Problem Set #4:Production & CostsQ.1Consider the following Cobb-Douglas production function for your company, which provides bus servicein Nanaimo.Q AL K F Where Q =output in millions of passenger miles, L= labour input in worker hours, K=capital input in bustransit hours and F= Fuel input in gallonsEach of the parameters of this model was estimated by regression analysis using monthly data over arecent 3 year period. Results obtained were as followsA= 1.2, ?=0.285 ?=0.638 ?=0.126The standard error estimates for each coefficient areSA = 0.4 S? = 0.15 S?= 0.12 S?= 0.07a) Estimate the effect on output of a 4% decline in workers hours (holding K and F constant)b) Estimate the effect on output of a 3% reduction in Fuel availability accompanied by a 4% declinein bus transit hours (holding L constant)c) Which input is significant in determining the output? How do you know?d) Estimate the returns to scale for this production systeme) Determine the expression for Marginal product of labour inputQ.2Your firm produces output that can be sold at a price of $10. The production function is givenbyQ L1 / 2 K 1 / 2 If K is fixed at 1 unit in the short run, how much labour should the firm employ to maximize profits ifthe wage rate=2.Q.3You recently replace Yen, the manager of the Roller Division at a major conveyor-manufacturing firm,despite her strong external sales record. Roller manufacturing is relatively simple, requiring onlylabour and a machine that cuts and crimps rollers. As you begin reviewing the companyâs productioninformation, you learn that labour is paid $16 per hour and the last worker produced 200 rollers perhour. The company rents roller cutters and crimping machines for $30 per hour and the marginalproduct of capital is 240 rollers per hour. What do you think Yen could have done to keep her job?Explain Q.4 Which of the following news items involve a short run decision and which involve a long run decision?Assume that factors of production include Land, Labour, Capital, Entrepreneurship and other capitalinputs). Explain(a) January 31, 2017: Toyota will open 75 more plant abroad than originally predicted, for a total of1275(b) February 25, 2016: For three hours on Tuesday, Cactus Club will shut down every single one ofits 80 restaurants so that servers (waiters and waitresses) can receive a refresher course.(c) June 2, 2010: Starbucks to replace baristas (men and women who serve the coffee) withvending machinesQ.5(i) Soniaâs Surfboards rents a factory building. If the rent is increased by $200 a week and otherthings remain constant, how do Soniaâs Surfboards short run average cost curves, averagevariable costs and marginal cost curves change? ExplainIf other things remain the same, the average fixed cost curve shifts upward, the average variablecost curve does not change, the average total cost curve shifts upward, and the marginal costcurve does not change (ii)Jusu Coffee House is raising its prices because the wholesale price of milk has risen 70% andthereâs a lot of milk in the coffee houseâs lattes. Describe how the price of milk changes Jusuâs CoffeeHouse short-run cost curvesQ.6The management of Chisom Industries is considering a plan to terminate a new employee Stu. Theaction stemmed from documented evidence supplied by the firm’s accounting department manager,Ayo, that Stu did not add as much to the firm’s overall output as did Maji, a worker hired two weeksearlier. Based on this evidence, do you agree that the Stu should be fired? ExplainQ.7While looking into your firmâs books you noted that the TC = 250,000+40Q+0,01Q 2. Determine theoutput level at which your firmâs average cost is minimized. (hint: remember the cost curves)Q.8The Sudheer Winery plans to open a new production facility in India. Based information provided bythe accounting department, the company estimates fixed costs of $200,000 per year and averagevariable costs of AVC = 100 + 0.5Qa. Estimate total cost and average total cost functionsb. Find the MC function