. Suppose a firm has the production function f (x1, x2) = 5x,x2. Find the firm's long-run profit-maximizing levels of x, and x2 if p 3, w, = 30, and w2 = 75. %3D
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- Suppose a producer faces the following production function: K^0,5.K^0,5 given that L is the unit of labour and K is the unit of capital. Suppose K is 16, labour wage rate is R10 and rental rate of capital is R50, derive the TC and MC functionsIf a firm has the production function q = f(L, K) = L + 2K, then its technology exhibits: constant returns to scale increasing returns to scale None of the above. decreasing returns to scale increasing marginal productSuppose a firm with a production function given by Q = 30K0.5L0.5 produces 1,800 units of output. The firm pays a wage of $50 per unit and pays a rental rate of capital of $120 per unit. MPL = 15K0.5/L0.5 ; MPK = 15L0.5/K0.5 . How many units of labor and capital should the firm employ minimize the cost of producing 1,800 units of output, and what would be the total cost?
- Suppose a firm with a production function given by Q = K0.4L0.6 produces 100 units of output. The firm pays a wage of $20 per units and pays a rental rate of capital of $40 per unit. (Note: MPL = 0.6K0.4L-0.4 and MPK = 0.4K-0.6L0.6 ) What is the minimum cost of producing 100 units of output?Find out the maximum possible output for a firm with two units of L and 50 units of k when its production function is Q = 5L + 3K. A firm has the production function X = LK (X = output, L = labour, K = capital); labour and capital prices are Ksh. 8 and Ksh. 10 per unit; and it desires to produce 32 units of output. What is the least cost combination of labour and capital? Consider the production function, Q = 86 L0.61 K0.39
- Q2. Suppose the production of airframes is characterized by a CobbDouglas production function: Q =LK. The marginal products for this production function are MPL = K and MPK = L. Suppose the price of labor is $10 per unit and the price of capital is $1 per unit. Find the cost-minimizing combination of labor and capital if the manufacturer wants to produce 121,000 airframes.A Cobb-Douglas production function for new company is given by ?(?, ?) =?³/⁵ ?²/⁵ where K represents the units of capital and L represents the units of labor. Suppose units of labor and capital cost $200 and $100 each respectively. If the budget constraint is $30,000, find the maximum production level for this company.Consider the following production function with inputs L and K: Q = (L 0.5 + K0.5)2. The input prices are r = 2 and w = 1. 1) What is the optimal use of labor and capital? 2) Consider a technological advacement such that Q = 2(L 0.5 + K0.5)2 and w = r = 1. What is the optial level of K and L? Any change in K/L? What is the new cost?
- 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.At zero level of production, _______ cost is always zeroA 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=1