Question

Answer these MC:

Use the following information to answer the five questions that follow. A firm has the following production function Q=10LK with the corresponding technical rate of substitution K/L. The wage rate of labor is $10 and the rental price of capital is $100.

24. Suppose the firm has 10 units of capital. In the short run, the cost of producing Q=400 is a) 40 b) 400 c) 1000 d) 1040

25. Suppose the firm wishes to produce Q=400 in the long run. How much capital will it employ? a) 2 b) 4 c) 10 d) 20

26. How much will it cost to produce Q=400 in the long run? a) 40 b) 400 c) 1000 d) 1040

27. If the firm doubles its output to Q=800, then the long-run total cost will a) Less than double b) More than double c) Exactly double d) Decrease

28. A firm with the production function Q=2L+4K has a _______ marginal product of labor and ______ returns to scale. a) constant; constant b) constant; increasing c) diminishing; increasing d) diminishing; constant

Answer 1

Total cost (TC) = wL + rK

Cost is minimized when MPL/MPK = w/r

(24) (d)

When K = 10 and Q = 400,

10 x L x 10 = 400

100L = 400

L = 4

Total cost (TC) ($) = 4 x 10 + 10 x 100 = 40 + 1000 = 1040

(25) (b)

MPL/MPK = K/L = $10/$100 = 1/10

L = 10K

When Q = 400,

10 x 10K x K = 400

100K² = 400

K² = 4

K = 2

L = 10 x 2 = 20

(26) (b)

Total cost ($) = 20 x 10 + 2 x 100 = 200 + 200 = 400

(27) (a)

When Q = 800,

10 x 10K x K = 4800

100K² = 800

K² = 8

K = 2.84

L = 10 x 2.84 = 28.4

TC ($) = 10 x 28.4 + 100 x 2.84 = 284 + 284 = 568

Cost is less than double of $400.

(28) (a)

Q = 2L + 4K

MPL = Q/L = 2 (Constant)

Doubling both inputs, new production function becomes

Q1 = 2 x (2L) + 4 x (2K) = 4L + 8K = 2 x (2L + 4K) = 2 x Q

Q1/Q = 2

Since doubling both inputs exactly doubles output, there is constant returns to scale.