If it is possible to substitute one factor for another to keep output constant
while reducing total cost, the firm is currently not minimizing its costs. In
such a situation, the firm should substitute one factor for another factor as
long as the marginal product of the one factor per dollar spent on it is
greater than the marginal product of the other factor per dollar spent on it
The firm is not minimizing its costs whenever these two magnitudes are
unequal. For example, if an extra dollar spent on labour produces more
output than an extra dollar spent on capital, the firm can reduce costs by
spending more on labour and less on capital.
Suppose we use K to represent capital, L to represent labour, and and
to represent the prices per unit of these two factors. The necessary
condition for cost minimization is then
Whenever the ratio of the marginal product of each factor to its price is not equal for all
factors, there are possibilities for factor substitutions that will reduce costs (for a given level of
output).To see why Equation 8-1 must be satisfied when costs are being
minimized, consider an example in which the equation is not satisfied.
Suppose the marginal product of capital is 40 units of output and the price
of one unit of capital is $10. Also suppose the marginal product of labour
pL
pK
MpPKK = MpPLL(8-1)