5. Selpats produces pens with the production function f(k, l) = 200vkl. The price ofcapital is wk = 40 and the price of labor is wL = 10.(i) Determine the optimal input bundle for producing y pens in the long run and find thelong-run cost function.(ii) Determine the optimal input bundle for producing y = 10,000 pens in the long run.(iii) Now suppose that capital is fixed at k = 25 in the short run. Find the short-run totalcost function and the short-run marginal cost function. Explain the relationship betweenthe short-run and long-run marginal costs when y = 10,000.(iv) Suppose that the price of output is p. Which value of y maximizes short-run profit?р.

Given production function Y=200KLPrice of Capital=40Price of Labor=10

Answered: 5. Selpats produces pens with the…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the production function q = ((K^α)+(L^α))^β. For this function to have diminishing marginal productivities and increasing returns to scale, it must be the case that: a. α>1 & αβ>1; b. α>1 & αβ1; d. α
Suppose that a firm's production function is Q = F(L) = -1L³-30L² + 5,000L. Its marginal product of labor is MPL = -3L2-60L +5,000. a. At what amount of labor input are the firm's average and marginal product of labor equal (other than at L = 0)? Instructions: Enter your answer as a whole number. units. b. Confirm that the average and marginal product curves satisfy the relationship discussed in the text. When the amount of labor input is less than the quantity identified in your answer above, the marginal product of labor is greater than the average product of labor. When labor is greater than the amount identified above, the marginal product of labor is less than the average product of labor.
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A firm can manufacture a product according to the production function Q = F(K, L) = KO.SL0.5. (a) What is the average product of labor, AP, when the level of capital is fixed at 36 units and the firm uses 16 units of labor? (b) What is the marginal product of labor, MP, when capital is fixed at 36 units?
A firm's short-run production function is displayed in the figure below. The firm's variable input is labor. Assume that when Əq (L) 4 units of labor are being used, the slope of the short-run production function reaches its maximum value of 7 (i.e. ƏL 7 when L = 4). As the level of labor increases beyond L = 4, the short-run production function is always becoming less Əq (L) steep (i.e. it is concave). The slope of the production function is equal to 5 when L = 5 (i.e. = 5 when L = 5). If 6 units ƏL Əq (L) of labor are being used, the slope of the production function is 3 (i.e. = 3 when L = 6). If the firm has to pay a wage ƏL of $15 (w = 15) for each unit of labor and can sell each unit of output at a price of $3 (p = 3), what is the firm's profit- maximizing level of output (q) in the short-run? 9₁ 18 14 8 0 4 5 6 q(L) L 7 / 8
2. Consider a production function: x(l, k) = Alªk³. Showing all of your work: (a) Under what conditions are the marginal products of labor 1 and capital k positive? (b) Under what conditions are the returns to labor and capital diminishing? (c) Under what conditions are the returns to scale increasing, decreasing, and constant?
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Maize is produced according to the production function q = 100(K°*L°) %3D Starting with a capital input of 4 and a labor input of 49, show that the marginal product of labor and the marginal product of capital are both decreasing. (i) (ii) Compute the marginal rate of technical substitution of labour for capital. (iii) Does this production function exhibit increasing, decreasing or constant returns to scale?
Suppose the production function is given by f(K,L) = 3Kl, where K denotes capital and L denotes labor. The price of capital is 2 TL/machine-hr, the price of labor is 24 TL/person-hr, and capital is fixed at 4 machine-hr in the short run. a) Find the short-run TC, TVC, and TFC curves for this production process. Sketch them on a single graph. Do not forget to label all axes and necessary points on your graph. b) Find short-run ATC, AVC, AFC, and MC curves for this production process. Sketch them on a single figure. Do not forget to label all axes and necessary points on your graph.
Given the following production function: q = 10KL. Assume that w = 25, r = 75 and C = 1200. (a) Mathematically find the minimum cost combination of capital and labour to produce a given level of output.b) Does the production function in part (a) show increasing returns to scale, decreasing returns to scale, or constant returns to scale? Explain. (c) Using isoquants and isocosts, graphically illustrate the effect of an increase in the wage rate, assuming the firm is producing at the same level of output.
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