Suppose that firm uses 3 units of labor (L) with 4 units of capital (K) in fixed proportion. Which of the following is correct? The law of diminishing MRTSLX holds and thus Lagrange multiplier method is applicable MRTSLK is not well defined and thus Lagrange multiplier method is applicable The law of diminishing MRTSLK holds and capital and labor are perfect complements. MRTS, x is not well defined and thus Lagrange multiplier method is not anlicahle

Suppose that firm uses 3 units of labor (L) with 4 units of capital (K) in fixed proportion. Which of the following is correct? The law of diminishing MRTSLX holds and thus Lagrange multiplier method is applicable MRTSLK is not well defined and thus Lagrange multiplier method is applicable The law of diminishing MRTSLK holds and capital and labor are perfect complements. MRTS, x is not well defined and thus Lagrange multiplier method is not anlicahle

Economics (MindTap Course List)

13th Edition

ISBN:9781337617383

Author:Roger A. Arnold

Publisher:Roger A. Arnold

Chapter21: Production And Costs

Section21.3: Production

Problem 3ST

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Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (4) and the amount of capital used (C) by the following function. S- 20100.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. Min s.t. -55,000 L.C20 (b) Solve the optimization problem you formulated in part (a). (Hnt: When using Excel Solver, start with an initial L>O and Co. Round your answers to the nearest integer.) at (L. C) =
Units of Units of Labor, L Capital, K 1 2 3 4 1 50.0 66.7 75.5 80.0 2 66.7 100.0 120.0 133.3 3 75.0 120.0 150.0 171.4 4 80.0 133.3 171.4 200.0 This table illustrates a production function because capital and labor long-run; are used in equal increments short-run; can both be varied O long-run; can both be varied short-run; are used in equal increments