4. A firm producing cars. The production function for shoes (Q) is: Q = K2 L"2 where K is capital and L islabor. The price of K is $8 and the price of L is $2.a. What type of production function is this?b. Does this production function exhibit constant, increasing or decreasing returns to scale?Explain.c. What is the average product of capital, average product of labor, marginal product of capital,and marginal product of labor?d. Does capital obey the "law of diminishing returns?" Explain.e. Suppose that firm wants to produce 144 cars, how much K and L should be employed tominimize costs?f. What is the minimum cost of producing 144 cars?g. Now suppose that firm is faced with the same problem as in (e and f) except that firm has afixed amount of K. In fact, K = 16. How much L should be employed to minimize costs, andwhat is the total cost.

A firm producing cars. The production function for shoes is : Q= K1/2 L1/2 .…

shoes (Q) irm producing car labor. The price of K is $8 and the price of L is $2. production vhere K is capital and . a. What type of production function is this? b. Does this production function exhibit constant, increasing or decreasing returns to scale? Explain. c. What is the average product of capital, average product of labor, marginal product of capital, and marginal product of labor? Does canital obev the "law of diminishing returns?" Explain

shoes (Q) irm producing car labor. The price of K is $8 and the price of L is $2. production vhere K is capital and . a. What type of production function is this? b. Does this production function exhibit constant, increasing or decreasing returns to scale? Explain. c. What is the average product of capital, average product of labor, marginal product of capital, and marginal product of labor? Does canital obev the "law of diminishing returns?" Explain

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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3. The Chipper Cookie Company's output is given by the Cobb-Douglas Production function P = 120L0.7 K0.3, where P is the number of units produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 600 and K = 600? b. Find the marginal productivities. c. Evaluate the marginal productivities with L= 600 and K = 600. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $1200 then there is a constraint L+ K = 1200. Use Lagrange multipliers (^) to find the values of L and K that will maximize production and find the maximum production f. Find and interpret 2 for this problem. only need part e and f!
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.2. Tiva has a crafts store that makes jewelry using beads (B) and copper (C). Her productionfunction for jewelry is given byQ = B0.4C0.4Suppose she can buy beads and copper at prices PB and PC, respectively.(a) Calculate Tiva’s marginal rate of technical substitution between B and C.(b) Does this production function have increasing, constant, or decreasing returns to scale?Explain. (c) Set up the cost minimization problem you would use to calculate Tiva’s cost functionC(Q) in Lagrangian form. (Note: You do not need to solve it or derive first orderconditions.Suppose Tiva decides to branch out in her jewelry offerings by getting a 3D printer. The costof producing new 3D printed jewelry isC(Q) = 25 + Q24For the rest of this problem, assume Tiva can produce fractions of jewelry, don’t worry aboutrestricting your answers to whole numbers.(d) Compute Tiva’s marginal cost and average cost of production for 3d printed jewelry.(e) Explain why she will shut down when the market price falls…
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