Previously, the level of employment was shown to be determined by the supply of and demand for labor; the level of output (with a given production function) was shown to be determined by the level of employment; and the level of prices was shown to be determined by the supply of money. Figure 17-2 illustrates the interrelationships of the variables in this classical model.

In Part B, the intersection of the two curves defines the point of full employment, N₁, and the real wage, (W/P)₁, necessary to achieve full employment. With this real wage in effect, employment is N₁, which defines full-employment output, O₁, in Part A. The price level of output depends on M and V, and the curve M₁V specifies a particular money supply and some constant velocity of money. From (or from), once M, V, and O are known, the price level is also known. ¹¹ In this case, given M, V and O₁, the price level is P₁.

Part D of Figure 17-2 is new; it shows the money-wage adjustment necessary to establish equilibrium. In Part B (W/P)₁is consistent with any number of pairs of values for W and P, and these possible pairs of values, when plotted, trace the upward-sloping straight line labeled (W/P), in Part D. For a real wage higher than (W/P)₁ the slope of the line in Part D would be steeper and would thus combine a higher W with each P or a lower P with each W. For a real wage lower than (W/P)₁, the slope of the line in Part D would be flatter and would thus combine a lower W with each P or a higher P with each W. Only one money wage will produce the real wage (W/P)₁, indicated by the slope of the line in Part D, at the given price level. With the price level P₁established in Part C, the required money wage is accordingly established in Part D as W₁. If the actual money wage in the market is higher than W₁ - the money wage now identified as that required for full employment - then the resulting unemployment and competition among workers for jobs will force the money wage to drop until the system regains its full-employment equilibrium position.

The interconnected parts of Figure 17-2 thus enable us to identify the full set of equilibrium values for this simple classical system: employment N₁, output O₁, price level P₁, and money wage W₁. Barring any shift in the production function or the supply curve of labor or any change in the money supply or its velocity, the indicated set of equilibrium values will remain unchanged period after period, in practice, of course, these elements will change over time, but

11. We may now change to MV = PO, using the equality sign instead of the identity sign. We now have an equation that sets forth the condition fro equilibrium. With MV and O, equilibrium P is that P at which P = MV/O.

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for each change, under classical assumptions, new equilibrium values will be established for the variables of the system. Tracing through several such changes will illustrate the mechanics of the system.

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Effects of a Change in the Supply of Money

Consider first the case of an increase in the money supply as indicated by the shift of the MV curve from M₁V to M₂V in Figure 1 7-2C. The increase in M (with constant V) means an increase in total spending per time period of V(M₂- M₁) and a rise in the price level from P₁ to P₂ for the output level 0₁. If the money wage does not rise proportionately with this rise in the price level, the real wage will fall, causing employers to try to expand output by hiring more workers, for a higher price for output without a higher money wage rate means greater profits with greater output. But a real wage below (W/P)₁ means that the quantity of labor available is too small to produce output O₁ let alone to expand output beyond this. Competition among employers for workers will then force the money wage up until it rises proportionately with the price level, leaving the equilibrium real wage unchanged at (W/P)₁ and the profit-maximizing output unchanged at O₁. The net result of the expansion of the money supply is a proportionate rise in the price level and in the money wage but no change in employment or output; the new equilibrium values are N₁, 0₁, P₂, and W₂.

This, of course, is just what we should expect on quantity theory reasoning. The level of output is determined by the real factors of labor productivity and the quantity of labor employed; the money supply only sets the price level for this output. Increasing or decreasing the money supply will cause the price level of output to rise or fall proportionately, but the level of output itself will remain unchanged. Any change in the money supply that is accompanied by a change in the velocity of money will break the proportionate relationship between M and P but will still leave the level of output and employment unaffected by changes in either M or V.

