9781118041581

Production in the Long Run 201

assume to the contrary that the ratios in Equation 5.4 differ. As an example, let

MPLbe 30 units per hour and PLbe $15 per hour; in turn, let MPKbe 60 and

PKbe $40. Then MPL/PL30/15 2 units per dollar of labor, while MPK/PK

60/40 1.5 units per dollar of capital. Because labor’s productivity per dollar

exceeds capital’s, it is advantageous for the firm to increase its use of labor and

reduce its use of capital. The firm could maintain its present output level by

using two extra units of labor in place of one fewer unit of capital. (The 60 units of out-

put given up by reducing capital is exactly matched by (2)(30) 60 units of

output provided by the additional labor.) The net savings in total cost is $40

(the saved capital cost) minus $30 (the cost of two labor hours), or $10. If one

input’s productivity per dollar exceeds another’s, the firm can produce the

same output at lower cost by switching toward greater use of the more pro-

ductive input. It should continue to make such switches until the ratios in

Equation 5.4 come into equality. At that point, the firm will have found its least-

cost input mix.

CHECK

STATION 4

Suppose that initially MPL/PLMPK/PK. Explain why the ratios will move toward equal-

ity as the firm switches to more labor and less capital.

EXAMPLE 3 A manufacturer of home appliances faces the production

function Q 40L L^2 54K 1.5K^2 and input costs of PL$10 and PK

$15. Thus, the inputs’ respective marginal products are

and

We know that the firm’s least-cost combination of inputs must satisfy MPL/PL

MPK/PK. This implies that

Solving for L, we find L K 2. This relation prescribes the optimal combina-

tion of capital and labor. For instance, the input mix K 8 and L 10 satisfies

this relationship. The resulting output is Q (40)(10) (10)^2 (54)(8) 

1.5(8)^2 636. The firm’s total input cost is TC ($10)(10) ($15)(8) 

$220. In other words, the minimum cost of producing 636 units is $220 using

10 units of labor and 8 units of capital.

[402L]/10[543K]/15

MPK Q/ K 54 3K.

MPL Q/ L 40 2L

Winning in

Football and

Baseball

The National Football League (NFL) lives by the golden rule of team parity.

Large-market teams in New York, Miami, or Dallas command greater revenues

from ticket sales, concessions, TV and cable contracts, team products, and

promotional deals. But small-market teams in Green Bay, Kansas City, and

Cincinnati can nonetheless field winning teams. To achieve parity, the NFL

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