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- 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 manufacturerSuppose 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.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)?
- True or false and explain Suppose a firm’s marginal product of labour is MPL = 10/L, where L is measured in labour hours, the price of the product is $600, and the cost per hour of labour is $30. The firm currently employs 150 labour hours. In order to maximize the firm’s profits in the short run, the manager should increase its labour employment by 40 labour hours.Saxxon Fifth Avenue's production function is given by Q = L+ K. Let w = 1 and r = 2 be the prices of labor and capital, respectively. (a) Find the equation of Saxxon Fifth Avenue's longrun total cost curve. Hint: Note that labor and eapital are perfect substitutes. (b) Suppose capital is fized at 5 units (i.e., K = 5) in the short run. Derive the equation for Sazzon Fifth Avenue's shortrun total cost curve. For simplicity, assume the fxed cost is sunk. (c) In a graph, draw Saxon Fifth Avenue's short-run total cost curve and longrun total cost curve.Explain in details whether the underlined part of statement is true or false.. In short-run production with two inputs where land is a fixed input labor is a variable input, once the marginal products of labors start to diminish, firms in perfectly competitive markets must stop hiring additional labors.
- If a perfectly competitive firm which produces two commodities, has the cost function C = 2Q² + 2Q³ where Q1 and Q2 denote the production level of commodity 1 and commodity 2 respectively. (Note: There are 3 questions in the test regarding the information given above) Which of the following is Hessian determinant of the above problem O a. H|=-16 O b. H|=14 Oc. H|=16 O d. H=-14A9. The diagram below depicts a firm's short-run production function and two isoprofit lines (and B). If the firm's optimal production point has switched from point B to point A, which of the following must have occurred? Output A. B. C. D. B A TB ΠΑ Labour a decrease in the price of labour; an increase in profits an increase in the price of labour; an increase in fixed costs; no change in profits a decrease in the price of labour; a decrease in fixed costs; a decrease in profits an increase in the price of labour; an increase in profitsPlease no written by hand solution 3) Read the Chicago Tribune article titled “At Amazon’s Monee Warehouse, Robot Co-Workers are the New Normal”. Over the long run, it appears that Amazon is working towards min- imizing its operating costs by reallocating its factors of production away from labor and towards robots (i.e., capital). Using the cost minimization model discussed in class, explain how rising relative wages likely incentive Amazon to invest in robots. 4) All else equal, which is steeper, the demand curve for a normal good or the demand curve for an inferior good? Explain.4 5) Assume that the price elasticity of demand (PED) for a firm’s out is PED = −0.75 and that the price of its output is currently at p = $10. (a) How would this firm’s revenues change if it increased its quantity produced by a little bit? Explain. (b) Instead of increasing its quantity produced, how would this firm’s revenues change if it increased its price a bit? Explain.
- Consider the following shortrun production function: Q =100L - L2 where Q is the output level and L is labour input. If the price of output in the market is K.sh 50 and labour costs K.sh 1200 per hour, how many hours would the firm use to maximize profits. What is the profit maximizing level of output?Answer the Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output ifit 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 that labor is the only input used by a perfectly competitive firm. The firm’s production function is as follows: Number of Workers: 0, 1, 2, 3, 4, 5, 6, 7 Units of Output: 0, 7, 13, 19, 25, 28, 29, 29 a. Calculate the marginal product for each additional worker. b. Each unit of output sells for $10. Calculate the value of the marginal product of each worker. c. Compute the marginal profit if the wage is $100 a day. 2. Your enterprising uncle opens a sandwich shop that employs 7 people. The employees are paid $12 per hour, and a sandwich sells for $6. If your uncle is maximizing his profit, what is the value of the marginal product of the last worker he hired? What is that worker’s marginal product?