Question

The graph below shows a firm's isoquants and isocosts. The firm is initially producing Q-20 with the cost minimizing combination of K and L, where Q is output, Kis capital and Lis labor. Suppose the owner decides to expand production to Q=40. However, he signed a lease on the capital necessary to produce Q=20, which he cannot get out of in the short run. Are the short run total costs of producing Q=40 smaller or larger than the long run total costs of producing Q=40? Briefly explain. 20 19 18 C-$120 17 16 15 C=$60 14 13 12 11 10 9 8 7 6 5 4 Q-40 3 2 Q-20 0 0 1 2 3 4 6 7 8 9 10 11 12 13 15 16

Answer 1

First find the price of labor and capital.

When isocost is represented by C = $60

Y-axis intercept of isocost = (Cost / Price of capital)

=> 15 = ($60 / Price of capital)

=> Price of capiatl = ($60 / 15) = $4

X - axis intercept of isocost = (Cost / Price of labor)

=> 5 = ($60 / Price of labor)

=> Price of labor = ($60 /5)

=> Price of labor = $12

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20 units of output is produced with 6 units of capital and 3 units of labor.

If there is lease signed and units of capital does not changed then firm needs 6 untits of capital and 10 units of labor to produce 40 units of output in short run on the isoquant (Q=40)

Cost of producing 40 units in short run = (Price of labor * Units of labor) + (Price of capital * Units of capital)

=> Cost of producing 40 units in short run = ($12 * 10) + ($4*6) = $144

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In the long run, 40 units of output will be produced at the tangency point of isocost (C=$120) and Isoquant (Q=40), hence firm will use 9 units of capital and 7 units of labor

=> Cost of producing 40 units in long run = (Price of labor * Units of labor) + (Price of capital * Units of capital)

=> Cost of producing 40 units in long run = ($12 * 7) + ($4 * 9) =$120

Shor run cost of producing Q=40 are larger than the long run cost of producing Q=40.