QUESTION 3 Let c(w1; w2; y) be a cost function, and let A > 1. We have: Oa.q A w; Aw2; y) = o(w1; w2; y) O b.q A w1; Aw2; y) = Ac(w1; w2; y) Oc. d A w1; Aw2: y) > Ao(w1; w2; y) Od.( A w1; Aw2: y) < Ao(w1; w2; y)
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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) 270eThis 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…A firm has a production function of q=2(LK), where the L represents hours of labor, K represents hours of machine usage and q represents the hourly production volume. Currently the price of labor is $20 per hour and the price of capital is $40 per hour. a. When the production level is at 40,000 units, use the LaGrange process to determine how much they should spend on labor and capital. b. If the purchasing agent requests an additional unit (40,001st unit), what is the minimum price you should charge on that specific unit? (Note: determine this without re-solving the Lagrange problem itself.)
- Suppose a Cobb-Douglas Production function is given by the function: P(L,K)=8L^0.7K^0.3Furthemore, the cost function for a facility is given by the function:C(L,K)=300L+500KSuppose the monthly production goal of this facility is to produce 20,000 items. In this problem, we will assume LL represents units of labor invested and KK represents units of capital invested, and that you can invest in tenths of units for each of these. What allocation of labor and capital will minimize total production Costs?Units of Labor LL = (Show your answer is exactly 1 decimal place)Units of Capital KK = Incorrect (Show your answer is exactly 1 decimal place)Also, what is the minimal cost to produce 20,000 units? (Use your rounded values for LL and KK from above to answer this question.)The minimal cost to produce 20,000 units is $ Hint: Your constraint equation involves the Cobb Douglas Production function, not the Cost function. When finding a relationship between LL and KK in your system of…A small bank is trying to determine the number of tellers to employ. The total cost of employing a teller is $100 per day, and a teller can serve an average of 160 customers per day. On average, 210 customers arrive per day at the bank, and both service times and interarrival times are exponentially distributed. If the delay cost per customer day is $200, how many tellers should the bank hire?question 8 For each of the following situations, Find the Total Cost function, TC(q) Identify the optimal input mix, L* and K* for the given q. A) q = 2*MIN(L,5K); w = 8, r = 10; i) (5 points) TC(q) = __________________ ii) (4 points) q = 20 L* = _________________ K* = _________________
- Your firm specializes in recycling used plastics into consumer goods. You have three production opportunities: 1. You can produce plastic utensils for a revenue of $30,000 while production will cost $15,000. 2. Alternatively, you can produce lampshades: you calculate that at the optimal production, you expect to sell 2,000 lampshades every year at $10 each, and your average total cost per lampshade will be $2. 3. You also have the option to shut down your factory and produce nothing at a cost of $1,000 a year. Which opportunity do you choose? 4 Instead of working hard, Kendall Square Inc’s manager can shirk and not improve costs. In order to incentivize her hard work, Kendall Square Inc’s shareholders want to give the manager a bonus if they see that variable costs are cut by half. What is the maximum bonus that shareholders would be willing to give?Q3, A firm operates with the following Cobb-Douglas production function where Q is output, L is labor hours per week, and K is machine hours per week. Cobb-Douglas Production Function: Q = 5(L1/3K2/3) The firm intends to produce 5,000 units of output per week by contracting employees for $40 per hour and renting machinery for $10 per hour. Determine the cost minimizing combination of labor and capital for the firm. Based on your solution in part (a), calculate the firm’s total cost of producing 5,000 units of output per week.A firm produces output according to the following production function:Q = F (K, L) = 4K + 8L(a) How much output is produced when K = 2 and L = 3?(b) If the wage rate is $60 per hour and the rental rate on capital is $20 per hour, what is the costminimizing input mix for producing 24 units of output?(c) If the wage rate decreases to $20 per hour but the rental rate on capital remains at $20 per hour,what is the cost minimizing input mix for producing 24 units of output?
- 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?(You will need to use a spreadsheet to tackle these questions.) 1. How much of q can be produced for £60,000 if the total cost function is TC = 86 + 152q − 12q2 + 0.6q3? 2. What output can be produced for £150,000 if TC = 130 + 62q − 3.5q2 + 0.15q3? 3. Solve for x when 0 = −1,340 + 14x + 2x2 − 1.5x3 + 0.2x4 + 0.005x5 − 0.0002x6Modified 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…