Suppose that a unit of capital costs three times as much as a unit of labor. If a firm currently has a technology such that MPK =50, MPL =30, how should this firm adjust its capital and labor choices?
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Suppose that a unit of capital costs three times as much as a unit of labor.
If a firm currently has a technology such that MPK =50, MPL =30, how should this firm adjust its capital and labor choices?
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- Suppose a firm’s production function is K^1/3 L^2/3 Mpk= L^2/3 / 3K^2/3 MpL=2K^1/3 / 3L^1/3 The rental rate of capital is $52, and the wage rate is $13. What is the cost minimizing capital to labor ratio? How many units of capital and labor should the firm use to produce 1200 units of output How much would it cost the firm to produce 1200 units? What is the short run and long run total costs of decreasing output to 1000 units? Assuming relocation is costless, should the firm relocate to a new location where w=15, r=40?Prunella raises peaches where L is the number of units of labor she uses and T is the number of units of land she uses. Her output is f(L,T) = LT bushels of peaches. If the cost of land is 2 and the wage for labor is 7, find the cost minimizing amount of labor to use subject to the constraint that output must be 137 bushels. Round your answer to the second decimal place, e.g., 12.345 = 12.35.Q₂ A production function is given by q = 500L + 700K. The price of capital is $120 and the price of labor is $100. If the firm wants to produce 1,400 units of output, how many units of labor should it use? Your Answer: Answer
- An electronics plant’s production function is Q = 5LK, where Q is its output rate, L is the amount of labor it uses per period of time and K is the amount of capital it uses per period of time. The Price of labor is $1 per unit of labor and the price of capital is $2 per unit of capital. a) What is the optimal combination of inputs the plant should use to produce 1000 units of output per period? b) Suppose that the price of labor increases to $2 per unit. What effect will this have on optimal L and K to produce Q=1000? c) Is this plant subject to decreasing returns to scale? Why or why not?Suppose that a firm's production function is given by Q = 2KL, where Q is quantity of output, K is capital, and L is units of labor. Note that MPL = K and MPK-L. The price per unit of labor and capital are $30 and $50 respectively. How many units of labor and capital should the firm use if it wants to minimize the cost of producing 480 units of output? L = 10, K = 24 L=12, K 20 L = 20, K = 12 L = 24. K = 10Output 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?
- Is it possible to increase the labor productivity (output per unit of labor) in a given production process which exhibits diminishing returns to labor? If so, how?A firm produces output according to a production function: Q = F(K,L) = min {4K,4L). a. How much output is produced when K= 2 and L = 1? unit(s) b. If the wage rate is $60 per hour and the rental rate on capital is $40 per hour, what is the cost-minimizing input mix for producing 8 units of output? Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $40 per hour but the rental rate on capital remains at $40 per hour? O Capital decreases and labor increases. O It does not change. O Capital increases and labor decreases. O Capital and labor increase.A firm produces output according to a production function:Q = F(K,L) = min {6K,2L}.a. How much output is produced when K = 2 and L = 3?unit(s)b. If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 6 units of output?Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $10 per hour but the rental rate on capital remains at $10 per hour?multiple choice Capital and labor increase. Capital decreases and labor increases. Capital increases and labor decreases. It does not change.
- A firm produces output according to a production function:Q = F(K,L) = min {6K,2L}.a. How much output is produced when K = 2 and L = 3? unit(s)b. If the wage rate is $30 per hour and the rental rate on capital is $10 per hour, what is the cost-minimizing input mix for producing 6 units of output?Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $10 per hour but the rental rate on capital remains at $10 per hour? (Choose one that is the best answer) Capital decreases and labor increases. It does not change. Capital increases and labor decreases. Capital and labor increase.You manage a store that mass-produces candies by teams of workers using assembly candy machines. The technology is summarized by the production function q = 3 LK where q is the number of candies per week in thousands, K is the number of assembly candy machines, and L is the number of labor teams. Each candy assembly machine rents for r = per week, and each team costs w = $1000 per week. Candy costs are given by the cost of labor teams and machines, plus $600 per thousand of candies for ingredients. Your store has a fixed installation of 2 candy assembly machines as part of its design. = $6,000 What is the cost function for your store – namely, how much would it cost to produce q candies? What are average and marginal costs for producing q candies? How do average costs vary with output? а. b. How many teams are required to produce 3 (thousands) candies? What is the average cost per thousand candies? You are asked to make recommendations for the design of a new production facility in the…A firm produces output according to a production function:Q = F(K,L) = min {6K,2L}.a. How much output is produced when K = 2 and L = 3?unit(s)b. If the wage rate is $45 per hour and the rental rate on capital is $25 per hour, what is the cost-minimizing input mix for producing 6 units of output?Capital: Labor: c. How does your answer to part b change if the wage rate decreases to $25 per hour but the rental rate on capital remains at $25 per hour? Capital decreases and labor increases. Capital and labor increase. It does not change. Capital increases and labor decreases. Only typed answer
