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Managerial Economics Homework 1 Assignment Solution




Question;1.If the demand curve for wheat in the United States is P=12.4 - Q_D where is the P is thefarm price of wheat (in dollars per bushel) and Q_D is the quantity of wheat demanded(in billions of bushels), and the supply curve for wheat in the United States is P= -2.6 +2Q_S where Q_s is the quantity of wheat supplied (in billions of bushels), what is theequilibrium price of wheat? What is the equilibrium quantity of wheat sold? Must theactual price equal the equilibrium price? Why or why not?2. The Haas Corporations executive vice president circulates a memo to the firms topmanagement in which he argues for a reduction in the price of the firms product. Hesays such a price cut will increase the firms sales and profits.a. The firms marketing manager responds with a memo pointing out that the priceelasticity of demand for the firms product is about -0.5. What is this factrelevant?b. The firms president concurs with the opinion of the executive vice president. Isshe correct?3. In the following diagram, we show one of Janes indifference curves and her budget line.a. If the price of good X is $100, what is her income?b. What is the equation for her budget line?c. What is the slope of her budget line?d. What is the price of good Y?e. What is Janes marginal rate of substation in equilibrium?Good X40180Good Y4. According to the chief engineer at the Zodiac Company, Q=AL^aK^B, where Q is theoutput rate, L is the rate of labor input, and K is the rate of capital input. Statisticalanalysis indicates that a=0.8 and B=0.3. The firms owner claims the plant has increasingreturns to scale.a. Is the owner correct?b. If B were 0.2 rather than 0.3 would she be correct?c. Does output per unit of labor depend only on a and B? Why or why not?5. The Haverford Company is considering three types of plants to make a particularelectronic device. Plant A is much more highly automated than plant B, which in turn ismore highly automated than plant C. For each type of plant average variable cost so longas output is less than capacity, which is the maximum output of the plant. The coststructure for each type of plant is as follows:Average Variable CostsPlant APlant BPlant CLabor$1.102.40$3.70Materials0.901.201.80Other0.502.402.00Total$2.50$6.00$7.50Total fixed costs$300,000$75,000$25,000Annual capacity200,000100,00050,000a. Derive the average costs of producing 100,000, 200,000, 300,000, and400,000 devices per year with plant A. (For output exceeding the capacity ofa single plant, assume that more than one plant of this type is built.)b. Derive the average costs of producing 100,000, 200,000, 300,000, and400,000 devices per year with plant B.c. Derive the average costs of producing 100,000, 200,000, 300,000 and 400,000devices per year with plant C.d. Using the results of parts (a) through (c), plot the points on the long-runaverage cost curve for the production of these electronic devices for outputs of100,000, 200,000, 300,000 and 400,000 devices per year.6. In 2008, the box industry was perfectly competitive. The lowest point on the long-runaverage cost curve of each of the identical box producers was $4, and this minimum pointoccurred at an output of 1,000 boxes per month. The market demand curve for boxes wasQ_D=140,000 10,000PWhere P was the price of a box (in dollars per box) and Q_D was the quantity of boxesdemanded per month. The market supply curve for boxes wasQ_S=80,000 + 5,000PWhere Q_S was the quantity of boxes supplied per month.a. What was the equilibrium price of a box? Is this the long-run equilibrium price?b. How many firms are in this industry when it is in long-run equilibrium?7. The Wilson Companys marketing manager has determined that the price elasticity ofdemand for its product equals -2.2. According to studies she carried out, the relationshipbetween the amount spent by the firm on advertising and its sales is as follows:Advertising ExpenditureSales$100,000$1.0 million$200,000$1.3 million$300,000$1.5 million$400,000$1.6 milliona. If the Wilson Company spends $200,000 on advertising, what is the marginal revenuefrom an extra dollar of advertising?b. Is $200,000 the optimal amount for the firm to spend on advertising?c. If $200,000 is not the optimal amount, would you recommend that the firm spends moreor less on advertising?8. Ann McCutcheon is hired as a consultant to a firm producing ball bearings. This firmsells in two distinct markets, each of which is completely sealed off from the other. Thedemand curve for the firms output in the first market is P_1=160-8Q_1, where P_1 is theprice of the product and Q_1 is the amount sold in the first market. The demand curvefor the firms output in the second market is P_2=80-2Q_2, where P_2 is the price of theproduct and Q_2 is the amount sold in the second market. The firms marginal cost curveis 5+Q where Q is the firms entire output (destined for either market). Managers askAnn McCutcheon to suggest a pricing policy.a. How many units of output should she tell managers to sell in the second market?b. How many units of output should she tell managers to sell in the first market?c. What price should managers charge in each market?9.. The Xerxes Company is composed of a marketing division and a production division.The marketing division packages and distributes a plastic item made by the productiondivision isP_0=200-3Q_0Where P_0 is the price (in dollars per pound) of the finished product and Q_0 is the quantity sold(in thousands of pounds). Excluding the production cost of the basic plastic item, marketingdivisions total cost function isTC_0=100+15Q_0Where TC_0 is the marketing divisions total cost (in thousands of dollars). The productiondivisions total cost function isTC_1=5+3Q_1 + 0.4Q_1^2Where TC_1 is total production cost (in thousands of dollars) and Q_1 is the total quantityproduced of the basic plastic item (in thousands of