Not use ai please A competitive firm employs labor and capital to produce its product according toL03K0.5. The market price is $100, the market wage is $10, and thethe production function y =rental rate for capital is $15.a. What is the marginal product of labor?b. Find the profit-maximizing levels of Land K.c. Show that profit is indeed maximized at L* and K* (i.e. Use the Hessian todemonstrate that the relevant second-order condition holds).

To determine the marginal product of labor (MPL), we examine how output changes when the level of…

Answered: A competitive firm employs labor and…

Exploring Economics

8th Edition

ISBN:9781544336329

Author:Robert L. Sexton

Publisher:Robert L. Sexton

Chapter11: The Firm: Production And Costs

Section: Chapter Questions

Problem 15P

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The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3 K1/3, where P is the number of anvils produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. C. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. MacBook Pro urses/34419/files/5014304?wrap=1
Please Answer with the step from sub parts 4 a,b,c. I need in 30 minutes thank u
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Tom Petersen is considering renovating bar stools at Dreamland. The productionfunction for new bar stools is given byq= 0.5L0.5where q is the number of stools produced during the renovation week and l represents thea number of worker hours employed during the period. The firm is a price taker for both bar stools(which sell for P) and workers (which can be hired at a wage rate of w per hour).a. What is the cost function for this firm C(w,q)?b. What is the supply function for bar stools q(P,w)?c. What is the profit function for this firm (P,w)?d. What is the firm’s demand function for labor function L(P,w)?
3. a. b. C. d. Don Corneo's firm has a Cobb-Douglas production function given as: Y = AK 0.5 N 0.5 Show that the production function exhibits Diminishing returns with respect to Capital, K. Show that the production function can exhibit Constant returns to scale Estimate the output per worker, N. Calculate the elasticity of substitution, o.
Suppose that labor is the only input used by a perfectly competitive firm.The firm's production function is as follows:a.Calculate the marginal product for each additional worker.b.Each unit of output sells for $10.Calculate the marginal product for each additional worker.cCompute the demand for schedule showing the number of workers hired.
New taskFor a producer under complete competition, the following production function applies. Q = F (K, L) = KL where Q is the size of production, K is the size of the capital investment and L is the amount of labor. Assume that the price of capital, r, is 5 and that the salary, w, is 10. a) Assume initially that the capital is locked at 4 units. How much labor will the producer use to produce 50 units of the final product? What will be the total cost of producing these 50 units? b) For the production function above applies The marginal product for work MPL = K The marginal product for capital MPK = L Enter the cost-minimizing combination of capital and labor in the production of 50 units. Also enter the size of the costs. c) Write down the equation for the isocost line for the manufacturer
2. The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3K1/3, where P is the number of anvils produced when L is the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. c. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. Only need paVAS e and fl
depending on the stages of production(increasing returns, diminishing returns, negative returns) can a rational firm limitits production within satge I, and explain the relationship between average and marginal product of labour.
A small specialty cookie company, whose only variable input is labor, finds that the average worker can produce 100 cookies per day, the cost of the average worker is $32 per day, and the price of a cookie is $1.00. Is the firm maximizing profit? The firm A. is not maximizing profit because the marginal revenue product of labor is greater than the wage. B. is not maximizing profit because the marginal revenue product of labor is less than the wage. C. is maximizing profit because the marginal product of labor is greater than the wage. D. is not maximizing profit because the price of the output is not equal to the wage. E. is not maximizing profit because the marginal product of labor is greater than the wage.
Exercise 11 Question Help Suppose that a firm's production function is: 112- q = 10L0.5K0.5 98- Its marginal product functions are: 84- MP, = 5KO.5/L0.5 - 0.5g/L 70- and MPK = 5L0.5/K.5 - 0.5g/K. 56- The cost of a unit of labor, w, is $50 and the cost of a unit of capital, r, is $50. Isoquants for output of 140 and 280 are illustrated in the figure to the right. 42- 28- Initially, the firm is producing 140 units of output and has determined that the cost-minimizing quantities of labor and capital are 14 and 14, respectively. 14- -q= 280 q= 140 98 Suppose now that the firm wants to increase output to 280 units. If capital is fixed 0- in the short run, how much labor will the firm require? 70 84 L, Units of labor 14 28 42 56 112 The firm will now require units of labor. (Enter your response rounded to two decimal places.) K, Units of capital

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