微观经济学作业答案3.doc

Managerial EconomicsHOMEWORK SET#3Name:Class:Student #: (Due day: Next class)Part 1:1. When the average product is decreasing, marginal producta.equals average product. b.is increasing.c.exceeds average product. d.is decreasing.e.is less than average product.Choose: e)The next two questions refer to a firm in a constant- cost industry with ATC(q) = 2,000/q + 100 + 5q and MC(q) = 100 + 10q.2. The long-run equilibrium price equals:a. $100 b. $200 c. $300 d. $500 e. None of the above is correct.Choose: c) Find minimum ATC by setting ATC = MC; this yields q = 20. Plug q = 20 into ATC to find the long-run equilibrium price of $300.3. Demand for industry output has just increased. If the market price initially rises to $600, each firm in the long run will produce:a. 20 units b. 50 units. c. 88.7 unit d. 100 units. e. More information is needed.Choose: a) The long-run equilibrium will again have each firm producing at minimum ATC. Each firm produces 20 units, as in Question 3.4. A straight-line isoquanta.is impossible.b.would indicate that the firm could switch from one output to another costlessly.c.would indicate that the firm could not switch from one output to another.d.would indicate that capital and labor cannot be substituted for each other in production.e.would indicate that capital and labor are perfect substitutes in production.Choose: e)5. A farmer uses M units of machinery and L hours of labor to produce C tons of corn, with the following production function C = L0.5 + M0.75. This production function exhibitsa.decreasing returns to scale for all output levelsb.constant returns to scale for all output levelsc.increasing returns to scale for all output levelsd.no clear pattern of returns to scaleChoose: b) 2L0.5+2M0.75=2C6. The difference between the economic and accounting costs of a firm are a.the accountants feesb.the corporate taxes on profitsc.the opportunity costs of the factors of production that the firm ownsd.the sunk costs incurred by the firme.the explicit costs of the firmChoose: c)7. Price ceiling are inefficient because:a. both producers and consumers lose.b. Producers lose, consumers may gain or lose, but a loss occurs on net.c. Producers lose, consumer gain, but a loss occurs on net.d. Producers and consumer may gain or lose, but a loss occurs on net.e. None of the above is correct.Choose: b) Consumers gain from a lower price, but lose because they are able to buy less. Produces clearly lose from the regulated price. There is always a welfare loss from price ceilings ( assuming that the price ceiling is binding).8. Assume that a firm spends $500 on two inputs, labor (graphed on the horizontal axis) and capital (graphed on the vertical axis). If the wage rate is $20 per hour and the rental cost of capital is $25 per hour, the slope of the isocost curve will bea.500.b.25/500.c.4/5.d.25/20 or 1/4.Choose: c) 20L+25C=500, C=-4/5L+209. Suppose that the price of labor ( ) is $10 and the price of capital ( ) is $20. What is the equation of the isocost line corresponding to a total cost of $100?a.PL + 20PKb.100 = 10L + 20Kc.100 = 30(L+K)d.e.none of the aboveChoose: b)The next three questions refer to the alfalfa market described in Figure 1.SD162025Tons of Alfalfa(millions)305075Price ($/ton)FFigure 110. If the government purchases enough alfalfa to raise the price from $50/ton to $75/ton, the cost of the program will be:a. $100 million. b. $225 million.c. $315 million. d. $675 million.e. None of the above is correct.Choose: d) The government pays $75/ton for the surplus of 25 16 = 9 million tons: 75(9) = $675.11. If the government raises the price to $75/ton, producer surplus will increase by:a. $400 million. b. $500 million.c. $562.5 million. d. $1,875 million.e. None of the above is correct.Choose: c) Producer surplus increase by the area of the trapezoid between P = $50 and P = $75, and Q = 20 and Q = 25 million: $25(20 + 25)/2 = $562.5 million.12. Suppose the government decides to support a price of $75/ton by paying producers not to produce the excess supply of alfalfa (which is 25 16 = 9 million tons). The minimum cost of this program will be :a. $157.5 million. b. $202.5 million.c. $315 million. d. $1,875 million.e. None of the above is correct.Choose:b) To idle acreage, producers must be paid at least the shaded area in Figure 1: 0.5(25 16 )(75-30) = $202.5 million.SPrice($/unit)75501625D30Ton(millions)2013.Producer surplus in a perfectly competitive industry isa.the difference between profit at the profit-maximizing output and profit at the profit-minimizing output.b.the difference between revenue and total cost.c.the difference between revenue and variable cost.d.the difference between revenue and fixed cost.e.the same thing as revenue.Choose:c)Part 2:A firms total cost function is given by the equation:TC = 4000 + 5Q + 10Q2.