Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor and the Marginal Product of Capital are given by:
MPL = ½ L-1/2K1/2and MPK = ½ L1/2K-1/2
a) Suppose the price of labor is w = 18, and the price of capital is r = 2. Derive the firm’s total cost function.
b) What is the firm’s marginal cost?
c) For this problem, you will sketch the graph of the firm’s isoquant for Q = 12 units of output, and on the same graph sketch the firm’s isocost line associated with the total cost of producing Q = 12 units of output. To get this total cost, you must use the Total Cost function from part a). Please scale your graph up to 72 units of Labor on the horizontal axis, and 72 units of Capital on the vertical axis (do not go above 72 units on either axis). For the isocost line, clearly identify the vertical and horizontal intercepts. For the isoquant, clearly identify 4 combinations of Labor and Capital that will produce Q = 12 (including the bundle that minimizes the firm’s cost of production). Make sure your graph is neatly and accurately drawn and carefully labeled.
It is solved below:
Suppose a firm’s production function is given by Q = L1/2*K1/2. The Marginal Product of Labor...
Please help! Please show all work! 2. (21 points. Suppose a firm's production function is given by Q = L 1/2*K12. The Marginal Product of Labor and the Marginal Product of Capital are given by: MPL = 72 L 1/2K1/2and MPK = 12L12K-1/2 a) Suppose the price of labor is w=18, and the price of capital is r=2. Derive the firm's total cost function. b) What is the firm's marginal cost? c) For this problem, you will sketch the graph...
Suppose a firm has a production function given by Q = L1/2 K1/2. Therefore, MPL = K1/2 / 2L1/2 and MPK = L1/2 / 2K1/2 The firm can purchase labor, L at a price w = 36, and capital, K at a price of r = 9. a) What is the firm’s Total Cost function, TC(Q)? b) What is the firm’s marginal cost of production?
Suppose a firm can use either Capital (K) or Labor (L) in a production process. The firms Production function is given by Q = 5L + 15K. The price of Capital is $20 per unit and the price of Labor is $8 per unit. a) (4 points) What is the firm’s Total Cost function? TC(Q) = ____________________________ b) (8 points) Suppose the firm is producing 30 units of output (Q = 30). Using a graph, draw the firm’s isoquant for...
Suppose in the short run a firm’s production function is given by Q = L1/2*K1/2, and that K is fixed at K = 36. If the price of Labor, w = $12 per unit of Labor, what is the firm’s Marginal Cost of production when the firm is producing 48 units of output? MC = ________________________
Suppose in the short run a firm’s production function is given by Q = L1/2*K1/2, and that K is fixed at K = 49. If the price of Labor, w = $6 per unit of Labor, what is the firm’s Marginal Cost of production when the firm is producing 28 units of output?
2. (12 total points) Suppose a firm can use either Capital (K) or Labor (L) in a production process. The firm's production function is given by Q = 5L + 15K. The price of Capital is $20 per unit and the price of Labor is $8 per unit. a) (4 points) What is the firm's Total Cost function? TC(Q)= b) (8 points) Suppose the firm is producing 30 units of output (Q = 30). Using a graph, draw the firm's...
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1. Suppose the production of digital cameras is characterized by the production function q F(K, L)- KL (MPL = K, MPK = L), where q represents the number of digital cameras produced. Suppose that the price of labor is $10 per unit and the price of capital is S1 per unit. (a) Graph the isoquant for q-121 000. (b) On the graph you drew for part a), draw several isocost lines including one that is tangent to the isoquant you...