Goodwin model (economics)

The Goodwin model, sometimes called Goodwin’s class struggle model, is a model of endogenous economic fluctuations first proposed by the American economist Richard M. Goodwin in 1967. It combines aspects of the Harrod–Domar growth model with the Phillips curve to generate endogenous cycles in economic activity (output, unemployment, wages) unlike most modern macroeconomic models in which movements in economic aggregates are driven by exogenously assumed shocks. Since Goodwin’s publication in 1967 the model has been extended and applied in various ways.

Output is given by the aggregate production function

where:

All of these variables are functions of time, though the time subscripts have been suppressed for convenience.

Unlike in the Harrod–Domar model, full capital utilization is assumed. Hence

at all times. The employment rate is given by

where n is total labor force which grows at the rate β. Additionally, labor productivity a, is assumed to also increase at the rate α. Note that in this case the rate of growth of the employment rate is given by

The growth rate of the absolute level of employment in turn is given by

Wages are assumed to change according to a linearized Phillips curve relationship given by

In other words, if the labor market is 'tight' (employment is already high) there is upward pressure on wages and vice versa in a 'lax' labor market. This is the aspect of the model that can loosely be associated with the "class struggle" portion of its name, however, this kind of Phillips curve can be found in many Macroeconomic models.

The workers' share in output is u, which by definition is

Hence the growth rate of the workers' share is

Labor's share in output increases with wages but declines with productivity growth as less workers are needed to produce the same amount of output.

Finally we have the capital accumulation equation and the resulting growth rate for output (since k and q grow at the same rate by assumption of full utilization of capital and constant returns to scale). It is assumed that workers consume their wages and capital owners save a portion s of their profits (note that the model generalizes to the case where capitalists save more than workers) and that capital depreciates at the rate delta. The growth rate of output and capital is then given by

This in turn implies that

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