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Effects of a Change in the Supply of Labor

Now let us imagine an increase in the labor supply, as shown by the shift from S_L to S’_L in Figure 17-3. With no shift in the production function and so no shift in the curve of the MPP of labor, any increase in employment will lower the MPP of labor. The full-employment equilibrium previously was at N1, with the MPP of labor or the real wage (W/P)₁. If there is to be full employment, the real wage must now fall from (W/P)₁ to (W/P)₂ for only at (W/P)₂ does the supply of labor equal the demand for labor. A fall in W/P is expected in classical theory under the pressure of unemployment now present at the real wage of (W/P)₁; competition among workers for jobs gradually forces down the money wage, and a drop in the money wage with no drop in the price level

The present construction enables us to face a complication earlier side-stepped - the fact that a drop in the money wage must lead to a drop in the price level, with a given money supply and constant velocity. As the money wage falls below W₁, firms expand employment beyond N₁, which raises output beyond O₁. When MV is unchanged, aggregate demand is unchanged. To provide a market for enlarged output requires a fall in the price level. (From MV = PO, P must fall by the amount necessary to offset any rise in O.) But, though P must fall, P will not fall as far as W. If it did, the new real wage W/P would remain equal to (W/P)₁, and there would be no incentive for firms to hire more labor and expand output and therefore no reason for P to fall in the first place. Furthermore, if P fell as far as W, with no change in O, MV would exceed PO. This would mean that some part of the money supply was idle, a situation denied by classical theory. Thus, both P and W fall, but P falls less than W, and this provides both an incentive to firms to expand output and a market for that expanded output. This situation appears in Part D of Figure 17-3 as the fall in W from W₁, to W₂ and the fall in P from P₁ to P₂. This is the fall in the real wage that gives firms the incentive to expand N from N₁ to N₂ and so expand O from O₁ to O₂. This also is the fall in P that makes it possible to

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sell the expanded output of O₂ with aggregate demand unchanged at MV in Part C.

A numerical “before” and “after” example may clarify the adjustments involved. The first row of the table below gives the equilibrium values for N, O, W, and P when labor demand is D_L, labor supply is S_L (Figure 17-3), the money supply is $75, and velocity is 4. The second row gives the new equilibrium values after the shift in S_L to S’_L. Full employment now calls for N of 150, at which level the MPP of labor is 1.66. If there is to be full employment, the real wage must fall from 2 to 1.66. Suppose that in the face of unemployment the money wage falls to $1.66. If P stayed at 1, this would reduce the real wage to $1.66/l, or 1.66, the value required for full employment. At this real wage, N is 150 and O is 400. But output of 400 cannot be sold at a price level of 1, since aggregate demand is MV of $300. Therefore P must fall, but any fall in P raises the real wage and causes a contraction in N. Any unemployment must lead to a further fall in W, which in turn calls for a further fall in P. In this fashion, through successive adjustments, the process finally ends with the consistent set of values in the second row below. ¹²

Given an increase in the labor supply, the crucial element of the process by which the system moves to its new equilibrium position is the adjustments that occur in the money wage and the price level. Whether unemployment threatens from an increase in the labor supply or for other reasons, flexibility of the money wage and price level is indispensable to the correction of unemployment. As long as the money wage responds to unemployment and as long as the price level responds to changes in output, full employment can always be regained according to this simple classical model.

12. On the assumption of profit maximization, employers will not expand employment unless greater profits are expected from the sale of the higher level of output. In this case, there will be greater profits, as may be seen from the figures. At the original equilibrium, labor’s share of the real output of 300 is N x MPP, or 100 x 2, or 200. The remainder, O - (N x MPP), or 100, may be called the “profit share.” At the new equilibrium, labor’s share of the real output of 400 is 150 x 1.66, or 250, leaving 150 as the “profit share,” an increase in profits of 50. In dollar terms, the flow of income at the original equilibrium is $300, or 300 x 1, divided into $200 for labor and $100 for profits. At the new equilibrium, it is the same $300, or 400 x 0.75, now divided into $187.50, or 150 x $1.25 for labor and $112.50 for profits. Though labor’s share is decreased in money terms from $200 to $187.50, the $187.50 adjusted for the fall in P from 1 to 0.75 is equal to $250 in “base period” prices. Similarly, the profits of $112.50 are equal to $150 in “base period” prices.

