The Simple Classical Model
In the spirit of the Simple Keynesian Model, this preliminary version of the Classical Model illustrates a central point in the simplest possible framework. In terms of the three points listed above, the simplification is an assumption that labor supply is fixed rather than a function of the wage rate.
The Production Function and the Demand for Labor
The Production Function
In the classical production function, output Y is taken to be a function of capital K and labor N. (The notation for labor suggests the number of hours or the number of workers.) In the short run the capital stock is taken to be fixed at K so that
Y = f(K,N).
Demand for Labor
The marginal product of labor is dY/dN = MPN, which should be a decreasing function of Y. A profit-maximizing firm should hire additional workers if P·MPN > W. At the margin P·MPN = W or, equivalently, MPN = W/P. The MPN curve thus is the demand for labor.
The Supply of Labor
In this simple case, the labor supply N* (Ns in the diagram) is fixed. In particular, it does not depend on the wage rate.
As long as the economy is on the upward sloping part of the production function, an increase in the labor supply should cause an increase in output and a decrease in the real wage rate.
The decrease in the real wage rate is not as bleak as it sounds because this is only a short run analysis. In the long run, the capital stock is not fixed and growth in the capital stock can cause an increase in the real wage rate.
An algebraic example also illustrates these points.