Microeconomics,, 16th Canadian Edition

Because w is fixed, MC varies negatively with MP. When MP
a maximum, MC is at a minimum.
19. Strictly speaking, the marginal rate of substitution refers to the
slope of the tangent to the isoquant at a particular point, whereas
the calculations in Figure 8A-1 refer to the average rate of
substitution between two distinct points on the isoquant. Assume
a production function

Isoquants are given by the function

derived from Equation 19.1 by expressing K as an explicit

function of L and Q. A single isoquant relates to a particular level

of output,. Define and as an alternative, more compact

notation for and , the marginal products of capital

and labour. Also, let and stand for and

respectively. To obtain the slope of the isoquant, totally

differentiate Equation 19.1 to obtain

Then, because we are moving along a single isoquant, set

to obtain

Q=Q(K,L)

[19.1]

K=I(L,Q ̄ ̄ ̄)

[19.2]



̄Q ̄ ̄ QK QL

∂Q/∂K ∂Q/∂L

QKK QLL ∂^2 Q/∂K^2

∂^2 Q/∂L^2



dQ=QK⋅dK+QL⋅dL

dQ