The Goodwin economic model is a dynamic macro model based on the ‘predator-prey’ ecology of, say, foxes and rabbits. As adapted for economics, the predator agent is called the wage share and the prey agent is termed the profit share. What each agent is sharing is the real annual output of the economy, or real output.

Real output, Q, is equal to labor productivity x labor force = a x L

The Goodwin Model derived in the above wikipedia link assumes that Q = k/σ where k is physical capital and σ, the capital output ratio[1] is constant. This clearly contradicts the equation of exchange, Q = MV/p, which implies that for M=k  that  σ = p/V.

In the study which follows, the assumption is made that V=3 so σ = p/3  for all results unless otherwise indicated.  Powerful empirical evidence to support this assumption is given by a plot of the  Marginal Productivity of Debt which is drawn from government data. Further discussion of this curve can be found here.

As  GDP  = pQ  and  Debt =pk, then  ΔGDP/ΔDebt = ΔQ/Δk =V/p .

From the curve below that V/p(1966) = 0.75  when p = 4 is estimated,  it can be calculated that V = 3 more or less.  Since real output depends on the employment percent λ,   it can be supposed that  V = 3*λ.   The volatility in the actual  ΔGDP/ΔDebt  is possibly explained by the fact that real employment  is noisier than employment calculated by the simulation.

A linear trend line is given for ΔGDP/ΔDebt.  However, I believe there is upward curvature in the actual curve which is 3λ/p. The discontinuity in the 3/p curve shown below is from a simulation in which  it was assumed that inflation was zero between 1979-83 due to the high interest rates imposed by Fed Chairman Paul Volcker during that period.

Wage share, u, is equal to wage bill divided by real output = wL/ paL = w/pa where w is nominal wages and p is price level.  The profit share, then, is 1-u.  At this point it may be useful to digress a bit on the subject of ‘real output’.  Classical economics presupposes that real output  Q = aL  consists of marketable goods and services.  Unmarketable goods/services such as battleships and Homeland Security wages add no marketable goods/services to the economy but add only costs.

If for p=1,  Q = k/σ  then suppose that a portion of the labor force is diverted to unmarketable ‘output’  G which is paid for with debased currency.  If the aggregate  real capital is the same then  Q-G = k/σ2  so that Q/(Q-G) = σ/σ2.   With constant k,  p = p2 =  Q/(Q-G)  so that  σ2  =  σ/p .

The diversion of capital and labor into unmarketable output is what the Austrians refer to as malinvestment and capital decumulation. The so called Austrian Business Cycle is a very long term process similar to the Kondratieff Cycle.  The ABC states that an upward price spiral started by inflation leads to exponential growth of malinvestment and ultimate economic collapse.

The reason the wage share is the predator in this relationship is due to an established empirical observation known as the downward rigidity of wages. What this means is that wages remain constant until there is a labor shortage, at which point they jump upward a finite amount.  This upward jump in wages increases the wage share at the expense of the profit share.  The Phillips Curve in its original form states a relation between %wage increase and %unemployment. It has since been confounded by Keynesians and Monetarists to be a relation between %inflation and %unemployment because both of these schools seem to believe that inflation is caused by wage increases. I adhere, however, to the original form because, as will be shown, inflation is a purely monetary phenomenon.

Phillips Curve

One might suppose that the reason wages are downwardly rigid is due to strong union organization. That, however is not the case. As Prof. Dr. Peter Flaschel notes [2] more important reasons are:

  • Wages are set by firms (and not by a Walrasian auctioneer)
  • It is not profitable for a firm to hire new laborers at lower wages than are paid to those already in the work force of this firm (assuming homogeneous labor for simplicity)
  • It is not profitable for a firm to cut the wages of all its employees simultaneously
  • It is not profitable for a firm to exchange its complete labor force against the cheaper work that can be obtained from the pool of the unemployed.

I would add the common sense observation that firms retain the most skilled and/or productive workers, so that periodic layoffs due to recessions improve the firm’s workforce.

Later on that same page, Flaschel adds:

  • Wage rigidity of this basic type combined with our Classical model (which has been supplemented by an explicit and “consistent” version of Say’s Law), however, imply that involuntary unemployment and Say’s Law are not incompatible with each other as it is claimed in Keynes . . . Classical economists could have discussed the existence of men involuntarily unemployed (had they wished to) without destroying at the same stroke the logic of Say’s Law in the market for goods.

It can be seen, then, that wages predate profits by claiming a larger share of output during labor shortages (booms) and wages do not decline in recessions because firms prefer to lay off employees rather than cut wages.

For constant price level and constant σ (capital-output ratio), the following results are reached:


The above shows the phase diagram which is a plot of %employment vs. wage share. For noninflating constant prices, the phase diagram forms stable loops around the equilibrium point. The pre 1933 equilibrium point is (wage share, % employment) = (.985,.94) which changes to (.97,.94) after the devaluation.

    Equilibrium wage share declines with a rise in price level, while equilibrium employment level maintains itself.

Real wages jump down due to the price level jump in 1933.


The price level jump causes a ‘nominal output’ different from real output to appear.

More interesting and useful results are shown in The Results section.