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Q: Consider a beekeeper. The beekeeper has the following production function where the input is the…
A: Hi Student, Thanks for posting the question. As per the guideline, we are providing answer for the…
Find the marginal products of capital and labour (MPK and MPL).
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- Consider the production function Q = (0.5K1/3 + 0.5L1/3)3 with a corresponding MRTS = K2/3/L2/3. a. Prove that this production function exhibits constant returns to scale. b. Suppose the firms want to minimize the cost of producing 8 units of output. It pays a wage rate W of $40 and capital cost R of $10. How many units of labor and capital should the firm use?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.The manager of Don Teeta Company Limited hires labour (L) and rents capital equipment (K) in a very competitive market. Currently, the wage rate of labour is GH¢2 per hour and capital is rented at GH¢5 per hour, the unit price of the product is GH¢0.75 and total cost of production is GH¢1,000. Suppose the firm’s production function (Q) is as follows: Q = 14K0.5L0.5 + 10 Determine the optimal input usage and the maximum profit.
- Answer the Constrained Optimization: Cobb-Douglas Production Function:1. Based from the factor shares of the two inputs, what will happen to the number of output if it the firm decides to triple both the amount of labor and capital?Assume labor (L) is the only variable input used in the production process, a firm’s production function is given by Q=7L+10L2-L3 where Q represents total product. Classify the production function in to the three stages of production.The engineers at Morris Industries obtained the following estimate of the firm’s production function Q = F ( K, L ) = min { 3K, 4L } How much output is produced when 2 units of labor and 5 units of capital are employed?
- 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 = 2.4A 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?Consider the production function Q = 2(KL)0.5a) What is the marginal product of labour and capital
- Consider the following production function for a firm: Q = 500K^0.8L^0.2 where K is the amount of capital employed and L is the amount of labor employed. The price of capital, PK, is $48 and the price of labor, PL, is $12. If the firm would like to produce 10, 000 units with minimum cost, they should be using units of capital and units of labor.Suppose the production function for a product is z = 65x2/5y3/5 where x is the capital expenditures and y is the number of work-hours. (a) Find the marginal productivity of x. (b) Find the marginal productivity of y.Consider the production function q = ((K^α)+(L^α))^β. For this function to have diminishing marginal productivities and increasing returns to scale, it must be the case that: a. α>1 & αβ>1; b. α>1 & αβ1; d. α