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The output at a certain factory is Q(K, L) 120K23 L13 units, where K is the capital investment measured in units of $1,000 and L the size of the labor force measured in worker-hours. a. Compute the output if the capital investment is $125,000 and the size of the labor force is 1,331 worker-hours. b. What will happen to the output in part (a) if both the level of capital investment and the size of the labor force are cut in half

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Answer:

a. Compute the output if the capital investment is $125,000 and the size of the labor force is 1,331 worker-hours.

Q(K, L) = 120K²/³ x L¹/³

  • K = $125,000 / $1,000 = 125
  • L = 1,331

Q(125,1331) = 120 x 125²/³ x 1331¹/³ = 120 x 25 x 11 = 33,000 units

b. What will happen to the output in part (a) if both the level of capital investment and the size of the labor force are cut in half

Q(K, L) = 120K²/³ x L¹/³

  • K = 125 / 2 = 62.5
  • L = 1,331 / 2 = 665.5

Q(62.5,665.5) = 120 x 62.5²/³ x 665.5¹/³ = 120 x 15.75 x 8.73 = 16,499.7 units

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