Consider the production function given by Y= altbK. The prices of labor and capital are wloand wK, respectively. a. Find the conditional input demand for L and K b. Find the cost function C. How will an increase in wk affect the labor demand in a? Show graphically
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- What is the difference between a fixed input and a variable input?Will decrea n he fong run, assume a firm uses both labor and capital to produce 25 units of output. The marginal product of the last unit of labor being employed is 100; the marginal product of the last unit of capital being employed is 500. The wage rate of labor is $10. If the firm is minimizing the cost of producing 25 units of output, what must be the unit price of capital?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 = 6 and r = 4. These prices then shift to w = 4 and r = 2.a. In which direction will the substitution effect change the firm’s employment and capital s tock?b. In which direction will the scale effect change the firm’s employment and capital stock?c. Can we say conclusively whether the firm will use more or less labor? More or less c apital?
- If capital and labour are perfect complements then the marginal products of capital and labour are undefined A True Faise Question 16 A firm uses 10 units of labour and 20 units of capital to produce 10 units of output. The marginal product of labour is 0.5. If there are constant returns to scale the marginal product of labour must be 0.25 True B False Question 17 Afirm uses 10 units of labour and 30 units of capital to produce 10 units of output. The marginal product of labour is 05. If there are constant returns to scale the marginal product of labout must be 0.25 A True FalseAnswer 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?1. A general form of the Cobb-Douglas production function is given by Q = AKº L³ where A, a, 3 are positive constants. A. Solve for the marginal products of capital and labor. B. For what values of a and 3 will the production function exhibit diminishing marginal returns to capital and labor? C. Solve for the marginal rate of technical substitution.
- Suppose we have a produ ction function for wheat Q = KL - 0.8K2 - 0.212 A. Given K = 10 Units, calculate the level of labourth at the AP reaches max andh ow Much wheatis produced at that point B. Given K = 10 at what level of labour outputreaches maximum C. How mu ch Ilevel of labor should the company hire in order to be efficient |QUESTION 2 K 6 isocost 3 L Based on the information in the graph aboive, what is the slope of the isocost line? # If the price of capital remains the same and the price of labor decreases, the isocost line will With the current mix of labor and capital, the marginal technical rate of subsitution is MRTS-3. If the prices of labor and capital remain as shown in the graph, then the firm will minimize the cost of production by +a) Why is the marginal product of a variable input like labour likely to increase initially in the short run as more of the variable input is hired? b) Why does production eventually experience diminishing marginal returns in the short run? Ans both.. otherwise don't ans
- 2. A production function is given by the equation Q = 100L04K0.6 Where L is the number of labour units and K the capital units. a. Find marginal product of labour (Q₁) at L=4 and K=10. Interpret the result. aQ L at L=4 and K-10. ƏL Q b. Find the partial elasticity with respect to labour (EQL = Interpret the result. C. When Q-200, the marginal rate of technical substitution at L=4 is -0.21. Interpret that value (MRTS).1. Consider the production function Q=K³/ª L/4 Further suppose that capital is fixed at 16 units. Answer the following questions: a. Find Q when L =16 units. What is the output (Q) when L increases to 81 units? e b. Find the average product of labor when L when L increases 81 units? 16 units. What is the average product of labor %3D c. Find the marginal product of labor when L 16 units. What is the marginal product of labor when L increases 81 units? d. Show that doubling all the inputs doubles the output.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.