A clarification of the Goodwin model of the growth cycle

We show that there is a difficulty in the original Goodwin model which is also found in some more recent applications. In it both the labour share and the proportion employed can exceed unity, properties which are untenable. However, we show that the underlying dynamic structure of the model can be reformulated to ensure that these variables cannot exceed unity. An illustrative example extends the original model, and we argue it is both plausible and satisfies the necessary unit box restrictions.