A One Sector Model

Abstract

We now want to introduce the time dimension into the production process explicitely. Inputs have to be made available before the outputs are available. We first consider a very simple model with only one producible commodity and one nonproducible good (called labour). To produce one unit of the commodity we need a units of this commodity as input (0 < a < 1) and a_o units of labour input. Both inputs have to be available one period before the availability of the output. But we assume that the wage is paid to workers only after the output has become available. Hence there is no interest cost on wage payments. If the price of the commodity is p, if the nominal wage rate is $\bar w$ and if the interest rate is r we have the unit cost equation

$$p = {a_o}\bar w + \left( {1 + r} \right)ap$$

or

$$p = \frac{{{a_o}\bar w}}{{1 - \left( {1 + r} \right)a}}$$