Liquidity Preference and the Theory of Interest and Money

Modigliani states in the introduction that his aim is to critically re-examine the most important existing theories of the rate of interest and money and to formulate a more general theory that accounts for the contribution of each approach and of the different basic hypotheses each makes (Part I, Section 1, p. 45). His method is to set up three alternative “macrostatic” systems of equations – covering the money market, the goods market via saving and investment, production, and the labor market – that share every equation except the one describing the supply of labor (or, in one variant, the demand for money), so that any difference in results between the systems can be traced to that single differing assumption rather than to some other unstated difference in setup (Section 2, pp. 46-48). The analysis is explicitly restricted to “static” conditions in the technical sense that price expectations are assumed to move in strict proportion with current prices (unit elasticity of expectation), and it is confined to determinants of equilibrium positions rather than to business-cycle dynamics, except in one later section that develops an explicit dynamic (difference-equation) version of the model (Section 1, p. 45; Section 10, pp. 62-64).

Modigliani splits the total demand for money into a transactions demand, tied to the institutional length of the income period and largely independent of the interest rate, and an asset demand for money to hold, D_a(r), which he argues must be a monotonically decreasing function of the interest rate with two important properties (Sections 4-6, pp. 48-54). First, there must be some minimum yield r’ at or above which every individual’s demand for money to hold falls to zero, because sufficiently attractive yields will induce anyone to give up cash entirely as an asset. Second, and “more peculiar,” there must be some minimum rate r’’ – reflecting the fact that securities are an inherently inferior, riskier way of holding wealth compared with money – below which nobody will hold assets except as money, so that the demand for money to hold becomes infinitely elastic (“absolute”) and the rate of interest cannot fall any lower (Section 5, pp. 52-53).

The LL curve, graphed from the equation M = L(r, Y), shows all combinations of the interest rate and income consistent with equilibrium in the market for the stock of money to hold, given a fixed money supply M; short-run equilibrium in each income period is reached where dealers are willing to hold, at the ruling system of interest rates, exactly the stock of money that is not needed for transactions (Sections 5, 7, pp. 54-57). Because the asset demand for money is finite above r’ and horizontal at r’’, the LL curve rises steeply from the horizontal axis, becomes flatter, and eventually turns perfectly horizontal at height r’’ – the graphical form of the “Keynesian case” discussed later. A rise in income raises transactions demand and thus (for fixed M) forces the equilibrium interest rate up, so equation (1) makes r an increasing function of Y (Section 7, pp. 55-56).

The IS curve, derived from the saving and investment schedules together with the equilibrium condition saving = investment, traces out combinations of income and the interest rate consistent with the goods market clearing, and it is this curve, not the LL curve, that embodies “long-run” equilibrium because ex ante saving and investment cannot be equated instantaneously (Sections 8, 10, pp. 58-59, 62). Money income cannot rise above the full-employment level except through inflation, and Modigliani shows that once prices and money wages rise in strict proportion with income (pure inflation), both saving and investment rise in that same proportion, leaving the equilibrium real interest rate unchanged; graphically, this means the IS curve becomes parallel to the income axis once it passes the point corresponding to full-employment income (Section 8, pp. 59-60).

In the “Keynesian” system, the supply of labor is assumed perfectly elastic at the historically ruling money wage w0 up to a “full employment” level of employment N0, after which the wage becomes fully flexible; in the classical systems, by contrast, the suppliers of labor – like suppliers of any other commodity – are assumed to behave “rationally” and to supply labor as a function of the real wage rate at every level of employment (Section 2, pp. 46-48). Combining these labor-supply assumptions with either the liquidity-preference money-demand equation or the crude quantity-theory equation (M = kY) yields Modigliani’s three systems: I, the Keynesian system (liquidity preference plus rigid wages); II, the “crude classical” system (quantity theory plus flexible wages); and III, the “generalized classical” system (liquidity preference plus flexible wages) (Section 2, p. 48).

Comparing the generalized classical system (liquidity preference with flexible wages, Sections 11, 14) against the Keynesian system, Modigliani concludes that under flexible wages the level of employment is in general “full employment,” determined by the intersection of the production and labor-supply equations, and does not depend on the quantity of money at all – so liquidity preference, by itself, is not sufficient to explain persistent underemployment (Sections 11-12, pp. 64-67). He states this conclusion as the first of three summary propositions at the end of Part I: liquidity preference is not necessary to explain underemployment equilibrium, and is sufficient by itself only in the limiting “Keynesian case”; in the general case it is neither necessary nor sufficient, and can explain underemployment only jointly with the additional assumption of rigid wages (Section 17, p. 75).

The “Keynesian case” is the special situation, possible even with fully flexible wages, in which the full-employment equilibrium interest rate that would clear the goods market falls below r’’ – the level at which demand for money to hold becomes infinitely elastic – so that no fall in wages and prices, however large, can lower the interest rate enough to restore full employment, and unemployment can persist as a genuine equilibrium of the real, “Keynesian” factors (the position and shape of the saving and investment functions) (Section 16(A), pp. 74-75). The “classical case,” by contrast, is the situation in which the equilibrium interest rate is high enough that the demand for money to hold is zero or negligible, so that changes in the interest rate leave the demand for money essentially unaffected and the earlier classical-system results (real variables independent of the quantity of money) apply without qualification (Section 16(B), p. 75).

Modigliani agrees that Lange is correct that Say’s Law makes the price level indeterminate under the quantity theory, but disputes Lange’s further claim that the traditional dichotomy between real and monetary economics is therefore self-contradictory, arguing instead that the neutrality of money and the determinacy of relative prices follow from the homogeneity of degree zero of the demand and supply functions for commodities, a property that depends on the homogeneity of expectations functions and rational behavior, not on Say’s Law (Section 13, pp. 68-70). Because that homogeneity survives even when Say’s Law is dropped, Modigliani concludes that the most serious version of Lange’s charge against the classical dichotomy can be dismissed, so long as the paper’s “static” expectations assumptions are maintained (Section 13, p. 70).

Modigliani rejects Lerner’s argument that, because saving and investment are identically equal ex post, they cannot determine the interest rate, dismissing this point as unimportant since it confuses an accounting identity with a causal claim about the independent decisions to save and to invest (Section 19, pp. 78-79). He further argues that Lerner’s alternative equation, M = f(r), is not a genuine demand-for-money schedule but an empirical relationship obtained only by first solving the entire system of equations – so that any apparent effect of the propensity to save or invest “on” this schedule is not evidence against their true role in setting the rate of interest, but a symptom that the schedule itself already embeds their effects (Section 19, pp. 80-82).

Modigliani agrees with Hicks that the cost of investing funds is what prevents the demand for money to hold from always falling to zero, but argues that Hicks’s further claim – that this cost of investing “explains” the rate of interest – does not follow, illustrating the logical gap with the analogy that the cost of transporting cars from Detroit to New York explains why car prices there are not zero, but does not explain the level of car prices themselves (Section 20, pp. 82-83). Using the case of a stationary state and of an expanding economy with securities as a hypothetical medium of exchange, he shows the rate of interest need not be zero even where the cost of investing is negligible, concluding that Hicks’s theory of interest must be rejected as faulty even though the cost of investing correctly explains why money is held at all (Section 20-21, pp. 84-86).

Modigliani’s concluding position is that both the “daily” (short-run) rate of interest and the long-run rate can be explained without contradiction, using the analogy of fish prices: the daily price of fish is explained by the day’s catch and demand, but the average price level around which daily prices fluctuate is explained by the more fundamental technical and psychological factors governing the fishing industry’s average returns (Section 21, pp. 86-87). Analogously, the short-run interest rate is set weekly by the demand and supply of money to hold (Section 7), but the level toward which this weekly rate tends is governed by the propensities to save and invest. His final three propositions state: (I) under flexible wages, the long-run equilibrium interest rate depends exclusively on real factors – the propensity to save and the marginal efficiency of investment – with money determining only the price level; (II) under rigid wages, the interest rate still depends on saving and investment propensities but now also on the quantity of money, since money income (and hence the quantity of active money) depends on the interest rate itself; and (III) in the “Keynesian case,” the long-run equilibrium rate is simply the rate at which the demand for money to hold becomes infinitely elastic, so that the rate of interest is determined “exclusively by institutional factors” (Section 21, p. 88).