Question 3: Assume that there are two inputs that a car producer uses: 1 engine and 4 tires. 1 car is produced using 1 engine and 4 tires as inputs. Supplier 1 is producing the engines and Supplier 2 is producing the tires. Price of 1 engine is v, and price of 1 tire is v2. The demand for the final product (car) is P = 200 – Q. Assume that costs of input producers (engine and tire producers) are zero. Also, the only costs of the car producer are engine and tires. Other costs of the car producer are assumed to be zero.
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- Suppose that Marie produces milk q using her own labor l and cattle k using the production functionq = f(k, l) = k2/3ℓ1/3Although Marie does not need to pay anyone to use either input, the opportunity costs of labor and cattle are w = 1 and v = 16, respectively, and P is the price of milk. a) Suppose that Marie’s stock of cattle is fixed at k0 = 8. Set up her short run cost minimization problem and find her labor demand ℓ(q) and cost function SC(q). b) Find Marie’s short run marginal cost SMC(q) and average cost SAC(q) functions and find the quantity at which short run average cost is minimized. c) Set up Marie’s short run profit maximization problem and find her short run supply curve q(P).The production engineers at Impact Industries have derived the optimal combinations of labor and capital. These are the only two inputs used by Impact. The following chart shows the combinations of labor and capital for three levels of output. Q is the output level. L* is the optimal amount of labor. K* is the optimal amount of capital. The price of labor is $90 per unit. The price of capital is $15 per unit. Q L* K* 120 5 20 180 7 7 240 12 24 a) If the manager of Impact Industries decides to produce 120 units, what will the long-run total cost and long-run average cost of producing 120 units? Show all calculations. b) If the manager of Impact Industries decides to produce 180 units, what will the long-run total cost and long-run average cost of producing 180 units? Show all calculations. c) If the manager of Impact Industries decides to produce 240 units, what will the long-run total cost and long-run average cost of producing 240…The production engineers at Impact Industries have derived the optimal combinations of labor and capital. These are the only two inputs used by Impact. The following chart shows the combinations of labor and capital for three levels of output. Q is the output level. L* is the optimal amount of labor. K* is the optimal amount of capital. The price of labor is $90 per unit. The price of capital is $15 per unit. Q L* K* 120 5 20 180 7 7 240 12 24 a) If the manager of Impact Industries decides to produce 120 units, what will the long-run total cost and long-run average cost of producing 120 units? Show all calculations. b) If the manager of Impact Industries decides to produce 180 units, what will the long-run total cost and long-run average cost of producing 180 units? Show all calculations. c) If the manager of Impact Industries decides to produce 240 units, what will the long-run total cost and long-run average cost of producing 240…
- The production engineers at Impact Industries have derived the optimal combinations of labor and capital. These are the only two inputs used by Impact. The following chart shows the combinations of labor and capital for three levels of output. Q is the output level. L* is the optimal amount of labor. K* is the optimal amount of capital. The price of labor is $90 per unit. The price of capital is $15 per unit. Q L* K* 120 5 20 180 7 7 240 12 24 a) If the manager of Impact Industries decides to produce 120 units, what will the long-run total cost and long-run average cost of producing 120 units? Show all calculations. b) If the manager of Impact Industries decides to produce 180 units, what will the long-run total cost and long-run average cost of producing 180 units? Show all calculations.Only need the (d) , thank you , do fast Suppose that Marie produces milk q using her own labor l and cattle k using the production function q = f(k, l) = (k^(2/3))*(ℓ^(1/3)) Although Marie does not need to pay anyone to use either input, the opportunity costs of labor and cattle are w = 1 and v = 16, respectively, and P is the price of milk. (a) Suppose that Marie’s stock of cattle is fixed at k0 = 8. Set up her short run cost minimization problem and find her labor demand ℓ(q) and cost function SC(q). (b) Find Marie’s short run marginal cost SMC(q) and average cost SAC(q) functions and find the quantity at which short run average cost is minimized. (c) Set up Marie’s short run profit maximization problem and find her short run supply curve q(P). d) Now consider Marie’s problem in the long run, where her stock of cattle may vary. Set up her long run cost minimization problem and find her labor ℓ c (q) and capital k c (q) demands and cost function C(q). (e) Set up Marie’s long run…There are two firms in the economy. Each firm employs positive amounts of capital and labour. The technology satisfies diminishing marginal rate of technical substitution of labour for capital. Currently, A’s marginal rate of technical substitution of labour for capital is 4 while B’s marginal rate of technical substitution of labour for capital is 2. A. Is the current production of the two firms efficient? If not, describe an exchange of inputs that would improve efficiency. B. Can these production levels of the two firms be observed in a perfectly competitive equilibrium of a production and exchange economy? Explain.
- Illustrate and explain two special cases of production functions: (1) Inputs to production that are perfectly substitutable, and (2) fixed proportions production function.Consider the following tasks that must be assigned to four workers on a conveyor-paced assembly line (i.e., a machine-paced line flow). Each worker must perform at least one task. There exists unlimited demand unless stated otherwise. Time to Complete Task (seconds): Task 1: 30 Task 2: 25 Task 3: 15 Task 4: 20 Task 5: 15 Task 6: 20 Task 7: 50 Task 8: 15 Task 9: 20 Task 10: 25 Task 11: 15 Task 12: 20 The current conveyor-paced assembly-line configuration assigns the workers in the following way: • Worker 1: Tasks 1, 2, 3 • Worker 2: Tasks 4, 5, 6 • Worker 3: Tasks 7, 8, 9 • Worker 4: Tasks 10, 11, 12 Assume a demand rate of 20 units per minute. What would be the takt time of the process (in seconds per unit)?Suppose that low-productivity workers all have marginal products of 8 and high-productivity workers all have marginal products of 16. The community has equal numbers of each type of worker. A firm cannot directly tell the difference between the two types of workers. Without any further information, the firm is willing to offer a wage at the average productivity. The local community college offers a course in microeconomics, which does not increase productivity for either type of workers. High-productivity workers think taking this course is as bad as a wage cut of $3, and low-productivity workers think it is as bad as a wage cut of $9. With the certificate, the firm is willing to offer a high wage of $16. Without it, the firm is willing to offer a low wage of $8. But the firm cannot still tell the true productivity. In this case, is it worth for the low-productivity workers taking the course? (Yes, No, or Uncertain) Thus, this situation will lead to a (pooling, or separating)…
- Assume that you are studying an economy which produces two goods, x and y, using two factors of production, capital K and labour L. The economy’s overall quantities of the two factors are given, and the capital intensity (the capital-to-labour ratio) in the production of y is always higher than the capital intensity in the production of x. At present there is an excess supply of y. Explain and illustrate graphically what will happen in the long run to:1) Prices of goods and production.2) factor prices and factor use intensities in each sector.Explain with the help of Graphs of Total Product (TP) and Marginal product (MP) the three laws of variable proportions and their significance in Industry and agriculture. Give the relationship between TP and MP at different stages of variable proportions. What is the relationship between Average Product curve (AP) and marginal product curve (MP) and explain at what point a progressive firm should change its labor or capital inputs with more skilled labor or with new technological machine in order to remain comparative in the market. What would happen to its product in the market if it does not change its machines or if it changes all its machines at the same timeThe production engineers at Impact Industries have derived the optimal combinations of labor and capital. These are the only two inputs used by Impact. The following chart shows the combinations of labor and capital for three levels of output. Q is the output level. L* is the optimal amount of labor. K* is the optimal amount of capital. The price of labor is $90 per unit. The price of capital is $15 per unit. Q L* K* 120 5 20 180 7 7 240 12 24