If a firm uses n inputs (n > 2), what inequality does the theory of revealed cost minimization imply about changes in factor prices (∆wi) and the changes in factor demands (∆xi) for a given level of output?
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If a firm uses n inputs (n > 2), what inequality does the theory of revealed cost minimization imply about changes in factor
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- Consider a firm for which production depends on two normal inputs, labor and capital, with prices w and r, respectively. Initially, the firm faces market prices of w=$5 and r=$15. Assume the firm has a cost budget of $1,500. a. Using the isoquant-isocost model, graphically show the optimal level of employment for this firm in the long run.b. Suppose the government now imposes a minimum wage of $10 for workers. Using the same graph as part a, graphically show the impact of the minimum wage on the optimal level of employment in the long run.c. Refer to the initial situation described in part a. Now suppose a new innovation causes the price of capital to fall to $10. Using a new isoquant-isocost model, graphically show how this change impacts the optimal levels of employment and capital in the long run. Clearly identify the resulting scale and substitution effects caused by the lower cost of capital.A widget manufacturer has a production function of the form q = 6L + 10K . If the wage rate (w) is $4 and the rental rate on capital (r) is $5. Are the returns to scale increasing, constant, or decreasing for this production function? What cost minimization combination of K and L will the manufacturer employs to produce 300 units of output? Suppose that the price of capital increases to $7 per unit. If manufacturer continues to produce 300 units,what cost minimization choice of inputs capital and labor should the firm used. Suppose that the capital input is fixed at K = 3 units in the short run, what is the short run total cost function with qAnswer each of the following questions as either true or false. For a statement to be “true,” it must always be true. If there is at least one case where the statement is not true (or if you need more information to be sure), answer “false.” You must justify each answer with an appropriate explanation or counterexample (which may include a relevant diagram). A firm can make widgets using capital and labor according to the production function f(K,L) = 100L + 0.5K. Denote the wage w and the rental rate on capital r. If r is sufficiently high, the firm will not hire any capital, no matter how many widgets it wants to produce.
- Your company operates with a technology that is characterized by a diminishing rate of technical substitution of labor for capital. Your firm is currently producing 64 units of output using 8 units of capital and 10 units of labor. At that operating point the marginal product of labor is 8 and the marginal product of capital is 4. The rental price of a unit capital is $4 and the wage rate is $2 Is your firm minimizing the total long-run cost of producing the 64 units of output? If so, how do you know? If not, show why not and indicate whether the firm should be using more capital and less labor, or less capital and more labor to produce an output of 64.A firm has production function F(K, L) = 1/4 (K1/2 + L1/2) . The wage rate is w = 1 and the rental rate of capital is r = 3. (a) How much capital and labor should the firm employ to produce y units of output? (b) Hence find the cost of producing y units of output (the firm’s cost function). (c) Differentiate the cost function to find the marginal cost, and verify that it is equal to the value of the Lagrange multiplierA company uses raw materials (M) and energy (E) to produce its product. The marginal product of raw materials MPM = 65 and the marginal product of capital MPg = 40. For each set of per-unit prices of labor and capital given below, determine whether the company is minimizing its total cost. If it is not, determine the direction of factor substitution the firm should make in order to do so. 2.1 P = $11 and Pg = $19 2.2 PM = $28 and Pg = $10
- Suppose that a unit of capital costs three times as much as a unit of labor.If a firm currently has a technology such that MPK =50, MPL =30, how should this firm adjust its capital and labor choices?Consider the long-run cost minimisation problem, with L on the horizontal axis and K on the vertical axis as usual. If the marginal rate of technical substitution for a cost minimizing firm is -8, and the rental rate of capital $5, what is the wage rate for labor? Group of answer choices 0.625 40 0.025 1.6Economics Suppose that production for good X is characterized by the following production function, Q = 4K0.5L0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $12 and the per-unit wage, w, is $20, then the average total cost of using 25 units of capital and 49 units of labor is Multiple Choice $6.25. $9.14.Correct $10.07. incalculable since there is insufficient information to determine the average total costs.
- Why would a profit-maximizing firm expand the use of each input until its marginal revenue product equals the price of the input?Toyota hired you as a manager for its operation in Pakistan. Suppose that the following is the short-run production function at their assembly plant in Pakistan: Q = 7L + 0.6L2 – 0.1L3 where L = Labor (Number of workers), Q is quantity of output (Cars assembled) per week Find the labor value when the MPL is Maximum. Find the value of MPL at its maximum. Assume Toyota Head Office is considering hiring more laborers either at their Quetta plant or alternatively at the Karachi plant. What will be your advice if workers’ marginal product is 400 at wage of Rs=100/hour in Karachi and marginal product is 350 at wage of Rs=800/hour in Quetta? At the end of the year it is expected that output will double with purchase of new equipment and machinery. The long-run production function is estimated to be Q = 60L+ 50K + 200 where L is labor and K is capital. Suppose initial L1 = 15 and K1 = 20 When inputs are…A widget manufacturer has an infinitely substitutable production function of the form q= 2K+L a. Graph the isoquant maps for q=20, q=40, and q=60. What is the RTS along these isoquants? b. If the wage rate (w) is $1 and the rental rate on capital (v) is $1, what cost-minimizing combination of K and L will the manufacturer employ for the three different production levels in part a? What is the manufacturer’s expansion path? c. How would your answer to part b change if (v) rose to $3 with (w) remaining at $1?
