = [π = + ]--- Keynes treatise on 푂 푂 푂 푂 푂 money Element of cost push inflation Equilibrum in the product Mkt INTERPRETATION: 1. Since E is the rewards of factors of production, that is income. As E rises and O remains the same, then π will rise. This is the phenomenon of cost push inflation. 1−푆 2. [ ] --- here investment is greater than savings. This is Demand – pull inflation to take 푂 place in the long run. The mechanism for equating E and S is the interest rate and so the causal mechanism for a rise in price under Keynes treatise is not money supply but the interest rate. 4 LIQUIDITY PREFERENCE HYPETHESIS Keynes in his criticism against the classical analysis, condemn the long run analysis and sand that “in the long run we are all Dead”. According to him the classical mechanism might fail to guarantee full employment for the following reasons: i. Wages and price may not be flexible but sticky downward ii. It is income rather than interest rate that Determine savings iii. The speculative Demand for money in the liquidity preference schedule is perfectly elastic with respect to changes in market interest rates. The Keynes liquidity preference hypothesis states that the Demand for money equation is as follows: Ld = KY Different from the monetarist Demand equation. Ld = KY, where K is the Sensitivity of money Demand to income Ld = LT + LP LT = f (Y) F1(Y) > O LP = f(Y) f1(Y) > O for Keynes LS = f(D) Speculative Demand f1(D) < O The existence of lii brings about the liquidity trap which limits the use of monetary policy hence fiscal policy. FRIEDMAN’S RESTAMENT OF THE QUANTITY THEORY OF MONEY Friedman reformulated the quantity theory the assets that “the quantity theory is in the first instance a theory of the Demand for money. It is not a theory of output or of money income, or of the price level”. The Demand for money on the part of ultimate wealth holders is formally identical with that of demand for a consumption service. For ultimate wealth holders, the demand for money is expressed by Friedman as: Md = f(P, Y, dp/dt, re, rb, W/w, πe, π) Where Md = Money Demand 5 P = Price level Ye = Expected income of individual Re = rate of exchange dp/dt = change in price with respect to time rb = Govt rate of bond W/w = ratio of non-human to human wealth N = stochastic terms. According to him, wealth can be held in five different forms: Money, bonds, equities, physical goods and human capital. USING PARTIAL ADJUSTMENT PRAMEWORK Given that: 푀푑 푑푝 푊 = f(푌푒, P, 휋푒, , re,rb, , N) 푃 푡 푡 푑푡 푤 푀푑 Forming expectation: = f(휋푒, 푌푒) 푃푡 푡 푡 The partial adjustment mechanism: 푀푑 푀푑 푀푑 푀푑 - = S( − ) 푃푡 푃푡−1 푃푡 푃푡−1 O < S < 1 D measures the speed of adjustment from actual to Desire D Md. Opening the bracket we have: 푀푑 푀푑 푀푑 푀푑 - = S – S 푃푡 푃푡−1 푃푡 푃푡−1 6 Collecting like terms: 푀푑 푀푑 푀푑 푀푑 = S + S – S 푃푡 푃푡 푃푡−1 푃푡−1 푀푑 푀푑 푀푑 = S + 1 – S ( ) 푃푡 푃푡 푃푡−1 푀푑 But = f(휋푒, 푌푒) 푃푡 푡 푡 By Substitution 푀푑 푀푑 = S (휋푒, 푌푒) + (1 - S) 푃푡 푡 푡 푃푡−1 Using partial Adjustment Mechanism, this is the Friedman’s Re-statement of quantity theory of 푀푑 푀푑 money. In the long run, at a stationary equilibrium = – If this is so, in the Long Run we 푃푡 푃푡−1 푀푑 푒 shall be able to get our Long Run Desired Md will be explicitly written as: = a1 + a2 푌 + a3 푌 푃푡 푡 푡 푀푑 푒 푀푑 + Et and our Short Run = a1 + a2 푌 + a3 휋 + Et + (1 - S) 푃푡 푡 푡 푃푡−1 INTERPRETATION: In this partial adjustment principle, we assume that when expected rate of inflation and income changes or their combination, our real money demand does not adjust instantaneously but gradually to changes in these independent variables. This implies that there is 푀푑 a time lag between when these variables will change and will adjust to the change. 푃푡 ASSIGNMENT 1. “Inflation is not a monetary phenomenon but a product of disequilibrium in the market” Discuss this assertion with reference to Keynes treatise on money. 2. Using partial adjustment principle, discuss the Friedman restatement of quantity theory of money. 7 .
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