eco204_summer_2009_practice_problem_18_solution

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Unformatted text preview: University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain ECO 204 Summer 2009 S. Ajaz Hussain Practice Problems 18 Solutions Please help improve the course by sending me an email about typos or suggestions for improvements Note: Please don't memorize these solutions in the expectation that similar questions will appear on tests and exams. Instead, try to understand how to derive the answer as you'll be tested on techniques and applications, not on memorization. Moreover, tests and exams will cover topics and techniques that may not be in these practice problems. You are urged to go over all lectures, class notes and HWs thoroughly. Question 1 (20082009 Test Question) Spurred by the success of major sports leagues such as the NBA, NHL, NFL and UFC you start a new sports league BED: "Battle of Economists unto Death". This profit maximizing league organizes gladiator style fights between prominent economists. BED's costs stem from printing tickets only. Suppose Q is measured in thousands. A typical match hall has a capacity of 2,000 or Q = 2. (a) In March 2009, Professor Peasando will battle Lord Maynard Keynes. Suppose demand for March 2009 is estimated to be P = 25 5Q and MC is estimated to be MC = 5. How many tickets will you print and sell? At what price? Answer: BED wishes to maximize profits. It sets MR = MC: 25 10Q = 5 Q = 20/10 = 2 This answer is feasible: therefore, you will print and sell 2,000 tickets at a price of: P = 25 5(2) = $15 1 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain (b) In April 2009, Professor Hussain will battle Ecoman. Suppose demand for April 2009 is estimated to be P = 25 5Q and MC is estimated to be MC = 5. However, before any tickets are printed, the MC estimate changes to MC = 10. How many tickets should you print and sell? At what price? Answer: BED wishes to maximize profits. It sets MR = MC. Since MC has been revised before printing (i.e. production), we simply recompute MR = MC using the new MC: 25 10Q = 10 Q = 15/10 = 1.5 This answer is feasible. Therefore, we will print and sell 1,500 tickets at a price of: P = 25 5(1.5) = $17.5 (c) In May 2009, Professor GIndart will battle Milton Friedman. Suppose demand for May 2009 is estimated to be P = 25 5Q and MC is estimated to be MC = 5. However, after all tickets are printed, the demand forecast is revised to P = 10 Q. How many tickets should you sell? What is the price of the tickets? Answer: BED wishes to maximize profits. With the initial demand and cost forecasts, BED will print tickets by setting MR = MC: 25 10Q = 5 Q = 20/10 = 2 Or 2,000 tickets. In light of new demand information, BED sets MR = MC but uses MR from the new demand curve and since demand has been revised after printing (i.e. production) uses MC = 0 as all printing costs have been incurred and are sunk. 10 2Q = 0 Q = 5 However, this exceeds the number of tickets already printed. Thus, BED will sell Q = 2 or 2,000 tickets at a price of: 2 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain P = 10 2 = $8 Question 2 Ajax computers manufactures, distributes and retails computers for microeconomic computing. It estimates demand to be P = 100 25Q, where P is in $ and Q is in `000s. The MC of manufacturing, distributing and retailing 1,000 machines is given by: MC = MCmanufacture + MCdistribution + MCretail = 25 + 5 + 20 (a) Calculate the revenue maximizing output and price. Answer: To maximize revenues, Ajax should set MR = 0: P = 100 25Q MR = 100 50Q MR = 0 MR = 100 50Q = 0 Q = 2 P = 100 25(2) = $50 (b) Calculate the profit maximizing output and price. Answer: To maximize profits, Ajax should set MR = MC. Note this is the rule before production, distribution and retail has begun: MR = MC 100 50Q = 50 Q = 1 P = 100 25(1) = $75 (c) Suppose after the machines have been produced, the MC of distribution increases from $5 to $10. How will this impact Ajax computers? 