along the isocost line from point A in either direction lowers output.
Thus, either move would raise cost per unit.
As shown in Figure 8A-4 , the lowest attainable cost of producing 6 units
is $24, and this requires using 12 units of labour and 3 units of capital.
The least-cost position is given graphically by the tangency point between the isoquant and
the isocost lines.The slope of the isocost line is given by the ratio of the prices of the two
factors of production. The slope of the isoquant at any point is given by
the ratio of their marginal products. When the firm reaches its cost-
minimizing position, it has equated the price ratio (which is given to it by
the market) with the ratio of the marginal products (which it can adjust
by changing its usage of the factors). In symbols,
This is the same condition that we derived in the text (see Equation 8-
2 ), but here we have derived it by using the isoquant analysis of the
firm’s decisions. [ 20 ]
Note the similarity of this condition for a cost-minimizing firm
to Equation 6-2 , where we saw how utility maximization for a consumer
requires that the ratio of marginal utilities of consuming two products
must equal the ratio of the two product prices. Both conditions reveal the
MMPPL =
KpL
pK