anonymous
  • anonymous
Suppose the production function of a firm is: Q =100L^0.5K^0.5 The price per unit of capital (r) and labor (w) are $40 and $50, respectively. a) Determine the type of returns to scale. b) If the firm is contracted to produce 1118 units of output, determine the quantity of capital and labor that the firm should use to minimize the total costs. c) Using bordered Hessian, prove that the second-order conditions for minimum is satisfied. d) Prove that the combination of capital and labor inputs derived in (b) is the efficient combination of capital and labor [Hint: Efficient combination of K and L is achieved when MPL/MPK= w/r].
OCW Scholar - Principles of Microeconomics
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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anonymous
  • anonymous
Suppose the production function of a firm is: Q =100L^0.5K^0.5 The price per unit of capital (r) and labor (w) are $40 and $50, respectively. a) Determine the type of returns to scale. b) If the firm is contracted to produce 1118 units of output, determine the quantity of capital and labor that the firm should use to minimize the total costs. c) Using bordered Hessian, prove that the second-order conditions for minimum is satisfied. d) Prove that the combination of capital and labor inputs derived in (b) is the efficient combination of capital and labor [Hint: Efficient combination of K and L is achieved when MPL/MPK= w/r].
OCW Scholar - Principles of Microeconomics
katieb
  • katieb
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At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

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