The outputs of firms 1 and 2 are given by Q =3L° and Q2 =4L° respectively ,0.6 ,0.6 where the L's stand for labour (measured in hours). If the total labour supply is 350 what would be the total output (Q +Q2) if (a) labour was split equally between the two firms. (b) labour was allocated efficiently between the two firms.
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- You are the owner of a puppet manufacturing company. Suppose that labour is the only variable input to the production process. If the marginal cost of production is diminishing as more units of output are produced, what can you say about the marginal product of labour?Hannah and Sam run Moretown Makeovers, a home remodeling business. The number of square feet they can remodel in a week is described by the Cobb-Douglas production function Q = F(L, K) Q = 10L0.25 K0.25 where Lis their number of workers and K is units of capital. The wage rate is $160 per week and a unit of capital costs $100,000 per week. Suppose that when initially producing 10 square feet a week, they use 0.04 unit of capital. a. What is their short-run cost of remodeling 100 square feet per week? Instructions: Round your answer to the nearest whole number. b. What is their short-run average cost of remodeling 100 square feet per week? Instructions: Round your answer to the nearest whole number. c. What is their long-run cost of remodeling 100 square feet per week? Instructions: Round your answer to the nearest whole number. d. What is their long-run average cost of remodeling 100 square feet per week? Instructions: Round your answer to the nearest whole number. %24 %24Digging calms by hand in Sunset Bay requires only labor input. The total number of calms obtained per hour (q) is given by :Q = 100√LWhere L is labor input per hour. A. Graph the relationship between q an LB. What the average productivity of labor in Sunset Bay? Graph this relationship and show that output per unit of labor input diminishes for increase in labor input. C. It can be shown that the marginal productivity of labor in Sunset By is given by:MPL =50√LGraph this relationship and show that labor’s marginal productivity is less than average productivity for all values of L . Explain why this is do.D. Explain the concept of diminishing returns to labor and how this concept related to increasing marginal costs.
- The Acme Anvil Company's output is given by the Cobb-Douglas Production function P = 60L2/3 K1/3, where P is the number of anvils produced when Lis the amount spent on labor and K is the amount spent on capital. a. What is the production if L = 150 and K = 150? b. Find the marginal productivities. C. Evaluate the marginal productivities with L = 150 and K = 150. d. Interpret the meanings of the marginal productivities found in part c. e. If their budget is $300 then there is a constraint L+ K = 300. Use Lagrange multipliers (2) to find the values of L and K that will maximize production and find the maximum production f. Find 2. 12| is called the marginal productivity of money and will give the number additional units produced for each dollar increase in the budget. Interpret 2 for this problem. MacBook Pro urses/34419/files/5014304?wrap=1Consider a firm that uses labour and capital as inputs for production accord- ing to some production technology y = f(K, L). Let c(y, w, r) be the cost of producing y units of output if the wage rate is w and the cost of capital is r. Let L* and K* be the optimal capital and labour demand for producing y units. Prove that dc(y, w, r) dc(y, w, r) _ K. L* and = K*. dw drSuppose that the production function for a phone is ? = 20K^0.5L ^0.5 . The marginal product of labor is 10(k/l)^0.5 , and the marginal product of capital is 10(L/K) ^0.5 . Suppose that labor can be hired for $6 and capital can be hired for $9. a. When the firm is producing 49 units at lowest cost, what will the firm’s marginal rate of technical substitution be? b. Solve for the lowest-cost combination of labor and capital that will allow the firm to produce 49 phones. Fractional units of labor and capital are allowed. c. What is the minimum cost of producing 49 phones?
- Suppose that the production of crayons ( qq ) is conducted at two locations and uses only labor as an input. The production function in location 1 is given by q1=10l0.51q1=10l10.5 and in location2 by q2=50l0.52q2=50l20.5a. If a single firm produces crayons in both locations, then it will obviously want to get as large an output as possible given the labor input it uses. How should it allocate labor between the locations to do so? Explain precisely the relationship between l1l1 and l2l2b. Assuming that the firm operates in the efficient manner described in part (a), how does total output ( qq ) depend on the total amount of labor hired (l)?(l)?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?Brian uses wool (K) and labour (L) to produce t-shirts (q). The production function is: q = min{1/3L, 2K}.If he uses 0.5 kg of wool and 3 hours of labour, he can produce 1 t-shirt. 1. The pice of wage per hour is given by w=$10 and the price of each kg of wool is given by r=$4. What is the L(q) and K(q)?
- Given that the level of labour is 10, the total production is 1,200, and the marginal product of labour is 200, what is the average product of labour?Suppose the production function for high quality brandy is given by : Q = √KL Where q is the output of brandy per week and L is labor hours per week ., in the short run K is fixed at 100, so the short run production function is Q = 10√L a. Ifthecapitalrentsfor10$andthewageare5$perhour.,writetheshortruntotalcost function. b. How much will the firm produce at a price of 20$ per bottles of brandy ? c. Howmanylaborhourswillbehiredperweek?1. Suppose the production function of a firm is given as: Q = 5L + 10L2 – 2L³ a. Find the number of labors that would yield maximum values of TP, AP, and