Question 4 4(a) The following equation is associated with the Cobb-Douglas production function: AY/ Y = a AK/ K + (1- a) AL/ L + AA/ A (where Y = output; K = capital stock; L = labour force; A = total factor productivity and a = capital's share of income). Derive the above equation from first principles. 4(b) Explain the meaning of the equation in dart (a) and its significance in production theory. 4(c) Use diagrams and mathematical analysis to explain how the Golden Rule level of Capital (k*gold) can be derived in the Solow growth model (assume you are dealing with a closed economy without a Government). Please include investment, population growth and advances in technology in the model. 4(d) Is the Golden Rule level of Capital the ideal steady state for the economy? Exploin

Question 4 4(a) The following equation is associated with the Cobb-Douglas production function: AY/ Y = a AK/ K + (1- a) AL/ L + AA/ A (where Y = output; K = capital stock; L = labour force; A = total factor productivity and a = capital's share of income). Derive the above equation from first principles. 4(b) Explain the meaning of the equation in dart (a) and its significance in production theory. 4(c) Use diagrams and mathematical analysis to explain how the Golden Rule level of Capital (k*gold) can be derived in the Solow growth model (assume you are dealing with a closed economy without a Government). Please include investment, population growth and advances in technology in the model. 4(d) Is the Golden Rule level of Capital the ideal steady state for the economy? Exploin

Managerial Economics: Applications, Strategies and Tactics (MindTap Course List)

14th Edition

ISBN:9781305506381

Author:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Publisher:James R. McGuigan, R. Charles Moyer, Frederick H.deB. Harris

Chapter7: Production Economics

Section: Chapter Questions

Problem 9E

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Returns to scale in production: Do the following production functions exhibitincreasing, constant, or decreasing returns to scale in K and L? (Assume Ais some fxed positive number.)(a) Y = K1/2L1/2(b) Y = K2/3L2/3(c) Y = K1/3L1/2(d) Y = K + L(e) Y = K + K1/3L1/3 (f ) Y = K 1/3L2/3 + A (g) Y = K 1/3L2/3 − A
10K L%. 1). Consider the production function Q = (a) What is the output when K = 100000 and L = 243? (b) Use the marginal analysis to estimate Q(99995, 243) and Q(100000, 245). (c) Use a calculator to compute these two values of Q to three decimal places and compare these values with your estimates in (b). (d) How big must AL be in order for the difference between Q(100000, 243+AL) and its linear approximation Q(100000, 245) + -DAL, to differ by more than two units?
. MTN 3G < Û iii. iv. 12:01 You 30/12/2023, 00:17 Question 5 a) You are a manager for Herman Miller, a major manufacturer of office furniture. You recently hired an economist to work with engineering and operations experts to estimate the production function for a particular line of office chairs. The report from these experts indicates that the relevant production function is Q = 2K0.5 10.5 Where: K represents capital equipment and L is labour. Your company has already spent a total of $9,000 on the 9 units of capital equipment it owns. Due to current economic conditions, the company does not have the flexibility needed to acquire additional equipment. Workers at the firm are paid a competitive wage of $100 per day and chairs can be sold for $400 each. i. ii. и @ 30% All Media Is the firm operating in the short-run or the long-run? Explain. What is your profit-maximizing level of output and labour usage? What is your maximum profit resulting from your answer in (ii)? If shareholders…
(a) What do we mean by "returns to scale"? (b) In this context, list and explain the three different types of returns to scale that a firm could experience in production.
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EXAMPLE 1.2 Consider the following data of a company for the year 1997:Sales = $ 1,20,000Fixed cost = $ 25,000Variable cost = $ 45,000Find the following:(a) Contribution
The Return of Detroit City: Enpar manufactures engine parts for Ford using steel as an input. Enpar operates two plants, one in Detroit, MI and one in Greenville, SC. The production functions for the two Enpar plants are: Detroit: QD=20SD -0.25 SD² Greenville: QG= 53SG - 0.5 SG² where QD and QG are the outputs of engine parts (in units) from the Detroit and Greenville plants, respectively. Sp and SG are the amounts of steel for the two plants. The firm has 159 units of steel available. How much steel should be sent to Detroit? Enter as a value. ROUND TO THE NEAREST WHOLE NUMBER.
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The Cobb-Douglas production function is commonly used to model the production of an output, based on two or more inputs. In this project, we will consider the inputs of capital and labour: • Capital, denoted by K, is the business's capital expenditures over a given time period. This could include money spent on space or equipment rental, maintenance, supplies, etc. • Labour, denoted by L, is the number of worker-hours used over the same time period. The output is the quantity of items produced, Q over the same time period. The key assumptions leading to the Cobb-Douglas production function are as follows. Assume A1 and A2 are true throughout this individual project. A1. If the labour is held fixed, a very small relative change in labour K, AK should always lead to a corresponding relative change in Q that is proportional to the relative change in labour. In other words, AK AQ Q (1) = CE K for some constant a > 0. A2. If the capital expenditures are held fixed, a very small relative…
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