given froduction function F=K^1/4 L^1/16 price of capital and labor are v and w 1)find short run cost function with quantity X, and that there are Y amount of capital purchased 2)find the long run contigent demand for capital and labor
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given froduction function
F=K^1/4 L^1/16
price of capital and labor are v and w
1)find short run cost function with quantity X, and that there are Y amount of capital purchased
2)find the long run contigent demand for capital and labor
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- The production function for good X in the table below exhibits increasing marginal returns to capital over what outout range? Production Function for Good X Choose Multiple Choice: Between o and 1,524 Between 2,391 and 3,048 Between o and 2,991 Between 3,016 and 2,945 L* K MPx=(AQ/AK) AP=(Q/K) Marginal Product of Capital Average Product of Capital Labor Capital Output 10 57 5.7 5.70 20 324 26.7 16. 20 30 657 33.3 40 1,072 41.5 26.80 se 1,524 45.2 30.48 60 1,976 45.2 32.93 70 2,391 41.5 34.16 se 2,724 33.3 34.05 9e 2,991 A 33.23 1ee 3,848 5.7 30.48 9. 11e 3,016 -3.2 27.42 120 2,945 -7.1 24.54Answer 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?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
- A firm can manufacture a product according to the production function Q = 2(K)1/4 (L)3/4 where K represents capital equipment and L is labor. The company has already spent $10,000 on the 4 units capital. a. Please show the expression for the average product of labor, APL and the marginal product of labor, MPL. If workers at the firm are paid a competitive wage of $100 and the product is sold for $200 each, what is optimal level of labor usage and what is the maximum profit?Consider a firm that produces output using industrial robots and skilled labor. Suppose it is the case that a reduction in the price of industrial robots causes the firm's labor demand curve for skilled workers to increase (i.e., to shift to the right). This implies that: There is diminishing marginal product of robots. O There is diminishing marginal product of skilled labor. O Robots and skilled labor are complements. O Robots and skilled labor are substitutes. The unit cost of skilled labor is below the unit cost of robots.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.
- 1) A firm uses two inputs K and L of capital and Labor respectively, to produce a single output Q according to the specific type of production function: Q= F (K, L) =k°L". a,b >0 The prices of capital and labor are rand w, respectively. (1) Find the cost minimizing input of capital (K) (1i) Find the cost minimizing input of Labor (L) Note: These are also called the demand functions of K and L. (li) Write down the cost function of the firm.The production function for good X in the table below exhibits increasing marginal returns to capital over what outout range? Production Function for Good X Choose Multiple Choice: Between o and 1,524 Between 2,391 and 3,048 Between o and 2,991 Between 3,016 and 2,945 L* K MPK=(AQ/AK) AP=(Q/K) Marginal Product of Average Product of Capital Labor Capital Output Capital 10 57 5.7 5.70 20 324 26.7 16.20 30 657 33.3 40 1,072 41.5 26.80 se 1,524 45.2 30.48 6e 1,976 45.2 32.93 70 2,391 41.5 34.16 se 2,724 33.3 34.e5 9e 2,991 A 33.23 100 3,048 5.7 30.48 11e 3,016 -3.2 27.42 120 2,945 -7.1 24.54
