A firm faces the production function Q = 6K0 L0.5. If it can buy input K at £32 a unit and input L at £8 a unit, what combination of L and K should it use to maximize production if it is constrained by a fixed budget of £36,000? %3D
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- 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 firm can manufacture a product according to the production function Q=3K1/2L1/2, and capital is fixed at 4. a) When the firm hires 16 units of labor. The average product of labor is......... b) when the firm hires 16 units of labor, the marginal product of labor is....... C) if the firm can sell its output at a price of $ 10 per unit and can hire labor at $ 10 per unit , it should hire?............units of labor maximize the profits.If the production function of a firm is given by Q=K^2L^3 and the input prices are r= 8 per unit and w= 2 per unit find the levels of labor and capital that maximize the level of output for a total outlay of 240 birr?
- Economics 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.Let the production function be Q = 4* K1/4 L1/4 assume that both factors are variable. (a) Derive the contingent demand functions for K and L (b) Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function. (c) Find the amount of K and L necessary to produce Q=8 when v=16 and w=1 (with minimal possible cost). (d) Find the average and marginal cost functions.Suppose the utility function of a person consuming two commodities X and Y with income Birr 600 is given by U =2xy. If the per unit price of X is Birr 20 and per unit price of Y is Birr 40. a) Calculate the utility maximizing level of consumption of X1 and X2. b) Find the MRSX, Y at the optimum.If the production function of a firm is given by Q=,and the input prices are r = Birr 8 per unit and w = Birr 2 per unit,
- A firm’s production function is - y = f(X1, X2)= X11/2 + X1X2 , Where X1≥0, X2≥0 1. Write down the firm’s production possibility set, and its input requirement set. 2. Is this production function concave, quasi-concave? 3. Is this production function homogenous? 4. Find its returns to scale when X1=1, and X2=1If the production function of a firm is given by Q=K2L3 and the input prices are r=Birr 8 per unit and w= Birr 2 per unit, find the levels of labor and capital that maximize the level of output bfor a total outlay of birr 240.Consider a firm that maximizes profit function x^2y subject to the input constraint 2x^2+y^2=3 where x, y are inputs in the production. Find the extra profits garnered by the firm if the input constraint is relaxed by changing 3 to 3.3. Consider only positive values for optimal inputs and the multiplier.
- A firm produces two different kinds A and B of a commodity.The daily cost of producing x units of A and y units of B is C(x,y)=20(x^2+xy+y^2).Suppose that the firm sells all at a price per unit of 240 for A and 180 for B. 1)find the daily production level that maximizes profit and confirm its maximum. 2)Suppose the firm is required to produce exactly 5 units in all.what are now the optimal production level of x and y.Let y = f(x1, x2)=x11/2 + x1x2 be a firm’s production function, where x1≥0, x2≥0. Write down the firm’s production possibility set, and its input requirement set. Is this production function concave, quasi-concave? Is this production function homogenous? Find its returns to scale when x1=1, and x2=1.You are the manager of a firm and you are required to optimize the Cobb-Douglas function given the following parameters. The maximum amount of money available to spend is $340 where the price of K=8 and the price of L=4. That is Pk=8 and Pl=4. The function is given as q=K0.4L0.6 . What is the constraint equation?