2. Money and Inflation

1. Write down the demand function for money and explain what determines the quantity of money demanded. How does this function compare with the quantity equation?

The demand function for money can be written

Md/P = L(r + Ep, Y)

where Md is the nominal quantity of money demanded, P is the price level, r is the real interest rate, Ep is the expected rate of inflation and Y is real income. The quantity equation is

M V = P Y

where V is the income velocity of circulation of money. Note that V is defined as the ratio of nominal income to the money supply,

V = (P Y)/M,

in which case the quantity equation holds by definition. But we can view V as desired velocity in which case the quantity equation becomes an equilibrium condition determining the equilibrium price level on the basis of the nominal quantity of money, real income, and desired velocity. Alternatively, the quantity equation can be viewed as an equilibrium condition giving the equilibrium quantity of money demanded at the desired level of V and the existing levels of prices and income. In the case where desired velocity is constant the quantity equation can be manipulated to yield

M = (1/V) P Y = k P Y.

where k is the public's desired ratio of real (nominal) money holdings to real (nominal) income. If we interpret M as the quantity of money demanded, this equation expresses the quantity of money demanded as a constant fraction of nominal income. If we divide both sides by P we obtain

M/P = k Y.

Normally, of course, the desired ratio of money to income will depend on the nominal interest rate---that is, k will be a function of r and Ep---

k = f(r + Ep)

in which case the previous equation becomes

M/P = k Y = f(r + Ep) Y = L(r + Ep, Y)

where f(r + Ep) Y is a more specific representation of the general functional form L(r + Ep, Y).

Suppose that there is continuous full employment in the economy and that velocity is rising by 1% per year. If output is growing by 3% per year, what rate of money growth will produce zero inflation?

Taking the total differential of the quantity equation, we have

d(MV) = d(PY)

M dV + V dM = P dY + Y dP

Dividing both sides by MV (=PY) we obtain

(M dV)/(MV) + (V dM)/(MV) = (P dY)/(PY) + (Y dP)/(PY)

This expression can be simplified to obtain

dV/V + dM/M = dY/Y + dP/P

which can be rearranged to yield

dP/P - dV/V + dY/Y = dM/M

The terms dM/M, dP/P, dV/V and dY/Y can all be multiplied by 100 to express them as percentage changes in the respective variables.

It is stated in the question that V is rising by 1% per year and Y is increasing by 3% per year. To hold P constant, the percentage growth of M per year must be

0 - 1 + 3 = 2

Explain why inflation is a tax on money?

The government prints money and spends it in the economy for the purchase of the goods (labour services, supplies, etc.) it needs to produce the services it supplies to the public. When the amount of money it prints is in excess of the quantity that will maintain the price level constant, there will be inflation. In fact, the inflation will be in proportion to the excess increase in the money supply. The public has given up goods (labour, supplies, etc.) to the government in return for newly issued currency. But the price level rises proportionally with this additional currency in circulation so that the real money stock remains unchanged and the real value of the addition to currency holdings is zero. The real quantity of money is unaffected by the nominal monetary expansion because the price level rises in proportion to the increase in the money supply.

The public has therefore given goods to the government for nothing of value in return---i.e., it has been taxed. This tax will fall heaviest on those people who tend to hold the most real money balances because when the price level rises it is they that will have to give the most goods to the government to maintain their real money holdings constant.

The great economist Milton Friedman has said that "Inflation is always and everywhere a monetary phenomenon." Explain what this statement means.

The price level P is the price of goods in terms of money. Its inverse, 1/P is the price of money in terms of goods or the value of money. Like any other commodity the value of money (i.e., its price in terms of other things) is determined by the supply and demand for it. An expansion of the money supply, holding the demand for money constant, will cause the value of money to fall and the price level to rise. An expansion of the demand for money, holding the quantity constant will cause the value of money to rise and the price level to fall. All price level changes---and, hence, all inflations and deflations---can be analyzed within the framework of the demand and supply of money. For this reason, inflation is obviously a monetary phenomenon.

It is probably reasonable to argue that Friedman, under the circumstances in which he made the statement, meant somewhat more than this. He also tended to argue that inflations of any significant magnitude and duration are always money supply phenomena in the sense that they are caused by excess monetary expansion---i.e., increases in the money supply relative to the normal growth of the demand for money that would result from growth of real income and the trend rate of change of velocity. While it is true that small inflations and deflations could be attributed to shifting trends in the demand for money, in every case where inflation has been a problem (that is, where there have been periods of substantial and persistent inflation) it can be attributed to excess expansion of the money supply. Of course, even if a movement in prices is the consequence of a shift in the demand for money, there is an adjustment of the supply of money that would have prevented it, but it is generally not possible for central banks to anticipate every shift of the demand for money so that they can offset it with appropriate adjustments of the money supply.

It has frequently been argued during periods of inflation that the observed rise in the price level has been the result of greedy price setting by firms or greedy wage setting by unions. It turns out, however, that profit maximizing firms, even if they are monopolies and "control" prices, will have no incentive to raise their profit maximizing prices without a prior shock either to their costs or to the demand for their product. And unions that are following the preferences of their members will choose to exert an optimum degree of real wage pressure and absorb and optimum degree of loss of jobs as employers move up their negatively sloped demand curves for labour, and will have no incentive to increase their wage demands without bounds. Both firms and workers, of course, will raise their prices and wages in response to an increase in the nominal demand for output resulting from an expansion of the nominal money supply (or a reduction in the demand for money). Because firms and workers do not have an incentive to raise prices and wages beyond optimum levels, persistent inflation cannot be caused by the actions of unions and firms in the absence of excess expansion of the money supply by the central bank.