The equilibrium output Y* implied by the Hicks-Hansen IS-LM model is not necessarily a full employment level of output. Is this sustainable? From Figure 3, it is obvious that neither money markets, bond markets nor goods markets will have any incentive to move output or interest rates out of equilibrium point E = (Y*, r*). But what about the labor markets?
To see the impact of labor markets, we need to consider the IS-LM model in its entirety, as completed by Franco Modigliani (1944). As in a Neoclassical macromodel, we presume that the economy possesses a labor market where the demand for labor (Nd) is defined as:
Nd = f(w/p)
where dNd/d(w/p) = f｢ < 0 and, for the supply of labor:
Ns = g(w/p)
where dNs/d(w/p) = g｢ > 0. However, unlike in the Neoclassical model, we are not imposing the market-clearing condition that Ns = Nd. This is a crucial difference which shall play an important part in the Keynesian model. Instead we shall assume that: Nd ｣ Ns, thus allowing for the possibility of excess supply of labor (i.e. unemployment). As a result, we cannot have employment determined in the labor market - we cannot determine anything directly from an inequality. We shall presume a short-run production function for the economy in the following general form:
Y = F(N, K0)
where we have assumed that output is function of labor and capital employed, but as are assuming a short-run, capital is held constant at K = K0. Thus, we can rewrite the production function as Y = F(N), where we have normalized K out of the system. This production function is no different from the Neoclassical one -- however, since we do not have N determined from the supply side, we must instead invert this production function to obtain:
N = F-1(Y)
so that, knowing output, we can then determine employment. We shall assume, nevertheless, that factors are still priced at their marginal products, consequently for labor:
FN = w/p
where FN is the marginal product of labor. Thus, the labor demand curve, Nd = f(w/p) can be written inversely as w/p = f-1(Nd) = FN. But clearly, as N = F-1(Y), then FN = dY/dN = 1/F-1｢ . It is obvious, then, that the chain of causation runs from output to wages: we must determine output (Y) before we can determine employment (N) and consequently the marginal product of labor and then the real age, w/p. The initial element in this chain, output, is determined by effective demand in the Hicks-Hansen IS-LM model outlined earlier.
The IS-LM model with a labor market is shown in the four-quadrant diagram in Figure 4. For any Keynesian system, we must start with the determination of output, and thus quadrant I. Aggregate demand conditions (IS-LM) establish the equilibrium level of output and, through the money market, the interest rate. The level at which both markets are cleared is Y* and r*. Note that there is no reason to assume that Y* is equal to the level of full employment (YF) - and, in this particular example, they are indeed not equal. Given the level of output, we can input this into quadrant II where we have our inverse production function, N = F-1(Y). This will give us the level of employment in an economy (N*).
Figure 4 - The Modigliani Model: IS-LM with Labor Market
Now it gets tricky, for at that level of employment N*, we get a real wage (w/p)* determined by labor demand, Nd via the marginal-productivity rule. However, at that real wage, labor is willing to supply Ns which is clearly greater than the amount to be employed. Hence, there is a level of unemployment of (Ns - N*). As long as the real wage, (w/p)* determined by demand conditions remains above the full employment real wage, (w/p)F, the labor market is not clearing and we have involuntary unemployment.
In the regular Neoclassical macromodel, such a position would be untenable since the labor market fails to clear whereas all the others do - an explicit violation of Say's Law. Now, the Neoclassical macromodel argues that unemployment results only if real wages are inflexible for some reason. However, notice that in this Keynesian model, real wages are completely flexible, but they are determined not by labor-market clearing conditions but rather by the level of employment and the labor demand curve - and hence, determined by output which, by the multiplier, is determined by effective aggregate demand.
As we see, in the Keynesian model, real wages are completely flexible, but yet we still have involuntary unemployment. Notice that there is no dynamic inherent in the labor markets that will change real wages from (w/p)* to (w/p)F. If a firm offered to pay a lower wage, then it would be violating the assumption of perfect competition and the marginal productivity (and consequently profit-maximizing) rule. Why? If firms offered lower wages so that w/p < FN, then, inverting, w/FN < p, price will exceed the marginal cost of output - thus firms are making "extraordinary" profits, which is incompatible with perfect competition. As Keynes assumed perfect competition, this inequality would not be sustainable. The old Neoclassical argument that unemployment arose from inflexible real wages is untenable in this context. If (w/p)* does not happen to be the full employment real wage level, it does not matter - lowering the real wages will not be a rational choice for any firm nor will it affect anything.