3 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Answer: From part (b) we know that when there was no uncertainty, Ajax should produce, distribute and retail Q = 1 units (or 1,000 machines). Now that Q = 1 units have been produced, the cost going forward rises from: MCdistribution + MCretail = 5 + 20 = 25 to: MCdistribution + MCretail = 10 + 20 = 30 With this increase in MC, the decision becomes "of the computers already manufactured, how many should be distributed and retailed?". Set MR = MC going forward: MR = MC 100 50Q = 30 50Q = 70 Q = 70/50 Q = 1.4 But Ajax only has Q = 1 units available for distribution and retail. Thus, even with the higher MC of distribution, Ajax should continue to distribute and retail 1,000 machines at $75 each. Note that when MC going forward increases, Ajax will always "sell" Q = 1 units as long as the new MC is below the original MC of $50. This is because, if the new MC going forward is below the original MC of $50, setting MR = MC will always yield a Q that is greater than Q = 1. But with a "capacity" of 1, this will mean that Ajax can only "sell" Q = 1. In sum: if the MC going forward is < 50, Ajax will always sell Q = 1 units at P = $75. Question 3 "Hee Haw" sells farm equipment and faces demand given by P = 3,000 Q, where P is the price in dollars and Q is output sold per month. In its East Coast factory, the firm's fixed costs are $250,000 per month, and its marginal cost of manufacturing the equipment is $1,000 per unit. (a) Find the firm's profit maximizing output and price. What are its profits? Answer: We can solve this part by using MR = MC: 4 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain MC = 1,000 MR = 3,000 2Q Setting MR = MC: 3,000 2Q = 1,000 2Q = 2,000 Q = 1,000 P = 3,000 (1,000) = $2,000 = R C = PQ [TFC + MC*Q ] = 2,000*1,000 [250,000 + 1,000*1,000] = $750,000 (b) Over the last year, the US dollar has appreciated against the Japanese yen (i.e., it takes fewer dollars to buy one Yen, or takes more Yen to buy a dollar). As a result, Japanese imports of farm equipment to the US have become more competitive. Hee Haw's marketing department judges that it would now have to cut price by $500 in order to sell the same output as in part (a): this is to say, that the demand curve has fallen by $500. Is such a pricecut part of a profit maximizing strategy? In this question suppose demand has fallen before actual production takes place. Answer: We know that the demand curve has fallen by $500 everywhere, implying that the new equation is: P = 2,500 Q This question is designed to test your concepts: most people would intuitively say that because the demand curve has fallen by $500, the optimal price in (a) must also fall by $500. This may be correct, but the only way to set the optimal price in light of new information is through MR = MC: MC = 1,000 MR = 2,500 2Q Setting MR = MC: 2,500 2Q = 1,000 2Q = 1,500 5 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Q = 750 Thus, P = 2,500 (750) = $1,750 = R C = PQ [TFC + MC*Q ] = 750*1,750 [250,000 + 1,000*750] = $312,500 What if, instead of setting MR = MC you had reduced the price in (a) by $500? Well, there, P = $2,000. Suppose you reduce by $500: P = $1,500 And output stays the same at 1,000. Then you can check that the profits will be: $250,000, which is lower than what we have gotten by MR = MC. (c) Suppose that the firm has produced the optimal level of output in part (a). But before this quantity is sold, demand unexpectedly falls to: P = 2,800 2Q (or, Q = 1,400 0.5P). One manager recommends cutting price to sell the entire inventory; another favors maintaining the price in part (a) (and therefore selling less than the total inventory). Do you agree with either manager? What optimal price would you set? Answer: When using MR = MC to determine the profit maximizing output, you should be careful whether the decision is to produce and sell, or, to sell. We computed the optimal output with profit maximization in mind and then demand fell. Now, we need to re determine the number of goods to be sold. Since we have already produced our goods, there is no MC of production. Hence, our MR = MC becomes: MR = 0 which is the same as revenue maximization. Then: MR = 2800 4Q = 0 Q = 700 P = $1,400 To convince yourself that this is the right strategy, ask what happens under the two different suggestions from the managers, and contrast that with our MR = 0 strategy: 6 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Manager I: Using the new demand curve, set price to sell 1,000 units (the output from part (a)) Manager 2: Keep prices in part (a) and sell the associated output using the new demand curve. Strategy Manager 1 Manager 2 MR = 0 (us) Price $800 $2,000 $1,400 Output Sold (not produced) 1,000 400 700 Revenues $800,000 $800,000 $980,000 Question 4 The following page contains Exhibits 1 3 from the Prestige Telephone Company. In this case, commercial customers were being charged $800/hr. (a) Suppose management had chosen the price of $800/hr using the cost plus rule. What was their markup in March 2003? Show your calculations. Assume TFC is allocated to