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–Domargrowth model with the Phillips curve to generate endogenous cycles in economic activity 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.
Model
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 productivitya, 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' 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. It is assumed that workers consume their wages and capital owners save a portion s of their profits and that capital depreciates at the rate delta. The growth rate of output and capital is then given by This in turn implies that
Solution
The two differential equations are the key equations of the model and in fact are the Lotka–Volterra equations. While the model can be solved explicitly it is instructive to analyze the trajectory of the economy in terms of a phase diagram. Setting the two equations above equal to zero we get the values of u and v at which growth of v and growth u, respectively, are zero. These two lines divide the positive orthant into four regions. The figure below indicates with arrows the movement of the economy in each region. For example, the north-western region the economy is moving north-east. Once it crosses the u* line it will begin moving south-west.
The figure below illustrates the movement of potential output, actual output and wages over time.
As can be seen the Goodwin model can generate endogenous fluctuations in economic activity without relying on extraneous assumptions of outside shocks, whether on the demand or supply side. The model has been applied and extended by many economists since its first presentation in 1967.
