Demand for Money and Value of Money

According to the Cambridge school, whereas the demand for nominal cash balance varies with the value of money, the demand for real cash balance does not; the demand functions for real money as for goods are homogeneous of degree zero in the price level of goods, and the demand for nominal money is homogeneous of degree one.

In doing this, these authors thought they were solving Helfferich’s vicious circle between utility and the value of money. In fact, as Oskar Lange (1942) and Don Patinkin (1948) demonstrated, they were confusing money prices with accounting prices. However, money prices, contrary to accounting prices, are relative prices, that is, the prices of goods expressed in money. Consider ( P _i, P _m ) the accounting prices respectively of good i and money. The money price of good i is equal to the accounting price of the good divided by the accounting price of money: P _i = ⅛-. As a consequence, whereas the budget constraint of households does not change with a proportional variation in the accounting prices of goods and money - leaving the money prices unchanged - it does with a nonproportional variation in these prices - which changes the money price level of goods. A rise in this level means a loss in the value of households’ money supply. Households have to diminish their demand for goods, assets and real balance - their demand for nominal money increases less than the money price level of goods. The IS and LM curves shift to the left. Symmetrically, a fall in the money price level of goods means a rise in the value of households’ money supply and results in a shift to the right of the IS and LM curves. Drawing the IS and LM curves supposes a given level of the money prices, that is, of the accounting prices of goods and money, and therefore of the value of money.

Although there is no dichotomy between the markets for goods, assets and money, when using an IS-LM model with flexible money prices, money wages and interest rate but a fixed level of real income, Patinkin demonstrated, in Money, Interest and Prices, An Integration of Monetary and Value Theory (1956 [1965]), that the quantity theory of money may be valid.

Suppose an initial equilibrium that is disrupted by a 100 per cent increase in the quantity of money. Households are enriched and may demand more goods, assets and real money: the markets for goods and assets are in excess demand and the market for money in excess supply. This (positive) effect of the increase in the quantity of money on demand in the markets for goods, assets and money is called the real balance effect. It causes a rise in the money prices of consumption goods and assets, that is, a fall in the interest rate. The fall in the interest rate causes a rise in the demand for investment goods, therefore in their money prices. The rise in the money prices of goods means a decrease in the value of the cash balances; it causes a (negative) real balance effect on the markets for goods, assets and money. Because the level of real income is fixed, the supply of goods is fixed, so that the rise in prices lasts until the value of cash balances and the interest rate return to their initial levels. This will be the case when the money price level has doubled. So the 100 per cent increase in the quantity of money results in a proportionate rise in the money price level, leaving the value of the real balance unchanged. The value of money has diminished by 50 per cent.

Now, this demonstration of the quantity theory, the description of the adjustments, begins with an initial equilibrium in which the accounting price of money is positive: P_m > 0. But the real balance effect does not describe the existence of this equilibrium with a positive value of cash balances, but its stability. If the IS-LM model used by Patinkin contains as much independent equations as unknowns:

equality between the number of unknowns and the number of independent equations is neither a necessary nor a sufficient condition for the existence of a solution. Nor does it insure that solutions, if they do exist, will be only finite in number. For our purposes, however, these highly complicated issues can be ignored.

Instead, we shall accept such equality as justifying the reasonableness of the assumption that one and the same set of money prices can simultaneously create equilibrium in each and every market. We shall also assume that only one of such set exists. (Patinkin 1956 [1965]: 37)

Frank Hahn (1965), Robert W. Clower (1967) and Ross M. Starr (1974) investigate the difficulties in proving the existence of a general equilibrium with a positive accounting price of money. Hahn recalls that Walras’s law does not imply that every good is scarce at equilibrium, that is, has a positive accounting price which clears its market. Some goods may be in excess supply and have a zero accounting price; these are free goods. Now, since the utility of money depends on its accounting price, a zero accounting price makes the money useless. In this case, there is no demand for money, so that a general equilibrium may be established although there is an excess supply on the market for money. It is a non-monetary equilibrium. This would be the case, for example, if the assets are liquid. This case is already mentioned by Patinkin: “the end result of making bonds completely liquid is to eliminate not the rate of interest but the use of money” (Patinkin 1956 [1965]: 109).

Clower underlines that the budget constraint of agents in Patinkin’s model does not describe a monetary economy because it allows barter: “any commodity, whether a good or money, can be offered directly in trade for every other commodity” (Clower 1967 [1969]: 204). Clower suggests that a distinction should be made between an income constraint, where the agent sells goods and demands money, and an expenditure constraint, where he supplies money and demands goods. Starr highlights the fact that the demand for money in period t is a demand for money to be spent in period t + 1, so that the utility of money at the end of period t depends on its utility in period t + 1 and therefore also depends on its accounting price in t + 1.

However, the horizon of both the agents and the model is finite, so that money has no utility at the end of the last period T; there is no period T + 1 for spending money. Then in T, money becomes a free good, its accounting price is zero. As a result of this zero price in T, the utility of money at the end of period T - 1 is also zero. Then in T - 1, money becomes a free good and its accounting price is zero. Then in T - 2, for the same reasons, money becomes a free good and its accounting price is zero. The same in T - 3, then in T - 4 and so on, in all periods. In the first period one then obtains a non-monetary equilibrium.

At the end of the twentieth century, the overlapping generations model initially developed by Maurice Allais (1947) and then Paul Samuelson (1958) to deal with the theory of capital appeared to be capable of solving the difficulties of the integration of monetary and value theory (Kareken and Wallace 1980). The model contains two generations of agents living two periods - the young and the old - so that the horizon of the model is infinite although the horizon of the agents is finite. The agents’ initial endowments of goods and their intertemporal preferences make them want to sell goods when they are young and buy goods when they are old. Because the old cannot issue bonds (they will be dead in the following period and therefore cannot reimburse), the young cannot sell goods for bonds. Bonds cannot dominate money. Money is the unique means of transaction between young and old: the young sell goods for money to the old, who sell money for goods.

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Source: Faccarello G., Kurz H.-D.. Handbook on the history of economic analysis. Volume III, Developments in major fields of economics. Edward Elgar,2016. — 659 p. 2016

Demand for Money and Value of Money

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