Final output in the economy is pro-duced using capital K and labor L. The production function is:Y = ĀK/ L^/5Assume that the supply of all inputs are exogenous and equal to L and K. Perfectly compet-itive firms are price-takers and choose how much capital and labor to demand by maximizingprofits. Let w and r denote the wage and rental rate of one unit of labor and capital respec-tively. (a) What are the 5 endogenous variables in this model? Also list the exogenous variablesand the parameters and provide a brief explanation of each.(b) Show the first order conditions for labor and capital. Explain the intuition for whythese conditions are optimal for a firm. Are there diminishing returns to these inputsin this model?

Endogenous variables are those variables which are determined with relation to other variables in a…

(a) What are the 5 endogenous variables in this model? Also list the exogenous variables and the parameters and provide a brief explanation of each. I (b) Show the first order conditions for labor and capital. Explain the intuition for why these conditions are optimal for a firm. Are there diminishing returns to these inputs in this model?

(a) What are the 5 endogenous variables in this model? Also list the exogenous variables and the parameters and provide a brief explanation of each. I (b) Show the first order conditions for labor and capital. Explain the intuition for why these conditions are optimal for a firm. Are there diminishing returns to these inputs in this model?

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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***PLEASE NOTE - An answer is NOT needed for parts A, B and C; these are included to assist with answering part D. Only an answer for part D is required, but it is derived from the previous answers*** Given: A farmer raises peaches using land (K) and labor (L), and has an output of ?(?,?)= ?0.5?0.5 bushels of apples. a. Find several input combinations that give the farmer 6 bushels of apples. Sketch the associated isoquant on a graph, with L on the x-axis and K on the y-axis. b. In the short run, the farmer only has 4 units of land. What is his short-run production function? Graph it for values of L from 0 to 16, with L on the x-axis and output on the y-axis. What is the name of the slope of this curve? c. Assuming the farmer still only has 4 units of land, how much extra output does he get from adding 1 extra unit of labor if he is already using only 1 unit of labor? How much extra output does he get from adding 1 extra unit of labor if he is already using 4 units of labor?…
F. None of the above 4) Please indicate whether the following production function has the characteristic of CRS, IRS and DRS. (b) F(K, L)=[aKP +(1-a)Le ]1/e, (1>a>0, 1>p) 1. CRS 2. IRS 3. DRS 4. None of the above
1. Do the following production functions exhibit increasing, constant of decreasing returns to scale in K and L? Explain/interpret your answer. (a) Y = KL (b) Y = KL (c) Y = K³L¹
Answer the given question with a proper explanation and step-by-step solution. Please use graphs to illustrate answers as well as explain the answer please!!!!
Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output if it the firm decides to triple both the amount of labor and capital?2. State the optimization problem of the firm.3. Solve for the formulas of the Marginal Product of Labor (MPL), and Marginal product ofCapital (MPK)4. Using your knowledge of the tangency condition in Producer’s theory, find the combinationof K and L that the firm should use to produce the maximum possible output. Do not solvethe problem using the Lagrangian method.Note: The tangency conditions just states that the slope of the production function must beequal to the slope of the isocost function.5. What is the maximum possible output that the firm could earn given the constraint it faces?
Suppose the representative firm of the economy has a production function of the form F(K, N) = AKO.5N 0.5 The marginal product of labor is then given by MP N = 0.5AK0.5N –0.5 . The current capital 3. stock is K = 40. (a) Holding fixed capital at 40, draw a graph of output as a function of labor. What are some important features of this graph? (b) If A = 4 what is the Labor Demand Curve, ND(w), as a function of the real wage w? (c) Suppose labor is supplied inelastically with NS(w)= 10. What is the equilibrium wage w, employment level N, and full employment output Y ? (d) Suppose that productivity unexpectedly increases to A = 6. What is the new equilibrium wage w, employment level N, and full employment output Y ? (e) Depict this change graphically. Denote the original labor supply and demand curves by NS and ND respectively. Denote the new labor demand curve after the productivity shock by ND' . (Does not need to be to scale).
The long run is defined as A) the period of time when all resources are variable. B) any time after one year. C) the period of time when most (more than 50 percent) resources are variable. D) the period of time when all resources are fixed.
The technically efficient combination of two products a busniness can produce in the current period given its existing resources and technology is: (a) The production possibilities frontier (b) The marginal rate of production transformation (c) The least cost combination of two products (d) The marginal physical product
Production. Assume a production with two variable inputs (L, K). Show graphically the following and explain: (a) fixed-proportions production function (b) inputs are perfect substitutes
The law of diminishing marginal returns states: Select one: a. As a firm uses more of a variable factor of production, total product (TP) eventually decreases. b. As the size of a plant increases, marginal product (MP) eventually decreases. c. As a firm uses more of a variable factor of production, its average cost (AC) eventually decreases. d. As a firm uses more of a variable factor of production, with a given quantity of the fixed factor of production, the MP of the variable factor eventually decreases.
10. An isoprofit curve will have which of the following properties? (a) If an extra unit of capital is used, output will rise by AQ = MP₁AL (b) If an extra unit of capital is used, the value of the extra output produced would be PMPKAK (c) If profits are being maximised, then profits can only be increased by using a different combination of inputs (d) If an extra unit of capital is used, the cost of producing the extra output produced will be rAKMPK (e) Profit maximisation will occur where the marginal rate of substitution is greater than the ratio of prices.