Definition & Reality in the General Theory of Political Economy

by Thomas Cool

Model

Regard a general equilibrium model with 15 units of highly productive labour (h), 75 units of modally productive labour (m) and 10 units of lowly productive, minimum wage workers and possible benefit recipients (l). The economy has exposed and sheltered sectors that produce output y_E and y_S, while a social welfare function (SWF) determines the optimal combination. In an open model, the y_E would be traded for y_Foreign, but here we assume that exports are directly equal to imports for consumption. The SWF will here be a Constant Elasticity of Subsitution (CES) function that neglects the distribution of income:

Output of the sectors is determined by production functions that depend upon the allocation of the labour factors h, m & l. Since we will compare two regimes, one with l and one without l, this factor cannot be complementary (necessary), and hence it is substitutable to some degree with the other factors. The sheltered sector is a one level CES with all factors substitutable:

The exposed sector is a two-level CES where highly and lowly productive labour are complementary, but both are substitutable with minimum wage labour: