= A firm has a short run production function Q AK0.5L0.5, where A is technology, K is capital set at level of 4, and L is Labor. The price of labor is w, and the price of capital is r. The price of output is p. Please derive firm's demand for labor, and express it as a function of wage. a. Ob.(AK0.5 C. PAK 0.52 2 d. 2w PAKO.S W PAKO.5 2w
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- The production function for Q is given as Q = 5K1/2L1/2where K is the amount of capital employed and L is the amount of labor employed. The price of capital is $8 and the price of labor is $4. Show the input choice when output reaches 59 and find the marginal cost of the 60th unit of output. Show your steps of calculation clearly.A manager hires a labor and rents capital equipment in a very competitive market. Currently the wage rate is Gh₵ 2 per hour and capital is rented at Gh₵ 5per hour, the unit price of the product is Gh₵ 0.25 and total cost is1000. Suppose the firm’s production is as follows: Q =14K⁰L⁰+10 Required What is the amount of labor and capital the firm should employ in order to maximize profit. What is the maximum profit.A firm uses labour, L and capital K, to produce a single product, X. capital is fixed but labour is variable. The firm’s production function is: X=-0.2L3 + 18L2 + 1620L. Where X is the number of units of the product per week, and L is the number of persons employed. A t what weekly output is marginal cost equal to average variable cost? if the price of the product is $0.20 per unit, what is the maximum weekly wage that the firm would pay rather than close down?
- 1/3 7 Consider the production function y = (0.5/ +0.52 of producing 8 units of output per day. It pays a wage rate wi of $40 per hour and capital cost w2 of $10 per hour. How many units of labor and capital should the firm use? Suppose the firm wants to minimize the cost. 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?Tom Petersen is considering renovating bar stools at Dreamland. The productionfunction for new bar stools is given byq= 0.5L0.5where q is the number of stools produced during the renovation week and l represents thea number of worker hours employed during the period. The firm is a price taker for both bar stools(which sell for P) and workers (which can be hired at a wage rate of w per hour).a. What is the cost function for this firm C(w,q)?b. What is the supply function for bar stools q(P,w)?c. What is the profit function for this firm (P,w)?d. What is the firm’s demand function for labor function L(P,w)?
- Consider the "Cobb-Douglas" production function given by Y = AKº L¹-a where A> 0 and 0 < a < 1. Which of the following is FALSE? The marginal product of capital is positive The marginal product of labour is positive There is diminishing returns to capital O There is decreasing returns to scaleGiven the following production function. If the price of the output is $100. What is the Marginal Revenue Product of the 4th worker (4th unit of labor)? Units of Labor Total Output MP ㅇ ㅇ 1 5 2 15 3 30 4 42 5 52 60 7 65 8. 67 9 63 10 55A cob Douglas production function for a firm is given as Q=4L ½K½. The firm has also established that wage rate and interest paid on capital are $3 and $5 respectively for a production period. The firm intents to spend $200 million for the period on production cost. Compute the levels of capital and labor that will maximize output. What is the maximum output?
- A widget manufacturer has a production function of the form q= VLK . If the wage rate (w) is $4 and the rental rate on capital (r) is $1. Are the returns to scale increasing, constant, or decreasing for this production Choose... function? What cost minimization combination of K and L will the manufacturer employs to Choose... produce 40 units of output? If the firm wants to decrease output level to 20. What cost minimization Choose... combination of K and L will the manufacturer employs? Suppose that the capital input is fixed at K = 100 units in the short run, what is Choose... the short run total cost function with qA firm's production function is q = min (0.5K, 5L).The current wage rate, w = $10 and the price of capital, r= $5. How many units of K and Lshould the firm hire in order to produce 180 units of output with the minimum cost?Please find the solution and also draw the isoquant and the isocost curveSuppose Mr. Saad is a producer of Lola Loo chocolate, following is the information available of his production plant. Quantity of Labour (L) Quantity of 1 2 3 4 5 Capital (K) 10 15 25 100 50 20 30 40 50 75 50 75 100 125 150200250 300 75 90 105 120 2 30 50 62 15 If K and Lare imperfect substitutes and complements from the information above draw at least three isoquant (map) and identify the level of production. H73 4