is 20 units of output and the price of one unit of labour is $2. Then we
have
Thus, the last dollar spent on capital adds only 4 units to output, whereas
the last dollar spent on labour adds 10 units to output. In this case, the
firm can reduce the cost of producing its current level of output by using
more labour and less capital. Specifically, suppose the firm used 2 more
units of labour and 1 fewer unit of capital. The 2 more units of labour
would cause output to rise by 40 units and costs to increase by $4; the 1
fewer unit of capital would cause output to fall back by 40 units and costs
to decline by $10. After this substitution of labour for capital, output
would be unchanged but costs would be lower by $6. Thus, the original
combination of factors was not a cost-minimizing one.
Of course, as the firm substitutes significantly between labour and capital,
the marginal products of both factors, and will change.
Specifically, the law of diminishing marginal returns says that with other
inputs held constant, an increase in the amount of one factor used will
decrease that factor’s marginal product. As the firm in the previous
example reduces its use of K and increases its use of will rise
and will fall. These changes help to restore the equality in Equation
8-1.
MpKPK = 1040 = 4 < MpPLL = (^202) = 10
MPL MPK,
L, MPK
MPL