Consider the production function: Q = L14 K 3/4 Does this production show increasing, decreasing, or constant returns to scale? Show your work. I. П. Derive an expression for the marginal product of labor III. Show mathematically whether the marginal product of labor is increasing, decreasing, or constant, as the labor input is increased.

Consider the production function: Q = L14 K 3/4 Does this production show increasing, decreasing, or constant returns to scale? Show your work. I. П. Derive an expression for the marginal product of labor III. Show mathematically whether the marginal product of labor is increasing, decreasing, or constant, as the labor input is increased.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter9: Production Functions

Section: Chapter Questions

Problem 9.2P

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1. Consider the production function Q=K³/ª L/4 Further suppose that capital is fixed at 16 units. Answer the following questions: a. Find Q when L =16 units. What is the output (Q) when L increases to 81 units? e b. Find the average product of labor when L when L increases 81 units? 16 units. What is the average product of labor %3D c. Find the marginal product of labor when L 16 units. What is the marginal product of labor when L increases 81 units? d. Show that doubling all the inputs doubles the output.
Consider this production function. Study hours 2. 4 10 11 12 14 15 or more 13 Grade 20 33 42 50 57 63 69 73 78 81 84 86 88 89 90 1007 90 - 80 70 60 S0 40 30 20 10 Hours of study per day Select one or more: a. The average product of labour is falling as hours of study increase. O b. The marginal product of labour is constant as hours of study increase. O c. The marginal product of labour is rising as hours of study increase. U d. The marginal product of labour is zero beyond 15 hours. Final grade 9-
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1. The following production function is used to produce wheat, q, from capi- tal, K, and labour, L: q = f(K, L) = «³K/3 + B³L/3 a) Describe the role of a and B in this production function. b) Derive the slope of an isoquant for this production function and in- terpret your result. Draw the isoquant in (K L) space, labeling where appropriate. The drawing does not need to be exact, but the curvature needs to be approximately correct. Explain why under- standing the curvature is so important. | c) Does this production function follow the "Law of Diminishing Marginal Returns"? Show your work and explain your answer.
1. Assume that a firm has the following production function: q = L0.5K0.6 d. Determine, both, the marginal product of labour and capital functions (ignore c.). e. Calculate, both, the marginal product of labour and capital when L = 64, K = 32 and interpret your answers. f. Calculate the marginal rate of technical substitution when L = 64, K = 32 and interpret your answer.
If capital and labour are perfect complements then the marginal products of capital and labour are undefined A True Faise Question 16 A firm uses 10 units of labour and 20 units of capital to produce 10 units of output. The marginal product of labour is 0.5. If there are constant returns to scale the marginal product of labour must be 0.25 True B False Question 17 Afirm uses 10 units of labour and 30 units of capital to produce 10 units of output. The marginal product of labour is 05. If there are constant returns to scale the marginal product of labout must be 0.25 A True False
Each extra worker produces an extra unit of output up to 6 workers. After 6, no additional output is produced. Draw the total product of labor, average product of labor, and marginal product of labor curves in a graph. Using the multipoint curve drawing tool, graph the total product of labor curve. Label this 'TP.' Carefully follow the instructions above, and only draw the required object. Then, in the graph in the bottom right: 1.) Using the multipoint curve drawing tool, graph the marginal product of labor curve. Label this 'MP.' 2.) Using both the line drawing tool and the three-point curved line drawing tool each once, graph the average product of labor curve. Label the line segment 'AP₁' and the curved segment 'AP2.' Carefully follow the instructions above, and only draw the required objects. After plotting the final point of your multipoint curve, press the Esc key on your keyboard to end the line. Output per worker 1.2- 1.1- 1- 0.9- 0.8+ 0.7- 0.6- 0.5- 0.4- 0.3- 0.2- 0.1- 0+ 0 2…