1. Suppose a production function is given by FIK... - KL? the price of capital is...
The production of tennis shoes takes the following form: Q = 3(KL)1/3 price of capital (K)= $120 per day price of labor = $30 per day If the price of a tennis shoes is $50 per pair, what is the optimum combination of K and L that maximizes profit or minimizes loss?
Suppose a production function is given by F(K, L) = KL2 ; the price of capital is $10 and the price of labor is $15. What combination of labor and capital minimizes the cost of producing any output? To produce a given level of output q, how many units of L and K are needed? Express the optimal inputs choices L(q) and K(q) as functions of the level of output q
10. Consider the production function: f(KL)=K L. Let wandr denote the price of labor and capital, and let p denote the price of the output good. (a) Find the cost minimizing input bundle and the cost function as a function of w., and q. (b) Find the profit maximizing output level and the profit as a function of w, r, and p. 11. Consider the production function: f(KL)=K+L. Let w and r denote the price of labor and capital, and...
A plant’s production function is Q = 2KL + K . The price of labor services w is $ 4 and of capital services r is $ 5 per unit. a) In the short run, the plant’s capital is fixed at K = 9. Find the amount of labor it must employ to produce Q = 45 units of output. b) How much money is the firm sacrificing by not having the ability to choose its level of capital optimally?...
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...
3. Suppose a firm has the production function Q = 50 KL 1) If the wage rate is $10 per unit of labor and the rental rate of capital is $5 per unit of capital, how much capital and labor should the firm employ in the long run to minimize the cost of producing 40,000 units? 2) Using the solution in part 1), what will the firm’s long-run total cost be?
2. Consider a firm producing pizza with production function q = KL, that faces input prices w= $10 and r = $100 for labor and capital, respectively. a. Derive the isoquant equation. Find the isoquant of an output q = 1. Draw it in a figure with l in the horizontal axis and k in the vertical axis. b. Does this firm's production exhibit increasing, decreasing or constant returns to scale? Briefly explain c. Find the labor demand, and the...
1. A plant's production function is Q = (L4/2 + K1/2)2. The price of labor is $10 per unit, and the price of capital is $30 per unit. In the short-run, capital is fixed at 9 units. The plant has a production quota of 1600 units of output that it must meet. a. Calculate the short-run minimum cost of producing 1600 units of output. (5 points) b. Assuming that the plant still meets its production quota, how much will it...
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...
3. Suppose the production of Crocs is characterized by the production function Q = LK, where represents the number of pairs of Crocs produced. Suppose that the price of labor is $10 per unit and the price of capital is $1 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 drew. What is the slope of the isocost lines?...