Find Ned’s marginal product of labor (MPL). Does it exhibit diminishing marginal returns? b. Find Ned’s marginal product of capital (MPK). Does it exhibit diminishing marginal returns? c. Find and draw an isocost function for C
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Ned’s Tuna has the following production function: q = K3/4L1/4, Where q is the number of tunas per hour, L is the number of workers and K is the number of boats. Suppose that w = $20/hour (PL) and r = $30/hour (PK). a. Find Ned’s marginal product of labor (MPL). Does it exhibit diminishing marginal returns? b. Find Ned’s marginal product of capital (MPK). Does it exhibit diminishing marginal returns? c. Find and draw an isocost function for C
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- 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 %24Hannah 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=10L^0.25 K^0.25 where L is their number of workers and K is units of capital. The wage rate is $500 per week and a unit of capital costs $500 per week. Suppose that when initially producing 10 square feet a week, they use 1 unit of capital.a. What is their short-run cost of remodeling 80 square feet per week? Instructions: Round your answer to the nearest whole number. $ b. What is their short-run average cost of remodeling 80 square feet per week? Instructions: Round your answer to the nearest whole number. $ c. What is their long-run cost of remodeling 80 square feet per week? Instructions: Round your answer to the nearest whole number. $ d. What is their long-run average cost of remodeling 80 square feet per week? Instructions: Round your answer…Suppose 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?
- For a firm to maximize profit, it must minimize the cost of producing whatever quantity it produces. Use the isocost and isoquant tools to present a firm that is choosing the optimal levels of labor and capital (i.e., tools) to produce a certain quantity and a certain cost. Then, show in your diagram how this firm would respond if it were to expand and spend more on its inputs, assuming it is best for the firm to become more “capital intensive” as it grows. Comment on WHY a firm might best become more capital intensive as it expands, even when the relative prices of labor and capital remain unchanged.Question 8 of 13 The following diagram depicts the production function of the farmers, where diminishing average product of labour is assumed. At A the average product of labour is 500,000/800 = 625 kg of grain per farmer. At B the average product of labour is 732,000/1,600 = 458 kg of grain per farmer. If you know that for 2,800 farmers the grain output is 894,000kg, then which of the following is/are correct? Kilogrammes of grain produced (thousands) 900 800- 700- 600- 500 400- 300- 200- 100- 0 0 400 800 B 1,200 1,600 Number of farmers 2,000 2,400 2,800 OA. The average product of labour when the labour input is 2,800 is 300. OB. The decreasing slopes of the rays from the origin to the production function along the curve indicate the decreasing average product of labour. OC. If the production function curve is an upward-sloping straight line, then there is no diminishing average product of labour. OD. It is possible that initially there is an economy of scale: for example, going from…Q2. Suppose the production of airframes is characterized by a CobbDouglas production function: Q =LK. The marginal products for this production function are MPL = K and MPK = L. Suppose the price of labor is $10 per unit and the price of capital is $1 per unit. Find the cost-minimizing combination of labor and capital if the manufacturer wants to produce 121,000 airframes.
- Suppose a brewery uses a Cobb-Douglas production function for his production. He studies the production process and finds the following. An additional machine-hour of fermentation capacity would increase output by 600 bottles per day (i. e. MPK = 600). An additional man-hour of labor would increase output by 1200 bottles per day (i. e. MP₁ = 1200). The price of a man-hour of labor is $40 per hour. The price of a machine-hour of fermentation capacity is $8 per hour. 1. Is the brewery currently minimizing its cost of production? Check using the minimization condition. 2. It turns out, the brewery is not optimally choosing the factors of production. To lower its production cost, which factor of production should the brewery increase and which factor should he decrease? 3. Suppose that the price of a machine-hour of fermentation capacity rises to $20 per hour. How does this change the answer from part 1?Suppose that widgets can be produced using two different production techniques, A and B. The following table provides the total input requirements for each of five different total output levels. Q = 1 Tech. K L A B Q=2 K L 4 1 6 2 13 Total Cost NO K 2 5 Assuming that the price of labor (P₁) is $1 and the price of capital (P) is $3, calculate the total cost of production for each of the five levels of output using the optimal (least-cost) technology at each level. To do this, complete the table below by calculating the total cost of production, filling in the missing values using the optimal (least-cost) technology at each level. (Enter your responses as whole numbers.) Q=5 Q=1 Q=2 Q=3 Q=4 $ 20 $ 27 $ 6 $ 11 $36 Q = 3 K L 9 4 4 8 How many labor hours (units of labor) would be employed at each level of output? How many machine hours (units of capital)? To answer this, complete the table below for the units of labor and units of capital that would be used to produce each level of output.…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…
- Q5. Jason is running a cleaning business, there are available labours (L) and machines (M) for Jason to use as inputs to produce cleaning service for his clients. a) Suppose Jason must use both labours and machines without any specific ratio to complete the service for his clients, please write down the general production function formula for Jason. hint: you could use any letter if you want] b) Under the function form of a), assume Jason's Marginal Rate of Technical Substitution (MRTSL, M) equals to 2, how do you interpret it? c) Assume Jason now can use only single input, either labour or machine to complete the service, please write down the general production function formula for Jason. hint: you could use any letter if you want] d) Under the function form of c), assume Jason's Marginal Rate of Technical Substitution (MRTSL, M) is always larger than the market price ratio between labour and machine (w/r), what should Jason do? why?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=10L^0.5K^0.5,where L is their number of workers and K is units of capital. The wage rate is $250 per week and a unit of capital costs $250 per week. Suppose that when initially producing 100 square feet a week, they use 10 units of capital.a. What is their short-run cost of remodeling 1,000 square feet per week? Instructions: Enter your answer as a whole number. $ b. What is their long-run cost of remodeling 1,000 square feet per week? Instructions: Enter your answer as a whole number. $Suppose that widgets can be produced using two different production techniques, A and B. The following table provides the total input requirements for each of five different total output levels. Q = 1 Tech. K L A B Q=2 K L 2 4 1 6 1 3 2 5 Total Cost L K Assuming that the price of labor (P₁) is $1 and the price of capital (PK) is $3, calculate the total cost of production for each of the five levels of output using the optimal (least-cost) technology at each level. Q=3 K L 4 9 4 8 To do this, complete the table below by calculating the total cost of production, filling in the missing values using the optimal (least-cost) technology at each level. (Enter your responses as whole numbers.) Q=4 K L 12 5 Total Cost How many labor hours (units of labor) would be employed at each level of output? How many machine hours (units of capital)? To answer this, complete the table below for the units of labor and units of capital that would be used to produce each level of output. (Enter your…
