Question

Suppose a small firm has a budget of $30 a day. The firm can purchase a unit of capital at $5 and a unit of labour at $1 a day. The firm's production function is given by Q = K*L, and the firm wishes to produce 45 units of output.

a) Draw a isocost line in a diagram (measure labour along the horizontal axis and capital along the vertical axis). What is the slope of the isocost line?

b) Find the various amounts of labour (L) necessary to produce the output level of 45 units, given, K=1, K=2, K=3, K=4, K=5, K=6, and draw the resulting isoquant in the same diagram as in part (a).

c) What is the cost minimising input combination that the firm should choose?
Briefly explain the condition for this optimum.

d) Suppose that the production process is using 6 units of capital. What should the firm do to minimize costs? Explain your answer in terms of the slopes.

Answer 1

Answer on Question #42370, Economics, Microeconomics

B = $30 a day.

PK = $5, PL = $1 a day.

Q = K*L, Q = 45 units of output.

a) B = PK*K + PL*L

5K + L = 30

The slope of the isocost line is k = 1/5

b) Find the various amounts of labour (L) necessary to produce the output level of 45 units, given, K=1, K=2, K=3, K=4, K=5, K=6, and draw the resulting isoquant in the same diagram as in part (a).

c) What is the cost minimising input combination that the firm should choose?

Briefly explain the condition for this optimum.

B = PK*K + PL*L

5K + L = 30

K*L = 45

L = 30 - 5K

K*(30 - 5K) = 45

5K^2 - 30K + 45 = 0

K^2 - 6K + 9 = 0

(K - 3)^2 = 0

K = 3 units

L = 15 units

d) If production process is using 6 units of capital it should use 45/6 = 7.5 units of labor to minimize costs.