(1) Write an expression for each of the following cost concepts:a. Total Fixed Costb. Average Fixed Costc. Total Variable Costd. Average Variable Coste. Average Total Costf. Marginal Cost(2) Determine the quantity that minimizes average total cost. Demonstrate that the predicted relationship between marginal cost and average cost holds.Solution:PART (1)a.b.c.d.e.f.PART (2)ATC is minimized where MC is equal to ATC.Equating MC to ATCATC is minimized at 20 units of output. Up to 20, ATC falls, while beyond 20 ATC rises.MC should be less than ATC for any quantity less than 20.For example, let Q = 10:MC = 5 + 20(10) = 205MC is indeed less than ATC for quantities smaller than 20.MC should exceed ATC for any quantity greater than 20.For example, let Q = 25:MC = 5 + 20(25) = 505MC is indeed greater than ATC for quantities greater than 20.Part 3:The Cummins Engine Co. is a successful producer of diesel engines for trucks. This part examines the firm s cost data and fill in the blanks and then find the profit maximizing (or loss minimizing) output level when P=$150. Please explain your decision.OutputqRevenueR($150*q)Total CostTCProfitpAverageTotal CostATCAverageVariable CostAVCMarginal CostMC132,100161.5475n.a.142,245160.3680145152,400160.0085155162,565160.3190165172,740161.1895175Answer:OutputRevenueTotal CostProfit131,9502,100-150142,1002,245-145152,2502,400-150162,4002,565-165172,5502,740-190The profit maximizing output level is q = 14. If it expands output by one unit to 15 units, it will take in an additional $150 in revenue, but it will pay an additional $155 in production costs. So, expanding output to 15 units will cause the firm to lose an extra $5 in profits. Likewise, if it reduces its output by one unit to 13, it saves $145 in costs, but it gives up $150 in revenue. Thus, profit would fall by $5 compared with producing 14 units of output. Although profits are negative (-$145), it is clear that looses will be minimized at q = 14.Part 4:Bud Owen operates Buds Package Store in a small college town. Bud sells six packs of beer for offpremises consumption. Bud has very limited store space and has decided to limit his product line to one brand of beer, choosing to forego the snack food lines that normally accompany his business. Buds is the only beer retailer physically located within the town limits. He faces considerable competition, however, from sellers located outside of town. Bud regards the market as highly competitive and considers the current $2.50 per six pack selling price to be beyond his control. Buds total and marginal cost functions are:TC = 2000 + 0.0005Q2MC = 0.001Q,where Q refers to six packs per week. Included in the fixed cost figure is a $750 per week salary for Bud, which he considers to be his opportunity cost.a. Calculate the profit maximizing output for Bud. What is his profit? Is this an economic profit or an accounting profit?b. The town council has voted to impose a tax of $.50 per six pack sold in the town, hoping to discourage beer consumption. What impact will the tax have on Bud? Should Bud continue to operate? What impact will the tax have on Buds outoftown competitors?Solution:a.Given the competitive nature of the market, Bud should equate P to MC.Since the cost function is an economic cost function, we can conclude that this is an economic profit.b.Tax shifts total cost curve to:TC = 2000 + 0.0005Q2 + 0.5QMC becomesMC = 0.001Q + 0.5setting P = MCGiven that this is zero economic profit, Bud should continue operating.The impact upon Buds competitors will be favorable or neutral. As he curtails output, 500 six packs worth of business will either shift elsewhere or choose temperance.Part5:The market for college hockey players is characterized by the following supply and demand curves, where Q is the number of athletes and P is the weekly wage in excess of their scholarship payments:QD = 1,600 20P,QS = -900 + 30P.a. Suppose there is a completely free market. What is the equilibrium weekly wage? How many athletes are hired?b. Now suppose that National Collegiate Athletic Association (NCAA) steps in and decides to crack down on payments to players. The NCAA is bothered not by the existence of these payments, but by their level, so the NCAA restricts players to be paid no more than $35/week above the scholarship payment. How man