3. Assume the production function is Q = 4K0.5L0.5, and K = 4 in the short run. Find the marginal product of labor. Using derivatives, show that the production faces diminishing marginal return to labor. If the market wage is w, express the optimal number of labor (L) in terms of w. Are they positively or negatively related, and why?

3. Assume the production function is Q = 4K0.5L0.5, and K = 4 in the short run. Find the marginal product of labor. Using derivatives, show that the production faces diminishing marginal return to labor. If the market wage is w, express the optimal number of labor (L) in terms of w. Are they positively or negatively related, and why?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Solve the exercise with a production function with diminishing returns: In this case, production increases as workers are added, but it increases less and less. a) Calculate the amount of production for each worker and add it to the table, taking into account the production function K 10 1 9. 2 8 3 7 4 6. 4 7 3 8 2 9 10 b) Explain why the production function exhibits diminishing returns to scale.
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Assume the production function is given by: f(x1, x2) = (2x9.253.x5)³. What is the absolute value of the technical rate of substitution of *1 on x2? Select one: b. 5 C. 6x9.5 27 25 d. 3x2 a9.75 x 40.5 e. None of the above Your answer is incorrect. Notice that f(x1,x2) = (3x9.255x5)3 = 8x9.7527x5 8a 5 x0.75 z9.26 x 27x1.5x25 J#2 6x2 x1×40.5 TRS = The correct answer is: None of the above
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Assume that the inputs are the perfect complement, if the price of one input (i.e wage rate) has increased, could we minimise cost by using less labour and more capital?
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The production function has the following form q= K + 2L where q is output, K is capital input and L is labor input. If the prices of inputs are w=5 and v=2 what is the cost minimizing (or efficient) combination of inputs to produce 6 units of output?
What is the marginal physical productivity (MPP) of the inputs given the function Q=18x21+2x1x2+2x22 ? Select one: а. МPPx1336х1+2x1MPPx2-2x1+4х1 b. МPPX1336x1+2x1MPPx2-2x2+4х2 С. MPPX1=36+2x2+2MPP×2=2x1+4x2 d. MPPX1=36x1+2×2MPPX2=2x1+4x2
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Which of the following statements is (are) TRUE?I. If labor and capital are perfect substitutes in production, the isoquant is a downward-sloping line.II. If a company needs to use inputs in fixed proportion such that the capital to labor ratio is always 2, the firm's isoquants are L-shaped.III. If the production function is given by Q = min(14, 7), the firm can produce, at minimum, 21 units of output. IIII, II, and IIIII and II Note:- Do not provide handwritten solution. Maintain accuracy and quality in your answer. Take care of plagiarism. Answer completely. You will get up vote for sure.
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