TFCCommercial on the basis of volume (i.e. by the fraction of total hours billed to commercial customers 1 ). Hint: think carefully about "total hours". Answer: Many companies use the cost plus rule as a "rule of thumb" to set prices. Of course, we know that one should use the optimal pricing rule P = {E/(1 + E)}MC, as do many companies. This rule is: P = (1 + markup) AC Now: P = $800. To obtain the markup we need the AC of commercial customers. By definition, the total cost of commercial customers is: CCommercial = TFCCommercial + AVCCommercial QCommercial 1 Accountants typically allocate fixed cost on the basis of volume: in this case they'd allocate TFC to commercial customers by the fraction of total revenue hours billed to commercial hours. This common practice is not correct. Nevertheless, assume it for this question. 7 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Exhibit 1 Prestige Data Services Summary of Computer Utilization, First Quarter 2003 Revenue Hours Intercompany Commercial Total revenue hours Service hours Available hours Total hours January 206 123 329 32 199 560 February 181 135 316 32 164 512 March 223 138 361 40 143 544 Exhibit 2 Prestige Data Services Summary Results of Operations, First Quarter 2003 January Revenues Intercompany sales Commercial sales Computer use Other Total Revenue Expenses Space costs Rent Custodial services February March $ 82,400 98,400 9,241 190,041 $ 72,400 108,000 9,184 189,584 $ 89,200 110,400 12,685 212,285 $ 8,000 1,240 9,240 $ 8,000 1,240 9,240 $ 8,000 1,240 9,240 Equipment costs Computer leases Maintenance Depreciation: Computer equipment Office equipment and fixtures Power 95,000 5,400 25,500 680 1,633 128,213 95,000 5,400 25,500 680 1,592 128,172 95,000 5,400 25,500 680 1,803 128,383 Wages and salaries Operations Systems development and maintenance Administration Sales 29,496 12,000 9,000 11,200 61,696 9,031 7,909 15,424 $ 231,513 $ (41,472) 29,184 12,000 9,000 11,200 61,384 8,731 7,039 15,359 $ 229,925 $ (40,341) 30,264 12,000 9,000 11,200 62,464 10,317 8,083 15,236 $ 233,723 $ (21,438) Materials Sales promotions Corporate services Total expenses Net income/(loss) Exhibit 3 Prestige Data Services Standard Costs - Average Month, First Quarter 2003 Variable Costs Power per hour Operations wages Total variable expenses per hour Fixed Costs Rent Custodial Computer lease Computer maintenance Depreciation Power Wages and Salaries Operations Systems development Administration Sales $4 $24 $28 $8,000 $1,240 $95,000 $5,400 $26,180 $200 $21,600 $12,000 $9,000 $11,200 Total Wages & Salaries Fixed Costs $53,800 Total non-variable expenses Sales promotion $189,820 $8,000 $197,820 << Total Fixed Costs 8 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain The question tells us to assume: TFCCommercial = (Commercial Hours/Total Hours) TFC of Prestige Telephone Company From the exhibits, note that TFC = $197,820. In March 2003, PTC had 361 revenue hours and 138 commercial hours. Thus the fraction of commercial hours is: (138/361) 0.38. Hence: TFCCommercial = (138/361) TFC = $75,620.94 Moreover, the exhibits and our solution to this case, indicate that AVC = AVCCommercial = $28. Thus: CCommercial = 75,620.94 + 28(138) $79,485 Hence: ACCommercial = CCommercial / QCommercial = 79,485/138 $576 Hence: P = (1 + markup) AC 800 = (1 + markup) 576 1 + markup = 800/576 markup = 800/576 1 markup 0.39 Hence, the markup is approximately 39% over ACCommercial. (b) Critique Prestige Telephone Company's use of the cost plus rule. Please offer an explanation of whether and if the rule is being applied correctly. Hint: Part of the answer depends on the cost function or the fact that AVC is constant. 9 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Answer: We've repeatedly critiqued the cost plus rule: We observed that the markup should be chosen on the basis of elasticity: if consumers are price sensitive, choose a lower markup and vice versa. PTC needs to ensure that the markup of 39% is in line with elasticity. We observed that the cost plus rule uses AC whereas, from the optimal pricing rule P = {E/(1 + E)MC, the company should use MC. In practice, using AC instead of MC isn't a problem as long as AC MC. Is this true here? No. The cost function is C = 79,485 + 28Q. Now MC = dC/dQ = 28. Clearly AC is nowhere near MC = 28 (which by the way also equals AVC since AVC = TVC/Q = 28Q/Q = 28). Thus, we suspect PTC may be on the wrong track with the cost plus rule 2 . Question 5 General Motors produces light trucks in several Michigan factories, where its annual fixed costs are $180m and marginal cost per truck is approximately $20,000. Regional demand for trucks is given by: P = 30,000 0.1Q, P is in $ and Q is annual sales of trucks. (a) What is GM's profit maximizing P and Q? What are light trucks profits? Answer: Set MR = MC 30,000 0.2Q = 20,000 10,000 = 0.2Q Q = 10,000/0.2 Q = 50,000 P = 30,000 0.1(50,000) = $25,000 Profits: = ($25,000 $20,000)(50,000) $180m = $250m $180m = $70m 2 In fact, if it used MC in the cost plus rule with a markup of 39%, we'd get P = (1 + m)MC = (1.39)(28) = $38.92 which is nowhere near $800! 