Question

The production engineers at Impact Industries have derived the optimal combinations of labor and capital. These are the only two inputs used by Impact. The following chart shows the combinations of labor and capital for three levels of output.

Q is the output level. L* is the optimal amount of labor. K* is the optimal amount of capital. The price of labor is $90 per unit. The price of capital is $15 per unit.

Q

L*

K*

120

5

20

180

7

7

240

12

24

a) If the manager of Impact Industries decides to produce 120 units, what will the long-run total cost and long-run average cost of producing 120 units? Show all calculations.

b) If the manager of Impact Industries decides to produce 180 units, what will the long-run total cost and long-run average cost of producing 180 units? Show all calculations.

c) If the manager of Impact Industries decides to produce 240 units, what will the long-run total cost and long-run average cost of producing 240 units? Show all calculations.

d) Are there economies of scale over the output range 120 to 180? Explain.

e) Are there diseconomies of scale over the output range 180 to 240? Explain.

Answer 1

w = $90; r = $15
Long run total cost, LRTC = wL* + rK*
Aong run average cost, LRAC = LRTC/Q

a. LRTC = wL* + rK* = 90(5) + 15(20) = 450 + 300 = 750
So, LRTC = $750
LRAC = LRTC/Q = 750/120 = $6.25

b. LRTC = wL* + rK* = 90(7) + 15(7) = 630 + 105 = 735
So, LRTC = $735
LRAC = LRTC/Q = 735/180 = $4.08

c. LRTC = wL* + rK* = 90(12) + 15(24) = 1080 + 360 = 1,440
So, LRTC = $1,440
LRAC = LRTC/Q = 1440/240 = $6

d. Yes, there are economies of scale over the output range 120 to 180 as LRAC is decreasing over this range.

e. Yes, there are diseconomies of scale over the output range 180 to 240 as LRAC is increasing over this range.