As we have pointed out in the section on economic paradigms, the production function is taken as a starting point for microeconomic production analysis. For example, the input might be labor, steel, or any other material. One way of looking at a production function with only one input is that we are holding all the other inputs fixed. Obviously, we could have a production function with n inputs and m outputs, but such a production function would be beyond the scope of this course. Economists studying policy problems general have limited data from within the firms.
Economists usually obtain empirical production functions from statistical analysis of industry data.
Thus the production firm represents the representative firm in the industry. If the exponent is less than or equal to 1, the production function is concave. The cost function is the minimum cost of producing the output over its range. The cost function is obtained by solving a cost minimization problem which also provides the conditional demands for inputs to produce each level of output. Cost minimization is an important decision problem in industry.