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Effects of a Change in the Demand for Labor

Growth in the capital stock or technological advances will cause the production function to shift upward over time, as shown by the movement from O to O’ in Figure l7-4A. At each possible level of employment, the MPP of labor is now greater than it was, since at each level of N the slope of O’ exceeds the slope of O. This is reflected in Figure 17-4B as an upward or right-ward shift in the demand curve for labor, indicating that it is now profitable for employers to hire more labor at each possible real wage. The equilibrium real wage rises from (W/P)₁to (W/P)₂; employment rises from N₁ to N₂and output rises from O₁ to O₂. With no change in the money supply, the greater output requires a fall in the price level from P₁ to P₂. At the new equilibrium real wage of (W/P)₂, price level P₂calls for money wage W₂. In the present case, the rise in the real wage necessary to reestablish equilibrium is produced by a fall in P and a rise in W.

The first row of the following table repeats the set of figures previously used to describe the original equilibrium values; the second row gives a set of

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In passing, we may note several basic propositions in economics that are clearly brought out by the present analysis. For one, the gradual rise in the real wage, or “standard of living” of labor, is primarily the result of the gradual upward shift in the production function, which is largely attributable to technological progress and a growing stock of capital. If, over the same period in which these developments raised the schedule of marginal productivity of labor from D_L to D’_L, the supply curve of labor had also moved from S_L to S’_L, the number of workers employed would have risen, but the real wage would have remained the same. The actual gradual rise in the real wage experienced over the long run in Western economies has resulted primarily from the fact that the growth in capital and the rate of technological advance have exceeded the rate of growth in the labor force.

A second proposition brought out by this analysis is that the long-run growth of output (whether produced as here by an upward shift in the production function, or as in the previous case by a shift to the right in the labor supply curve, or as in practice by both) leads to a falling price level unless accompanied by an expansion in the money supply. Although an expansion of output with no rise in the money supply will in practice cause V to rise, V cannot rise without limit. Therefore, as output expands in the long run, M must expand to avoid what otherwise must be a gradually falling P. Although these propositions have been brought out by the classical model, they are accepted in principle by most economists today.

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Effects of a Rigid Money Wage

From an initial equilibrium with given MV, an increase in the supply of labor calls for a fall in the money wage and a lesser fall in the price level to establish a new full-employment equilibrium at a lower real wage. Classical theory assumes perfectly competitive markets, and an excess supply of labor in such markets will automatically depress the money wage. If we now drop the assumption of perfect competition in the labor market, the results may be different. Consider, for example, the imperfection of competition that results when workers are organized into, labor unions. There will be no barrier to a rise in the money wage when excess demand for labor appears, but there will now be a barrier to a fall in the money wage when excess supply appears.

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In other words, the money wage is flexible upward but may be rigid downward. Furthermore, in an imperfect market the money wage may be forced up even though there is no excess demand for labor. To illustrate, let us begin with a full-employment equilibrium position for the economy and observe the effect of a money wage that is arbitrarily pushed up, say by union pressure.

In Figure 17-5 there is full-employment equilibrium with a real wage of (W/P)₁and values for other variables indicated by subscript 1. Suppose now that the money wage is forced up from W₁ to W₂. If the price level were to remain at P₁, a rise in the real wage would occur proportionate to the rise in the money wage. But, with the given M and V, the price level must rise; for in the absence of a rise in P there is a rise in the real wage, which means a decrease in O, and, with aggregate demand given by MV, a lower O means a higher P. While P must therefore rise, it cannot, however, rise as far as W, for if it did there would be no change in the real wage and so no change in output. The original output cannot all be sold with unchanged aggregate demand of MV at a higher P, so P must rise in proportion to the fall in O.

