Suppose that the production function is Q= 20K²L* for a firm. If price per unit of labor is 5 Turkish Liras (P, = STL), price per unit of capital is 10 Turkish Liras (P =107Z) and the financial capasity of firm for production is 600 Turkish Liras (C = 6007L ), find the amounts %3D of K and L that minimize cost of the production for the firm.
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- 10)Given the production function f (L K) = L2 / 3. K1 / 3, where L is the working hours and K is the capital. assuming that the capital price is r = 4 euros and the price per hour of work is w = 27 euros and that all the factors of production are variable, what is the minimum cost of producing 10 units of product? Choose one: A) 260e B) 230e C) 240e D) 250e E) 270eSuppose you own a small business. Last month, your total revenue was $8,800. In addition, you paid $3,500 in monthly rent for office space, $300 in monthly rent for equipment, $2,500 to your workers in wages for the month, and $1,900 for the supplies you used that month. If you correctly determine that your economic profit last month was $200, then it must be true that your implicit costs are $3,600 per month. your implicit costs are $600 per month. your implicit costs are $400 per month. your implicit costs are $1,800 per month.Suppose a firm’s total cost is C = rK + (q 2 /2K), where K = the firm’s capital (plant size), q is output and r is the price of a unit of capital. 1. What is short-run average total cost (C/q) and what is marginal cost dC/dq, assuming K is fixed at K0 (2 points) 2. Suppose K is not fixed, but output is fixed at q0. Given this exogenous output and exogenous price of capital r0, what level of capital (K*) is most efficient – that is, minimizes total cost C? Do not forget to check the second order condition (4 points) 3. Find and interpret ∂K*/∂r.
- Profit is found as total revenue (TR) minus total cost (TC). With that in mind, let us now consider the possible profits for the firm that we looked at in assignments 7 and 8, where the firm’s capital is fixed at 2 units and where the cost of capital is $40 per unit per period, while the cost of labor (or wage rate) is $30 per unit of labor per period and the firm has the following short run production function: Labor: 0 1 2 3 4 5 6 7 8 9 Output: 0 6 24 60 120 170 210 240 260 270 Now, let us further assume that the firm is perfectly competitive (i.e., it is a price taker) and that it can sell each unit of the output that it produces for $3 [remember, for price takers, the price (P) is also the marginal revenue (MR)]. (a) Use this information set up a diagram (i.e., an excel chart) that shows total cost (TC) and total Revenue (TR) of the firm per period in the short run with the level of output on the horizontal axis. (b) Also, use…Output Y is produced according to Y = F(K, L), where K is the capital stock and Lis the number of workers. The production function F(K, L) has constant returns toscale and diminishing marginal returns to capital and labour individually. The levelof technology is assumed to be constant over time. Capital per worker is denotedby k = K/L and output per worker by y = Y/L, and the two are related according toy = f(k), where f(k) = F(k, 1) is the per-worker production function. Investment is equal to saving, which is a constant fraction s of income Y. Capitaldepreciates at rate δ and the number of workers grows at rate n. The change incapital per worker over time is ∆k = sf(k) − (δ + n)k. Consider a country that has reached its steady-state capital per worker. Then, inone year, the country suffers severe flooding that destroys part of its capital stock.Assume this is treated as a one-off event that is not expected to reoccur. explain what happens to incomeper worker in the short run and the…Modified True or False: State whether each statement is true or false. If the statement is false, briefly explain why it is so, and then restate it to make it true. Spreading overhead is the process of dividing total fixed costs by more units of output, which implies that average fixed cost declines as quantity declines. Diminishing returns, or decreasing marginal product, imply diminishing marginal cost. At the output level where MR = MC, if the corresponding P is above AVC but below ATC, the loss-minimizing move is to shut down or stop production. A firm that is breaking even, or earning a zero level of profit, is one that is earning exactly a normal rate of return, which implies that new investors are not attracted, but current ones are not running away either. Zero economic profit implies zero accounting profit. In the long run, if price is below average total cost, then it pays to just shut down. The shapes of long-run cost curves follow directly from the assumption of a fixed…
- Let the production function be Q = 4∗K1/4L1/4 assume that both factors are variable. (a) Derive the contingent demand functions for K and L (b) Substitute the contingent demand functions in the total cost that you minimized in part a) to obtain the total cost function. (c) FindtheamountofKandLnecessarytoproduceQ=8whenv=16andw=1 (with minimal possible cost). (d) Find the average and marginal cost functions.Ouroboros’ total cost (TC) as a function of its production level q is given by the equationbelow:TC(q) = 2?² − 12,000q + 30,000,000a. How much is the fixed cost of production for Ouroboros? b. If q=5,000, how much is the total cost for Ouroboros? c. Evaluate the marginal cost for Ouroboros when q=3,000. d. For this part, suppose that Ouroboros has two corporate customers. The firstcorporations’ demand as a function of Ouroboros’ price is given by ??(?) = 10,000 − ? and the second corporation’s demand function is given by ??(?) = 20,000 − ?.Calculate Ouroboros’ maximum possible profit level.This question illustrates the argument on p.114 of the book. A and B own neighboring properties. Beneath their properties is a common well that contains 200 units of oil. The cost to A of extracting oil from the well in period t depends on the number of units of oil in the well at the beginning of the period t, ut, and the number of units of oil A extracts in period t, xAt ; specifically, the average cost of extraction for A per unit in period t is xAt /ut. The analogous cost function for B is xBt/ut. The market price of a barrel of oil is 1, there are two periods (t = 1, 2), and the discount rate is zero. The oil is a common property resource. a) (2) Suppose that A and B "unitize" and cooperatively decide how much oil to extract, and split the profit between them. The jointly profit-maximizing policy is that each extracts 50 units of oil from her well in each of the first two periods, after which the well is dry. How much discounted profit will A and B each make? b) (2) Suppose…
- Suppose that the production function takes the form X = min(10L, 5K) and that a competitive firm faces a wage rate of £60 per week and a weekly capital rental of £32. (a) How much must the firm spend to produce 100 units of output, and what is the average cost of production when X = 100? (b) What is the incremental cost of producing the 101st unit of output? (c) What happens to the cost of producing 100 units of output if the wage rate and the rental cost of capital rise by 25 per cent each? What happens to the average and marginal cost? (d) What happens to the cost of producing 100 units of output if the wage rate increases by £1, or if the cost of capital increases by £1?The cost formula for a company can be modeled by C=1092+40x+0.1x2C=1092+40x+0.1x2 where xx represents the number of items made. A formula for the company's income is modeled with R=108x−0.9x2R=108x-0.9x2, where xx is the number of items sold. A company will break even when its costs equal its income. How many items must a company make and then sell to break even? Answer: (If there are multiple answers, separate the answers with a comma.)rofit is found as total revenue (TR) minus total cost (TC). With that in mind, let us now consider the possible profits for the firm that we looked at in assignments 7 and 8, where the firm’s capital is fixed at 2 units and where the cost of capital is $40 per unit per period, while the cost of labor (or wage rate) is $30 per unit of labor per period and the firm has the following short run production function: Labor: 0 1 2 3 4 5 6 7 8 9 Output: 0 6 24 60 120 170 210 240 260 270 Now, let us further assume that the firm is perfectly competitive (i.e., it is a price taker) and that it can sell each unit of the output that it produces for $3 [remember, for price takers, the price (P) is also the marginal revenue (MR)]. (a) Use this information set up a diagram (i.e., an excel chart) that shows total cost (TC) and total Revenue (TR) of the firm per period in the short run with the level of output on the horizontal axis. (b) Also, use…