Suppose a firm's production function is given by Q = 10L0.2 K (1-0.2) Wage rate is $10 and rental rate is $5. Derive the function of the output expansion path. Show all work and upload your work in Question 4. (You don't need to draw a graph.) The slope of the expansion path is equal to (round your answer to two decimal places)
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- Suppose a firm is producing some output level q1 using a combination of capital and labor for which the RTS (MPL/MPK) at this input combination is 1. Suppose further that the wage rate is $20 and the rental rate on capital is $10. Which of the following statements is correct? A. The firm can reduce its costs of producing q1 by using more labor and less capital B. The firm can reduce its costs of producing q1 by using more capital and less labor C. The firm is currently minimizing the costs of producing q1 D. Whether or not the firm is minimizing the costs of producing q1 is indeterminateThe production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and Lis labor and q is output. a) Find the marginal product of labor and the marginal product of capital. b) Find the marginal rate of technical substitution between labor and capital. c) Denote the wage of labor by w and the rental of capital by r. What is the cost minimization condition for a firm? Show it diagrammatically. d) Now suppose w =30 and r= 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) Part A, B, CThe price of factor A is GHC20 per units and the price of factor B is GHC300.00 per unit. The marginal product of factor A is 40 units and the marginal product of factor B is 60 units. Should the firm increase employment of factor A and decrease employment of factor B to minimise the total long run cost of producing existing output? Explain
- A firm employs 100 workers at a wage rate of €10 per hour, and 50 units of capital at a rate of €20 per hour. The firm is currently operating at a point on its isoquant curve. At this point, the marginal product of labour is 30, and the marginal product of capital is 50. Which of the following statements is correct? A. The firm is producing its current output level at the minimum cost. B. The firm could reduce the cost of producing its current output level by employing more capital and less labour. C. The firm could reduce the cost of producing its current output level by employing more labour and less capital. D. The firm could reduce the cost of producing its current output level by employing less capital and less labour. E. Both C and D are true.The price of factor A is GHC20 per unit and the price of factor B is GHC300.00 per unit.The marginal product of factors A is 40units and the marginal product of factor B is 60units.Should the firm increase the employment of factor A and decrease the employment of B to minimize the total long run cost of producing existing output?ExplainA firm employs M workers per week and the length of the workweek at the firm is H Let MPM be the added output from an additional employee and let MPH be the added output from a one hour increase in the workweek at the firm. MEM and MEH are, respectively, the marginal expense of an added worker and of an added hour of work. At present, the cost of an added unit of output produced by hiring more workers is $5 while the cost of an added unit of output produced by employing existing workers for more hours is $3. Is the firm maximizing profits given its current employment level and workweek? If your answer is yes, explain why. If your answer is no, explain why not and discuss what adjustments the firm should make. It's a general question. There's no given output being produced by added workers and additional hours.
- . In the short run, labor is a hat-making firm’s only variable input. Wage rate is $5.00/hour. The firm currently employs a certain amount of labor H (hours), such that the marginal product of labor is 10 hats per worker-hour, and average product is 15 hats per worker-hour. MPL(H) = 10; APL(H) = 15. (Note: marginal and average products of labor for this firm are not constant. 10 and 15 are their values at a particular point, H, not everywhere.) What is the marginal cost of a hat for that firm?The production function for a product is given by q= 10K^(1/2)L^(1/2) where K is capital, and L is labor and q is output. a) Find the marginal product of labor and the marginal product of capital. b) Find the marginal rate of technical substitution between labor and capital. c) Denote the wage of labor by w and the rental of capital by r. What is the cost minimization condition for a firm? Show it diagrammatically. d) Now suppose w =30 and r = 120. What is the minimum cost of producing q=1000. (You must show your work by clearly writing the equations that you use to derive the cost minimizing levels of L and K.) Part A, B, CA firm has a production function of Q = KL + L, where MPL = K + 1 and MPK = L. The wage rate (W) is $100 per worker and the rental (R) is $100 per unit of capital. The firm is producing 100 units of output. In the long run, what is the firm's Marginal Rate of Technical Substitution?
- A widget manufacturer has a production function of the form q = 6L + 10K . If the wage rate (w) is $4 and the rental rate on capital (r) is $5. Are the returns to scale increasing, constant, or decreasing for this production function? What cost minimization combination of K and L will the manufacturer employs to produce 300 units of output? Suppose that the price of capital increases to $7 per unit. If manufacturer continues to produce 300 units,what cost minimization choice of inputs capital and labor should the firm used. Suppose that the capital input is fixed at K = 3 units in the short run, what is the short run total cost function with qTrue or false and explain Suppose a firm’s marginal product of labour is MPL = 10/L, where L is measured in labour hours, the price of the product is $600, and the cost per hour of labour is $30. The firm currently employs 150 labour hours. In order to maximize the firm’s profits in the short run, the manager should increase its labour employment by 40 labour hours.Consider the following production functions, to be used in this week’s assignment:(A) F(L, K) = 20L^2 + 20K^2(B) F(L, K) = [L^1/2 + K^1/2]^2For each of production functions (A) and (B) given above, do the following steps.(i) Calculate the marginal product of labor MPL(L, K) = ∂F(L, K) / ∂L.(ii) Calculate the marginal product of capital MPK(L, K) = ∂F(L, K) / ∂K.(iii) Calculate the absolute value of the technical rate of substitution as the ratio of marginal products andsimplify as far as possible: |TRS(L, K)| = MPL(L, K) / MPK(L, K). PLEASE SHOW ALL WORK