9781118041581

input combinations along the Q 636 isoquant, (L 6, K 12), (L 10,

K 8), and (L 14.2, K 6), are indicated by points A, B, and C, respec-

tively. A separate isoquant has been drawn for the output Q 800 units. This

isoquant lies above and to the right of the isoquant for Q 636 because pro-

ducing a greater output requires larger amounts of the inputs.

The isoquant’s negative slope embodies the basic trade-off between inputs.

If a firm uses less of one input, it must use more of the other to maintain a

given level of output. For example, consider a movement from point B to point

A in Figure 5.2a—a shift in mix from (L 10, K 8) to (L 6, K 12). Here

an additional 12  8 4 units of capital substitute for 10  6 4 units of

labor. But moving from point B to point C implies quite a different trade-off

between inputs. Here 4.2 units of labor are needed to compensate for a reduc-

tion of only 2 units of capital. The changing ratio of input requirements directly

reflects diminishing marginal productivity in each input. As the firm continu-

ally decreases the use of one input, the resulting decline in output becomes

greater and greater. As a result, greater and greater amounts of the other input

are needed to maintain a constant level of output.

Using the production function, we can obtain a precise measure of the iso-

quant’s slope. The slope of an isoquant is just the change in K over the change

in L (symbolically, K/L), holding output constant. Consider again point B,

where 10 units of labor and 8 units of capital are used. Recall from Example 3

that MPL 40 2L and MPK 54 3K. Thus, at these input amounts, MPL

40 2(10) 20 and MPK 54 3(8) 30. This means that a decrease in

labor of one unit can be made up by a two-thirds unit increase in capital.

Therefore, the slope of the isoquant at point B is:

The general rule is that the slope of the isoquant at any point is measured

by the ratio of the inputs’ marginal products:

Notice that the ratio is MPL/MPKand not the other way around. The greater

is labor’s marginal product (and the smaller capital’s), the greater the amount

of capital needed to substitute for a unit of labor, that is, the greater the ratio

K/L. This ratio is important enough to warrant its own terminology. The

marginal rate of technical substitution (MRTS)denotes the rate at which one

input substitutes for the other and is defined as

For example, at point B, the MRTS is 20/30  .667 units of capital per unit of

labor. At point A (L 6, K 12), the marginal products are MPL 28 and

MRTS¢K/¢L (for Q constant)MPL/MPK.

¢K/¢L (for Q constant)MPL/MPK.

¢K/¢L[2/3 capital units]/[ 1 labor units 4 2/3.

Production in the Long Run 203

c05Production.qxd 9/5/11 5:49 PM Page 203