Microeconomics,, 16th Canadian Edition

Diminishing marginal productivity implies and
and hence, as we move down the isoquant of Figure 8A-1,
rising and is falling, so the absolute value of MRS is
diminishing. This is called the hypothesis of a diminishing marginal
rate of substitution.
20. Formally, the problem is to choose K and L in order to maximize

subject to the constraint

To do this, form the Lagrangean,

where is called the Lagrange multiplier.

The first-order conditions for this maximization problem are

ddKL = QQKL =MRS

QLL< 0 QKK

Q

QL

Q=Q(K,L)

pK⋅K+pL⋅L=C

£=Q(K,L)+λ(pK⋅K+pL⋅L−C)

λ

QK=λ⋅pK

[20.1]

QL=λ⋅pL

[20.2]