Granted that unemployment does not arise from inflexible real wages, w/p, might it nonetheless be dependent on inflexible money (i.e. nominal) wages, w? There is an important disjuncture here which Keynes (1936) himself realized. We are given employment which, via the labor demand function, helps us determine the real wage, (w/p)*. However, recall that in the LM equations, we had M/p = L(r, Y) for money market equilibrium. The price level, thus, enters twice in the system - in the real wage and in the real money supply. Now, if the LM curve is to be determinate, then the real money supply, M/p, and thus the price level, p, must be determinate. But from where? Keynes proposed to look at the labor market: as (w/p)* is determined exactly, then if we fix the money wage, w, we immediately can determine what the price level, p, is and consequently can pin down the real money supply and thus the LM curve. Thus, with money wage w "given" (whatever it is), the price level will adjust to give us the profit-maximizing (w/p)*.
We see that this "given money wage", introduced early on in the General Theory, is merely little more than an accounting device in order for us to be able to pin down a determinate price level, p. Consequently, whether it is flexible or fixed should not matter: it was assumed fixed by Keynes in order to act as a numeraire. In order to prove that nothing hinged upon this assumption, Keynes made the nominal wage flexible in Chapter 19 of the General Theory. However, he was wrong in supposing that this was inconsequential - and this is where the great trouble began.
What are the consequences of permitting flexible money wages? If indeed there is a great amount of unemployment, then labor market "pressures" will be such that workers' money wages will be bid downwards (this might imply something akin to "money illusion" on the part of labor supply - as pointed out by Leontief (1936, 1947) and virtually admitted by Keynes (1936: 7-9; 1937) - but this is a bit of a detour at this point). Now, if there is no change in aggregate demand conditions, there will be no change in employment and, hence, by marginal productivity conditions, (w/p)* must remain the same - so that if money wages w decline, the price level must decline by an exactly proportional amount. Thus, the question should be asked again: what are the consequences of declining money wages and equiproportionally declining price levels?
Keynes (1936: Ch. 19) himself considered several possibilities on the central components of the theory of effective demand:
(1) Consumption: declining money wages and prices should not affect anything because real wages, and thus real worker income, is left unchanged. If there is any lag, it will be that wages fall faster than prices, thus worker income and hence consumption will decrease. Thus, on the whole, consumption will be unaffected and, if a lag is allowed, it will fall and output and employment with it.
(2) Investment: again, as real wages are the same there is no effect on investment; if there is a lag and real wages fall temporarily, then lower costs of production may induce more investment, but if, as Keynes posited, firms are "forward-looking", they ought to realize that aggregate demand is falling and thus will probably cut back investment (if they don't, they might raise investment temporarily, but then the accumulating inventory will force them to cut back later). So, on the whole, investment ought not to be affected by falling money wages. There might be a temporary rise in investment, but eventually it will fall back even further.
(3) Money demand: if money wages fall, the transactions demand for nominal money falls, pure and simple. Alternatively, declining real prices will increase the supply of money. Whatever the perspective, the real interest rate declines. If interest declines, investment rises and thus output and employment. In sum, the LM curve shifts to the right.
This last result, the impact of falling money wages on the LM curve, is known as the "Keynes Effect". As long as unemployment persists, money wages will be pressured to decline and as long as money wages decline, LM will gravitate to the right - back towards full employment output (YF). The "Keynes Effect", laid out by Keynes (1936: Ch. 19) himself, was to become the Achilles' Heel of Keynes's system. This possibility was pounced upon by virtually all critics - from hostile ones such as Pigou (1937, 1938, 1943) to sympathetic ones such as Hicks (1937), Kaldor (1937), Dillard (1948), Klein (1947) and Tobin (1947).