10 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain (b) GM is getting ready to export trucks to China. Based on marketing surveys, GM has found the elasticity of demand to be constant at E = 9. The additional cost of shipping is $800 per truck. A manager argues that the price in China should be at least $800 higher than the domestic price. Is this manager correct? Answer: The MC in China is = $20,000 + $800 = $20,800. Since E is constant, use the optimal pricing rule: P = (E/(1 + E))MC P = (9/8)($20,800) = $23,400 Thus the price is China should be lower than the domestic price. The manager is wrong and should be fired. (c) GM produces another version of the light truck at a marginal cost of $12,000 per truck. At the current price of $20,000, sales of the light truck have been disappointingly low with the result that GM has an inventory of 18,000 unsold trucks. The best estimate for the remaining trucks is: P = 30,000 Q One manager recommends keeping price at $20,000. Another favors cutting prices to clear the entire inventory. In your opinion, what should GM do? Answer: Both managers are wrong and should also be fired. Since the trucks have been produced, there is no MC. Thus, the rule is imply MR = MC or MR = 0. Now: MR = 30,000 2Q and so: MR = 0 30,000 2Q = 0 30,000 = 2Q Q = 15,000 P = 30,000 15,000 = $15,000 Thus, GM should discount the inventory and sell 15,000 of its inventory of 18,000 trucks. The other 3,000? Give it to charity. 11 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain How would your answer change if the inventory had been 14,000 trucks instead? Hint: how many trucks do you want to sell? How many trucks can you sell? Question 6 A British Columbia resort offers yearround activities: in winter skiing and other cold weather activities and, in summer golf, tennis, and hiking. The resort's operating costs are essentially the same in winter and summer. Management charges higher rates in the winter resulting in average occupancy rates of 75% than in the summer when its average occupancy rate is 90%. Can this policy be consistent with profit maximization? Note what the question is asking: is it correct that management has 25% excess capacity in the winter compared to a 10% excess capacity in the summer? Should management drop prices in the winter to fill more rooms? Answer: Yes. Remember what the optimal price rule says: P = {E/(1 + E)}MC which says that price depends on E and MC. The question tells you MC is the same for winter and summer. Hence, to account for differential prices across seasons, it must be that the E varies across winter and summer (the seasonal "segments") Is it plausible that E differs across seasons? Yes. The winter clientele are more price inelastic than the summer clientele. In the summer, there are more choices and thus clientele are more elastic compared to winter clientele who are willing to pay higher prices to partake in winter sports. A nave manager may be tempted to lower prices in the winter to raise occupancy rates, but the optimal thing to do is to keep prices high even if it means that there would be spare, unused, capacity. Question 7 We've discussed the optimal price rule: P = {E/(1 + E)}MC. In real life, many small businesses use the cost plus rule to set prices: P = (1 + markup)AC. Discuss the correct way to set the markup. Answer: Compare the formulas P = {E/(1 + E)}MC and P = (1 + markup) AC. For the markup rule common in business to be correct, AC must be close to MC and the markup must be set being cognizant of the price elasticity. The price sensitive market should have a low markup whereas the price insensitive market should have a high markup. To see this, note that if the cost plus rule is applied correctly: 12 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain {E/(1 + E)} = (1 + markup) markup = {E/(1 + E)} 1 markup = {E (1 + E)}/(1 + E) markup = 1/(1 + E) This expression is always positive (so long as |E| > 1). Now, as |E| increases (the market becomes more price sensitive), (1 + E) rises and 1/(1+E) decreases, which implies that the markup must also decrease. The reverse argument holds when |E| decreases. Question 8 (2008 2009 Final Exam Question) The following table reproduces portions of Exhibit 11 from the DHL case. Exhibit 11 Revenue and Cost Lane Examples: DOX and WPX U.K. to United States (1990) DOX WPX Revenue $5,723,000 $2,342,000 Outbound Cost 2,392,915 667,712 Hub Cost 596,608 490,436 Line Haul 3 1,121,882 647,915 Delivery 1,376,953 386,049 Gross Margin 234,642 149,888 Gross Margin % 4.1 6.4 Shipments 231,139 68,580 Revenue/Shipment $24.76 $34.15 Note: Please see footnote at the bottom of this page. (a) Calculate the AVC of DOX and WPX for this lane. Show all calculations. Answer We need AVC = TVC/Q. To get TVC, note that by definition: Gross Margin = R TVC TVC = R Gross margin For DOX: TVC = 5,723,000 234,642 = 5,488,358 3 Line haul refers to the air segment of the shipment 13 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Thus AVC = TVC/Q = 5,488,358/231,139 = $23.74 For WPX: TVC = 2,342,000 149,888 = 2,192,112 Thus: AVC = TVC/Q = 2,192,112/68,580 = $31.96. (b) Suppose DHL's headquarters in Brussels sets prices to maximize profits. If Brussels raises the price of a document from $24.76 to $25.01, how many documents will be sent from the U.K. to the U.S? State any assumptions. Answer We are given a price change and asked to compute the impact on quantity. The new price is $25.01 which is 1% more than the initial price of $24.76 (note how: 1.01*$24.76 = $25.01). Now, to compute elasticity, use the margin %: Margin % = (Margin/Revenue)*100 = 4.1 (Margin/Revenue) = 0.041 If DHL is charging the optimal profit maximizing price and AVC = MC (for example if the TVC is linear): (P MC)/P = 1/E If MC = AVC: (P MC)/P = (P AVC)/P = (P AVC)Q/PQ = (Margin/Revenue) = 1/E Thus: 1/E = 0.041 E = 1/0.041 E = 24.39 Or: % Change in Q % Change in P = 24.39 Now: % Change in P = 1% 14 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Thus: % Change in Q = 24.39% Currently, on this lane, there are 231,139 DOXs shipped. Thus, the new number of DOX shipped will be: (1 0.2439)*231,139 = 174,764. (c) Compute the price elasticity of the WPX segment. Answer Repeat the steps above. Optimal pricing requires: (P MC)/P = 1/E If MC = AVC: (P MC)/P = (P AVC)/P = (P AVC)Q/PQ = (Margin/Revenue) = 1/E 1/E = 0.064 E = 1/0.064 E = 15.625 (d) Suppose DHL lowers the cost of shipping packages through learning by doing. Assuming the elasticity in part (c) is constant, what must the MC of packages be in order for the price of a document to be equal to the price of a package on the U.K. to U.S. lane? Show all calculations. Answer Through the optimal pricing rule: (P MC)/P = 1/E Solve for MC: (P MC) = P/E MC = P + P/E The WPX E is 15.625. Now, if price for WPX = price of DOX: P = $24.76 Thus: MC = 24.76 24.76/15.625 = $23.18 15 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Assuming MC = AVC (linear TVC function), the MC would have to be $23.17 per WPX shipment (substantially lower than that of DOX). Question 9 Kim Breweries is located in Markham. It brews beer on premises and ships to many locations all over Canada. The brewery's managers recommend pricing the beer by distance in order to cover transport costs (for example, the price in Montreal would be higher than Toronto). Evaluate this pricing strategy. Answer: Kim is setting prices by cost (which is proportional to distance). We know that if a firm is charging the profit maximizing price, then P = {E/(1 + E)}MC, which shows that price depends on the Marginal cost and price sensitivity. Thus, pricing by distance ignores the demand side of optimal pricing. The brewery's approach is incorrect because it doesn't take into account the nature of demands in the various markets across Canada. For example, if the Montreal market is price elastic, it may have a lower price than Toronto despite the higher transportation costs. Question 10 (20072008 Test Question) Sweet Ajax a Canadian company manufactures Halal maple syrup, sold in Canada and USA. Sweet Ajax's marketing group estimates demand for each month of 2009 to be: P = 3,000 Q Where P is in Canadian dollars and Q is units of output. Sweet Ajax's fixed costs are $250,000 per month and its marginal cost is $1,000. You're in charge of planning output and price each month. (a) Suppose you're planning output and prices for February 2009. What's your decision? Show all calculations and steps clearly. Answer: To figure out how much to produce and sell, Sweet Ajax sets MR = MC. The interpretation of MR is