The process by which a new equilibrium is reached is one in which P. 0, and N must all adjust to the rigidly fixed money wage W₂. The new equilibrium values for P, O, and N are designated by the subscript 2. As compared to the initial equilibrium there are now a higher real wage, a lower output level, and

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a higher price level. The higher real wage, which was artificially brought about by forcing up the money wage, forces employment down from N₁to N₂. Since the amount of labor supplied is greater with a higher real wage, the amount of unemployment is not merely the difference between N₁ and N₂, but is the larger difference between N₃and N₁. With the higher real wage, those workers fortunate enough to keep their jobs are, of course, better off than they were before the rise in the money wage.

To illustrate this situation, a numerical example follows similar to those given earlier. Since the new equilibrium is not one of full employment, the last three columns have been added to show the resulting unemployment. (S is labor supplied; D is labor demanded; U is labor unemployed.)

With full-employment equilibrium defined by a real wage of 2, we can see from the figures that unemployment must result from the arbitrary raising of the money wage from $2.00 to $2.40.

As long as the money wage is arbitrarily held above the level consistent with full employment, we have an equilibrium situation with unemployment. Although we have noted several times before that classical theory denied this possibility of equilibrium with unemployment, the denial was made only on the assumption that we were dealing with an economy in which the money wage was flexible. Underemployment equilibrium is therefore entirely consistent with classical theory when that theory is stripped of the assumption of flexible wage rates, an assumption indispensable to its full-employment conclusion.

In the General Theory, Keynes replaced the classical assumption of a flexible money wage with that of a rigid money wage, an assumption certainly more closely in agreement with the facts of observation. In so doing, Keynes could easily enough show that equilibrium with unemployment is possible. Though a great deal more is involved, what should be clear from analysis of the present case is that the corresponding change in assumption in the classical theory leads to the same possibility of underemployment equilibrium reached by Keynes in the General Theory.

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Monetary Policy and Full Employment

In the classical scheme, if the money wage is held artificially above the level necessary for full employment, an appropriate expansion of the money supply may be an antidote. According to quantity theory, an increase in M

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with V and O stable, will raise P proportionately. With a rigid money wage, the rise in P reduces the real wage and provides the profit incentive to employers to expand employment and output toward the full-employment level. There is, therefore, some appropriate expansion in the money supply that is sufficient first to raise P to the level that reduces the real wage, W/P, to the full-employment equilibrium level and second to purchase the full-employment output that results.

In terms of Figure 17-5D, to achieve the full-employment real wage of (W/P)₁ with the money wage inflexible at W₂requires a price level of P₃, since at that level W₂/P₃, equals W₁/P₁ or (W/P)₁. With real wage of (W/P)₁, output is O₁. Therefore, in Part C, MV must be increased to equality with P₃O₁ to generate demand adequate to purchase full-employment output O₁ at price level P₃. ¹³

The previous numerical example may be modified to show how an appropriately expansionary monetary policy may offset the effect of a rigid money wage. The first two rows of the following table are the same as before - the first describes the initial full-employment equilibrium, the second the underemployment equilibrium that results from a money wage artificially pushed up. The third row shows the return to a full-employment equilibrium that results from the appropriate expansion of M.

Note that the strict quantity theory does not hold because part of the additional demand created by the expansion of M is absorbed by the expansion of output that accompanies the fall in the real wage. M rises from $75 to $90, or by 20 percent; P rises from 1.10 to 1.20, or by less than 10 percent.

Thus, it would seem that monetary policy provides the solution to unemployment created by a rigid money wage. But it is equally apparent from the crude model before us that this method of securing full employment in the face of artificially high wage rate works only as long as the increase in M is not offset by a decrease in V. Aggregate demand must increase with the increase in M. Classical theory saw no “leakage” between an increase in M and an increase in aggregate demand. We can begin to see why monetary policy was the policy weapon of classical economists. When we return in the next chapter to Keynesian theory, we will see that this simple tie between changes in the money supply and

13. With V constant,

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changes in aggregate demand disappears. In Keynesian theory, aggregate demand cannot be so simply increased or decreased by expansion or contraction of the money supply.

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