Question

Cost equations are often used to obtain factor demands. How can factor demands be obtained from a cost equation? Why would one obtain factor demands this way instead of obtaining them from the profit maximization problem directly?

Answer 1

Answer to question

As cost of equation used oftenly to obtain factor demand so as doing reverse factor demand can be obtained through cost of equation. Let understand through a theory:

In economics, a conditional factor demand is the cost-minimizing level of an input (factor of production) such as labor or capital, required to produce a given level of output, for given unit input costs (wage rate and cost of capital) of the input factors.

Since the optimal mix of input levels depends on the wage and rental rates, these rates are also arguments of the conditional demand functions for the inputs. This concept is similar to but distinct from the factor demand functions, which give the optimal demands for the inputs when the level of output is free to be chosen; since output is not fixed in that case, output is not an argument of those demand functions.

Also factor demand can also obtained from profit maximization directly but by cost equation it give effiecent and correct answer.