additional revenue from producing and selling another unit while the interpretation of MC is additional cost of producing and selling another unit. If a company is maximizing profits, MR = MC. Now: 16 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain MR = MC 3000 2Q = 1000 2Q = 2000 Q = 2000/2 = 1000 P = 3000 1000 = $2000 This is what you'll plan to produce. Unless there is new information before production begins, you will give the order to produce 1000 units, priced at $2000 each. (b) Suppose that before production of the output in part (a) begins, your finance group informs you that the Canadian dollar has appreciated substantially against the US dollar (i.e., it takes more U.S dollars to buy a Canadian dollar). The marketing department estimates that the max WTP ("willingness to pay") has fallen by $500 and recommends that prices in February should be $500 less than the price in part (a). Do you think they are right? Show all calculations and steps clearly. Answer: It's important to note the timing of this new information the new demand curve is given to you before production has begun. Thus, it is as if you're starting the problem from scratch: you should set MR = MC. The new demand curve is: P = 2500 Q. Setting MR = MC: 2500 2Q = 1000 2Q = 1500 Q = 1500/2 = 750 P = 2500 750 = $1750 Compared to part (a), the price should be lowered by $250 even though max WTP has fallen by $500! Note that the marketing department is incorrect. (c) Now suppose that after production of the output in part (a) begins, your finance group informs you that the Canadian dollar has appreciated substantially against the US dollar (i.e., it takes more U.S dollars to buy a Canadian dollar). The marketing department estimates that the 17 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain max WTP ("willingness to pay") has fallen by $500 and recommends that prices in February should be $500 less than the price in part (a). Do you think they are right? Show all calculations and steps clearly. Answer: It's important to note the timing of this new information the new demand curve is given to you after production has been completed. Recalling that in this question all MCs are due to production (not selling) costs, the MC will be 0. With the new demand curve P = 2500 Q and setting MR = MC: MR = 0 So that you're maximizing revenues (i.e. when MC = 0 profit maximization is equivalent to revenue maximization). Thus: 2500 2Q = 0 Q = 1250 That is, with the new demand and to maximize revenues, you should plan to sell 1,250 units. But you only have 1,000 units for sale. Hence, you will sell 1,000 units and the price will be: P = 2500 1000 = $1500 Compared to part (a), the price should be lowered by $500 max WTP. So the marketing department is correct. (d) Return to the original question. Suppose MC decreases from $1,000 to $500 before production begins. What is the optimal price and output compared to part (a)? Answer: The timing of the information is crucial here. Observe that MC has changed before production begins. Hence, the company should optimize using MR = MC: 3000 2Q = 500 2Q = 2500 Q = 2500/2 Q = 1250 18 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Which is the same output in part (c) except that this time this is the output to be produced and sold. Thus, you will order 1250 units to be produced and sold. The price will be: P = 3000 Q P = 3000 1250 P = $1750 Question 11 In 1996, the drug Prilosec became the best selling antiulcer drug in the world. Prilosec's marginal cost (production and packaging) was only about $0.60 per daily dose. The manufacturer initially sets the price at $3 per daily dose. Research on demand for leading prescription drugs estimates price elasticities to be in the range 1.4 to 1.2. Does setting a price of $3 (or more) make sense? Answer: There are several ways to answer this question. One way is as follows: the current markup (relative to price) is: (P MC)/P = (3 0.6)/3 = 0.8 Is this markup justified given current E of between 1.2 and 1.4? The optimal markup rule states that at the profit maximizing price: (P MC)/P = 1/E The average E is 1.3. Hence, 1/E is: 1/E = 1/1.3 0.77 Given demand conditions, the markup should be around 77% which is very close to the actual markup of 80%. The actual price is therefore close to the optimal price. 19 ...
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This note was uploaded on 05/02/2011 for the course ECO 204 taught by Professor Hussein during the Fall '08 term at University of Toronto- Toronto.

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