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. A conditional factor demand function expresses the conditional factor demand as a function of the output level and the input costs.[1] The conditional portion of this phrase refers to the fact that this function is conditional on a given level of output, so output is one argument of the function. Typically this concept arises in a long run context in which both labor and capital usage are choosable by the firm, so a single optimization gives rise to conditional factor demands for each of labor and capital.
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.
^Varian, Hal., 1992, Microeconomic Analysis 3rd Ed., W.W. Norton & Company, Inc. New York.
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