This post is my attempt to respond to the SRW’s graphical model of Keynesian and monetarist recessions. In particular, I have a different take on what is a Keynesian recession. I don’t think it has necessarily anything to do with sticky prices or leverage — although these are all important in the real world, you don’t need them to describe variations in output and employment; you don’t need real productivity shocks, either.
I’m going to try to elaborate on this passage, in which Keynes is addressing Hicks’ IS-LM:
Put shortly, the orthodox theory maintains that the forces which determine the common value of the marginal efficiency of various assets are independent of money, which has, so to speak, no autonomous influence; and that prices move until the marginal efficiency of money, i.e. the rate of interest, falls into line with the common value of the marginal efficiency of other assets as determined by other forces. My theory, on the other hand, maintains that this is a special case and that over a wide range of possible cases almost the opposite is true, namely, that the marginal efficiency of money is determined by forces partly appropriate to itself, and that prices move until the marginal efficiency of other assets fall into line with the rate of interest.
Consolidate the financial sector + government into a “bank”. There is no bond market per se — households purchase deposits in the bank and receive the (overnight) government mandated rate, . Anyone can borrow from the bank and pay an overnight rate of as well. However, there is a capital market, in which capital goods are bought and sold, and these also deliver a (continuous) income stream.
Firms in our model are owned jointly by households that supply capital to them. There are only two firms — consumption goods producing firms and capital goods producing firms. This is a continuous recursive competitive equilibrium. At each point in time, the stock of capital is fixed, but the growth rate of this stock is variable. Assume continuous market clearing at all times (but remember the government is “fixing” the nominal rate).
Households hire managers to operate the firms. There are no intermediate inputs, so earnings are just the difference between revenue and labor payments, and these earnings are passed onto capital suppliers — firm managers have no slush fund in which they can keep earnings for themselves.
The optimization problem of the firm manager is to maximize earnings per unit of capital supplied, , given the quantity of capital supplied by households.
Households, by shifting capital among the consumption goods and capital goods producing firms, ensure that both firms deliver the same earnings. In that case, there is no arbitrage possible by holding a deposit or holding capital, so that
- is the price of a capital good at time t
- is the overnight rate
- is the (exponential) depreciation rate
- is earnings per unit of capital
where is the mean rate between periods and . The above holds if the integral converges, for example if . If desired, you can add variance terms to b(t), but the specific form of this equation is not important. What is important is that changes in short run earnings are not going to correspond one to one with changes in the price of capital goods.
Let’s combine this with our simple model of firms. For example, suppose that the consumption goods producing firm, F, and capital goods producing firm, G, have production functions:
Note that the capital goods producing firm is more capital intensive — production of consumption goods includes services that are more labor intensive. In that case, the earnings can be expressed as
In particular, the aggregate labor demand curve depends on the proportion of capital allocated towards consumption:
What is happening here is that fluctuations in the prices of consumer goods create fluctuations in the ratio of capital goods to consumer goods prices. As households withdraw capital from the consumer goods producing firms and increase the capital supplied to capital goods producing firms , the differences in labor intensity creates shifts in aggregate labor demand and aggregate output. Even though there are no productivity shocks or rigid prices. Markets are clearing at all times.
In graphical terms, capital goods prices are a function of the exponential weighted average of consumption good prices, and so move separately:
But the ratio of returns for capital and consumption producing firms is given by the ratio of capital to consumption goods prices and the square root real wage.
A 1% increase in the ratio of q to p will force the real wage fall by 2% — the labor demand curve will keep shifting to the right until this happens:
The only way that output and employment could be kept constant would be if the labor supply curve also shifted to the right to match the rightward shift in the labor demand curve. Basically, as households attempt to save by withholding purchases of consumption goods, they must relinquish these savings by lowering their wage demands if they are to remain employed. Even though firms will cut prices in response to a decline in demand, they will shed labor even faster.
Looking at Output Gaps
If we define trade cycle unemployment or conjunctural unemployment as changes in employment due to movements in the labor demand curve not attributable to real productivity shocks, then there is such a beast even under assumptions of full market clearing.
Rather than having interest rates adjust to maintain full output, output and employment adjusts when demand for consumption decreases.
In this simple example, we have an interpretation of Keynes’
the marginal efficiency of money is determined by forces partly appropriate to itself, and that prices move until the marginal efficiency of other assets fall into line with the rate of interest.
The forces “partly appropriate to itself” correspond to expectations of future prices, and the other prices that adjust to match are the decline in the real wage necessary to accommodate the expectation of future return.
Of course, a better analysis would also include changing risk-premiums, and something like a production in advance constraint, in which case other effects would be dragged in. But the purpose of this discussion is to argue that you do not need sticky prices, sticky wages, or real productivity shocks to explain output gaps. The supply side moves in response to nominal profit expectations even under a flexible price model.
A temporary increase in the demand to save is enough of an explanation for cyclical unemployment.
Update: Made some edits for clarity. Added bonus video for those who made it to the end!