Consider a country that produces computers (C) and food (F) using capital (K) and labor (L). Both industries are perfectly competitive. The factors of production are complements. As a result, unit factor requirements are fixed and given by: akc=3, akF=1, aLc = 2 and aLF = 4. Suppose that this economy has 100 units of capital and 150 workers. (c) Suppose that the world price of computers is $16 and the world price of food is $12. Assume that the Home country produces both goods. What are the free trade factor price levels W and R?
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- Consider a country that produces computers (C) and food (F) using capital (K) and labor (L). Both industries are perfectly competitive. The factors of production are complements. As a result, unit factor requirements are fixed and given by: aKc = 3, aKF=1, aLc = 2 and aLF = 4. Suppose that this economy has 100 units of capital and 150 workers. (c) Suppose that the world price of computers is $16 and the world price of food is $12. Assume that the Home country produces both goods. What are the free trade factor price levels W and R? (d) How many computers and units of food will the economy produce? (e) Suppose that the endowment of labor increased to 200. Compute the new equilibrium wage, rental rates and quantities produced in the new equilibrium. Provide the intuition of your results.Consider a country that produces computers (C) and food (F) using capital (K) and labor (L). Both industries are perfectly competitive. The factors of production are complements. As a result, unit factor requirements are fixed and given by: aKc = 3, akr = 1, aLc = 2 and ALF = 4. Suppose that this economy has 100 units of capital and 150 workers. (b) How does the capital-labor ratio in each industry depend on the relative wage W/R?Consider a country that produces computers (C) and food (F) using capital (K) and labor (L). Both industries are perfectly competitive. The factors of production are complements. As a result, unit factor requirements are fixed and given by: akc = 3, akF = 1, aLC = 2 and aLF = 4. Suppose that this economy has 100 units of capital and 150 workers. (a) Which industry is capital intensive?
- 1. Pekan Nenas has 20 competitive pineapple orchards, all of which sell pineapples at the world price of RM2 per pineapple. The following equations describe the production function and the marginal product of labor in each orchard: where Q is the number of pineapples produced in a day, L is the number of workers, and MPL is the marginal product of labor. (a) (b) (c) Q = 100L - L² MPL = 100 - 2L, (d) What is each orchard's labor demand as a function of the daily wage W? What is the market's labor demand? Pekan Nenas has 200 workers who supply their labor inelastically. Solve for the wage W. How many workers does each orchard hire? How much profit does each orchard owner make? Calculate what happens to the income of workers and orchard owners if the world price doubles to RM4 per pineapple. Now suppose that the price is back at RM2 per pineapple but a flood destroys half the orchards. Calculate how the flood affects the income of each worker and of each remaining orchard owner. What…Consider the following two systems of production, which produce the same quantity. A (assemble by hand) requires: 35 workers 1 robot B (assemble by robot) requires: 5 workers 4 robots Price of one unit of inputs (thousands): worker: £2 robot: £50 Draw the axes of a cost diagram as follows: · units of labour on the x-axis, with a scale from 0 to 70 · units of capital on the y-axis, with a scale from 0 to 5. Now mark system A and system B as points on this diagram. Draw an isocost line at C = £120. Comment on which system you would choose, and why.1. Let y = f(x1, x2)=x11/2+ X1X2 be a firm's production function, where x20, x220. - a. Write down the firm's production possibility set, and its input requirement set.“ b. Is this production function concave, quasi-concave? c. Is this production function homogenous, homothetic? + d. Find its returns to scale when x1=1, and x2=1.e
- 2. Consider the production function: f(K,L) = K*L%. Let w and r denote the price of labor and capital. (a) Find the cost minimizing input bundle as a function of w, r, and q. Find the cost function. (b) Suppose two countries, A and B, have the access to the same production technology f(-) given above. Firms in both countries are cost-minimizers. Yet, the firm in country A uses relatively more labor and less capital than the firm in country B to produce the same level of output. What will ex- plain this?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.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.…
- 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…2. A firm uses capital (K) and labour (L) to produce luxury office chairs. The production technology is given by Q = K ³/4L¹/4, where Q is the number of chairs produced.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^0.25 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…