pounds). There is a perfectly competitivemarket for the basic plastic item, the price being $20 per pounda. What is the optimal output for the production division?b. What is the optimal output for the marketing division?c. What is the optimal transfer price for the basic plastic item?d. At what price should the marketing division sell its product?10. James Pizzo is president of a firm that is the industry price leader, that is, it sets the priceand the other firms sell all they want at that price. In other words, the other firms act asperfect competitors. The demand curve for this industrys product is P=300-Q, where P isthe price of the product and Q is the total quantity demanded. The total amount suppliedby other firms is equal to Q_r, where Q_r = 49P. (P is measured in dollars per barrel, Q,Q_r and Q_b are measured in millions of barrels per week.)a. If Pizzos firms marginal cost curve is 2.96Q_b, where Q_b is the output of hisfirm, at what output level should he operate to maximize profit?b. What price should he charge?c. How much does the industry as a whole produce at this price?d. Is Pizzos firm the dominant firm in the industry?11. The Boca Raton Company announces that if it reduces its price subsequent to a purchase,the early customer will get a rebate so that he or she will pay no more than those buyingafter the price reduction.a. If the Boca Raton Company has only one rival, and if its rival too makes such anannouncement, does this change the payoff matrix? If so, in what way?b. Do such announcements tend to discourage price cutting? Why or why not?12. Your company is bidding for a broadband spectrum license. You have been asked tosubmit an optimal bidding strategy. You expect that bidders will have independentprivate values for the licenses because each bidder presently has a different structure inplace. You elieve the valuations for these licenses will be $200 million and $700 million.Your own valuation is $650 million. There is some uncertainty about the auction designthat will be used, so you must suggest an optimal bidding strategy for the followingacution designs:a. Second-price, sealed-bid auctionb. English auction.c. Dutch auction13. William J. Bryan is the general manager of an electrical equipment plant. He must decidewhether to install a number of assembly robots in his plant. This investment would berisky because both management and the workforce have no real experience with theintroduction or operation of such robots. His indifference curve between expected rate ofreturn and risk is as hsown in the figure.a. If the riskiness () of this investment equals 3, what risk premium does require?b. What is the riskless rate of returnc. What is the risk-adjusted discount rate?d. In calculating the present value of future profit from this investment, what interestrate should be used?ExpectedRate ofReturn(percent)18----------------------------------------------------1260123Risk ()14. Suppose the typical Florida resident has wealth of $500,000, of which his or her home isworth $100,000. Unfortunately Florida is infamous for its hurricanes, and it is believedthere is a 10 percent chance of hurricane that could totally destroy a house (a loss of$100,000). However, it is possible to retrofit the house with various protective devices(shutters, roof bolts, and do on) for a cost of $2,000. This reduces the 10 percent chanceof a loss of $100,000 to a 5 percent chance of a loss of $50,000. The homeowner mustdecide whether to retrofit and thereby reduce the expected loss. The problem for aninsurance company is that it does not know whether the retrofit will be installed andtherefore cannot quote a premium conditioned on the policyholder choosing this action.Nevertheless, the insurance company offers the following two policies from which thehomeowner can choose: (1) The premium for insurance covering total loss is $12,000 or(2) the premium for insurance covering only 50 percent of loss is $1,500. The typicalhomeowner has a utility function equal to the square root of wealth. Will the homeownerretrofit the house, and which insurance policy will homeowner buy? Will the insurancecompany make a profit (on average) given the homeowners choice?15. The market for digital cameras is relatively new. Ajax Inc. produces what it regards as ahigh-quality digital camera. Knockoff Inc. produces what it regards as a low-qualitydigital camera. However, because the market is so new, reputations for quality have notyet developed, and consumers cannot tell the quality difference between an Ajax digitaland a Knockoff digital just by looking at them.If consumers knew the difference, theyd be willing to pay $200 for a high-qualitycamera, and theyd be willing to pay $100 for a low-quality camera. It costs Ajax $85 toproduce a high-quality camera, and it costs Knockoff $55 to produce a low-qualitycamera.A recent MBA hire at Ajax suggests that Ajax could differentiate itscamera from Knockoffs by offering a full-coverage warranty (which would fully coverany defect in the camera at no cost to the customer). The MBA estimates that it wouldcost Ajax $20 per year to offer such a warranty. The MBA also estimates that it wouldcost Knockoff $40 per year should Knockoff attempt to copy Ajaxs warranty strategy.Consumers will feel that the camera with the longest warranty is high-quality and thatwith the shortest warranty is low-quality. The camera companies want to maximize theprofit per camera.16. The cost of pollution (in billions of dollars) originating in the paper industry isCp=2P +P^2Where P is the quantity of pollutants emitted (in thousands of tons). The cost of pollutioncontrol (in billions of dollars) for this industry isCc=5 3)a. What is the optimal level of pollution?b. At this level of pollution, what is the marginal cost of pollution?c. At this level of pollution, what is the marginal cost of pollution control?


Paper#55471 | Written in 18-Jul-2015

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