2. Assume that the production of output is given by Q(K,L)=K02106, where K = quantity ofcapital and L= quantity of labor (number of workers). Let P, r, and w be the price of output,rental rate of capital, and wage rate, respectively. Assume P = 10, r = 2, and w = 8.(a) Find the short-run and long-run demands for labor.(b) Are the short-run and long-run demand curves for labor downward sloping? Explain.(c) Findw OLfor both the short run and long run demands for labor. Interpret the results.Low(d) Suppose the government offers a 50% subsidy on capital expenditures. Find the short-run and long-run demands for labor. Interpret the results.

The objective of the question is to determine the short-run and long-run demands for labor given the…

Answered: 2. Assume that the production of output…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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1. Consider a static labour supply model for an individual. Assume that the person works a positive number of hours. Assume that the utility function is of the following form: U=x0.5 +8(T-h)(0.5) where x is consumption and his hours of work, and 8 is a parameter of the utility function. The person is paid a wage of w for each hour worked. The person has no other source of income other than employment earnings. Assume that the price of x equals 1. a) Specify the utility maximization problem, write down the Lagrange function, and solve for the first order conditions. b) Solve for the MRS condition between consumption and hours of work. c) Assume that 8=2 if the person has a child living at home, and 8=1 otherwise. Explain (and either show mathematically or graphically) how this will affect the optimal number of hours of work of the person.
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XYZ Co. operates in a competitive market. Its production function is q = L^α K^β . The firm takes the wage, rental rate and price as given. a) Derive the firm's conditional labor and capital demand functions. b) How does the firm react to an increase in the wage rate? c) Derive the firm's cost function.
Assume a firm has the following short-run production function: q(L) = L+6L2-1/2L3 If this firm is going to maximize profits in the short-run by producing a strictly positive level of output (q>0), what is the lowest level of labor (L) they would employ? A.) Minimum L=?
= $30 and wage rate Let the production function be given by: q = 10(L^2)K, with rental rate v W = $20. 1. How much K and L are employed to produce 11,250 units of output? 2. Suppose that the firm wants to increase output to 19, 440 units of output, now how much K and Lare employed to produce with minimize cost? 3. Suppose that in the short run the amount of capital is fixed at K = 10, what is the firm short run fixed cost? 4. Suppose that in the short run the amount of capital is fixed at K = 10, what is the short run total cost of producing 900 units of output?
Consider the following production function: q=100L0.8K0.4 Currently the wage rate (w) is $2.00 and the price of capital (r) is $4.00. If the firm is using 100 units of capital in production, how much labor should be employed to minimize costs? Labor input = units. (Enter a numeric response using a real number rounded to two decimal places.)
Given the production function, Y = AK "L(¹-a) assume that a = 1/3. The labor supply equation is LS = 60*w - R In TABLE ONE, each column represents a labor market in medium-run equilibrium. In column two, an increase in on-the-job-search (OJS) has shifted labor supply to the right. In column three, workers' awareness of higher productivity has shifted labor supply back to the left. 1. Complete TABLE ONE. [Round w to two decimal places.] W = 2/3Y L TABLE ONE Y A K L W R (u) 1 (a) (b) 6000 398 8.23 (c) 21 2 5444 (d) 6000 (e) 8.54 70 (u) = Bw-L-R 3 5.3 6000 415 (h) 75 (1)
Assume that the production function for competitive firm is given by F(L)=9L1/3, where L is the number of units of labour used in the production process. Suppose that the cost per unit of labor is $3 and the price of output is $9 per unit, how many units of labor will the firm hire?
Solve the attachment.
If a firm has the the production function F(K, L) = min(3K, 4L) What is its contingent demand for labor, Le(w, v, q)? q 4w+3v q (b) 3w+4v (c) 1/31 (d) 1/1 (e) W when w 4v 3
Consider the following production function: Q = 3K + 6L where K is Capital, L is Labour and Q represents output. What kind of production function (perfect substitutes, imperfect substitutes, perfect complements etc) does this equation represent? Explain your answer clearly.
A firm's production function is f(x₁, x₂) = (min{x₁,5x2})¹/². If the price of the first factor is w₁ = 20, then the = 5 and the price of the second factor is w2 supply function is given by y = 9p y = min{5p, 8p} y=p/18 Oy=pmax{w₁, 5w₂}² y = p min{w₁, 5w₂}²

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