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- question 8 For each of the following situations, Find the Total Cost function, TC(q) Identify the optimal input mix, L* and K* for the given q. A) q = 2*MIN(L,5K); w = 8, r = 10; i) (5 points) TC(q) = __________________ ii) (4 points) q = 20 L* = _________________ K* = _________________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.When a firm is using a technically efficient input combination, the firm is also producing in an economically efficient manner. What is your take on this statement?
- 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?A firm produces output according to the following production function:Q = F (K, L) = min{4K, 4L}(a) How much output is produced when K = 2 and L = 3?(b) If the wage rate is $60 per hour and the rental rate on capital is $40 per hour, what is the costminimizing input mix for producing 8 units of output?(c) If the wage rate decreases to $40 per hour but the rental rate on capital remains at $40 per hour,what is the cost minimizing input mix for producing 8 units of output?A farmer uses K units of machinery and L hours of labor to produce C tons of corn, with the production function, C = 2 L0.5 K. The farmer currently uses L = 20 and K = 10. Suppose the input price ratio is w/r = 1. What would you tell the farmer to do in order to minimize his cost of production given the current level of output?
- Output is produced according to a production process given by: Q = 4LK, where L is the quantity of labor input and K is the quantity of capital input. If the price of K is $10 and the price of L is $5, then what is the cost-minimizing combination of K and L capable of producing 32 units of output?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.Suppose that we have a linear production function Q = 10L + 2K. (Quantity = labor + capital) If the price of labor is $5 per unit and the price of capital services, r, is $2 per unit. Find the optimal input combination given that the firm wishes to produce 200 units of output.
- Find the production which has the following cost function (q is output, v= cost of capital, w=labour cost): C = qv^1/3w^2/3Suppose that production for good X is characterized by the following production function, Q = K0.5L0.5, where K is the fixed input in the short run. If the per-unit rental rate of capital, r, is $15 and the per-unit wage, w, is $25, then the average fixed cost of using 9 units of capital and 81 units of labor is $75. incalculable since there is insufficient information to determine the average fixed costs. $80. $5.A firm's production function is q = 26x^0.33y^0.67, where x and y are the amounts of factors x and y that the firm uses as inputs. If the firm is minimizing unit costs and if the price of factor x is 6 times the price of factor y, the ratio in which the firm will use factors x and y is closest to. A. x/y = 0.08 B. x/y = 0.25 C. x/y = 0.5 D. x/y = 2.4
