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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 12 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 (2008 2009 Final Exam Question) The Table below reproduces Table B from the DHL case: International Air Express Market Shares by \$ Revenues (1988) Company Market Share DHL 44% Fedex 7% TNT 18% UPS 4% Others 27% Source: Table B in DHL case. (a) Calculate the CR4 in the international air express market. State any assumptions. Answer: CR4 is the cumulative market share of the top 4 firms. Assuming none of the firms in the "other" category has a market share of > 4%, the CR4 is: CR4 = 44 + 18 + 7 + 4 = 73 (b) Estimate the HHI from the data in the Table above. Brief explain whether the estimate overstates or understates the true HHI. 1 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Answer: HHI is cumulative squared market share of all firms. The table does not list individual firms in the "other" category. Thus, treating the "other" category as a single firm we have an estimate of the HHI: HHI = 442 + 182 + 72 + 42 + 272 = 3,054 The actual HHI is overstated. By treating "others" as one firm we are squaring the sum of the other firm' market shares not summing up the squares. That is, we are doing (a + b)2 not a2 + b2. Thus we are over stating the HHI. (c) If Fedex and UPS merge what is the change in the global HHI? Show your reasoning. Answer: Before the merger, the HHI for Fedex and UPS stemmed from (s2Fedex + s2UPS). Post merger it stemmed from (sFedex + sUPS) 2. Hence the change in the HHI is 2 sFedex sUPS = 2(7)(4) = 56. Question 2 (20072008 Test Question) The following page has Exhibit 11 from the Matching Dell case. Suppose Dell and Compaq announced a merger in 1998. Should this proposed merger be blocked by antitrust authorities? Show all steps carefully and keep any explanation brief. 2 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain All figures for 1998 Corporate Revenue (\$bn) Value of PC Sales (\$bn) Value of PC sales / corporate revenue Worldwide PC market share (\$) Worldwide PC market share (units) Worldwide average selling price (\$) U.S. PC Market share (\$) U.S. PC Market share (units) U.S. Average Selling Price (\$) U.S. / worldwide PC sales CAGR of Worldwide PC business, 1994 1998 Value Units Corporate Financials Return on Sales Salestoassets Ratio Assetstoequity Ratio Return on equity Return on Invested capital (1997) Days of Inventory Cost Structure Advertising / Sales R&D / Sales SG&A / Sales PC sales by channel (units; worldwide) Direct Catalog, phone, online sales representatives Distributor / reseller Retail Other PC Sales by customer category (units; worldwide) Home & small office Small & midsize business Large Business Government Education Stock Appreciation, 12/30/94 12/31/98 Dell 18.2 17.7 96.80% 10.40% 8.60% 2,271 15.10% 13.20% 2,343 63.7% Compaq 31.2 27.9 89.4% 16.4% 14.7% 2,100 16.6% 16.7% 2,047 44.4% IBM 81.7 16.9 20.7% 9.9% 8.8% 2,127 9.1% 8.2% 2,278 40.2% HP 47.1 11.8 25.0% 6.9% 6.3% 2,054 7.9% 7.8% 2,088 50.0% Gateway 7.6 7.1 92.8% 4.2% 4.0% 1,961 8.1% 8.4% 1,982 84.9% 51.9% 56.2% 24.3% 28.7% 12.9% 18.0% 40.1% 44.8% 27.3% 36.5% 8% 2.65x 2.96x 62.9% 186% 7.0 8.8% 1.35x 2.03x 24.2% 35% 34.2 7.7% 0.95x 4.43x 32.6% 13% 49.4 6.3% 1.40x 1.99x 17.4% 16% 70.4 4.5% 2.65x 2.15x 25.7% 45% 10.0 1.1% 1.5% 9.8% 1.1% 4.3% 16.0% 2.1% 6.2% 20.4% 2.6% 7.1% 16.6% N/A N/A 13.8% 86.6% 37.4% 49.2% 6.9% 0.0% 6.5% 4.4% 3.3% 1.1% 66.6% 24.6% 4.4% 7.5% 2.4% 5.1% 69.6% 18.4% 4.6% 0.6% 0.0% 0.6% 75.1% 23.2% 1.2% 90.3% 88.4% 1.9% 4.7% 1.0% 4.0% 18.3% 37.0% 33.6% 6.4% 4.6% 5617% 28.5% 32.6% 27.5% 6.0% 5.3% 432% 30.6% 32.7% 26.0% 6.2% 4.6% 402% 33.3% 30.8% 27.2% 5.9% 2.8% 174% 58.2% 19.1% 9.3% 5.1% 8.2% 374% 3 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Answer: The "rule of thumb" for horizontal mergers is: "block the merger if the change in the HHI is greater than 100". Denoting the market shares (as a percentage of market revenues) of the two companies by s1 and s2, the change in HHI will be: 2 s1 s2. To see this, suppose there are 3 companies in the market. The premerger HHI is: Premerger HHI = s21 + s22 + s23 Now suppose companies 1 and 2 merge. Assuming the "whole" is equal to the "sum of parts", the market share of the merged company is: (s1 + s2). Thus, the postmerger HHI is: Postmerger HHI = (s1 + s2)2 + s23 The change in HHI is: HHI = post merger HHI pre merger HHI: HHI = (s1 + s2)2 + s23 { s21 + s22 + s23} HHI = s21 + 2s1s2 + s22 + s23 s21 s22 s23 HHI = 2 s1 s2 The table below gives `s' for the US and the world. Suppose we choose the US market as the relevant market. Then: change in HHI from a (US) merger between Dell & Compaq : HHI = 2 sDell sCompaq HHI = 2 (15.1(16.6)) HHI = 501.32 > 100 And therefore, based on the horizontal merger guidelines, the merger should be blocked. If the merger is challenged by the government, the attorneys for the merger companies can counterargue/challenge on several grounds: They can challenge the government's definition of the relevant market. For example, in the (US) Sirius and XM Satellite radio merger, the government argued that if the merger were to go through, the satellite radio market would become highly concentrated. In fact, there being two satellite radio companies, the CR1 = 100 and HHI = 10,000. The companies challenged this conclusion on the basis that the right market to measure 4 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain market share was not "satellite radio" but "all" radio which includes satellite and terrestrial (land) radio. With that definition, the market shares of Sirius and XM Radio and therefore the change in HHI would be < 100. In fact, the merger was allowed on these grounds. Another example was the Whole Foods & Wild Oats merger. These companies retail organic produce and their merger was challenged on the grounds that the merger would result in a highly concentrated organic food market. The two stores argued that the relevant market definition is "all" grocery stores (including for example, WalMart and Costco). They argued this point successfully and the merger went through. They can argue that the whole does not equal the sum of parts: that is: (s1 + s2)PostMerger (s1 + s2)PreMerger This occurs frequently in banking 1 . When banks merge, they will eliminate overlapping redundant potions such as branches (why have two branches across the street from each other?), back offices, operations, IT, etc. Question 3 Gamsi, Laffont, and Vuong in "Econometric Analysis of Collusive Behavior in a SoftDrink Market," Journal of Economics and Management Strategy (Summer 1992) estimated the following demand equations for Coke and Pepsi "syrup" 2 . Qc = 26.17 3.98Pc + 2.25Pp + 2.60A c 0.62A p + 9.58S + 0.99 I Qp = 17.48 + 1.40Pc 5.48Pp 4.81A c + 2.83A p + 11.64S + 1.92 I All data was quarterly from 19681986. Here: Q = quarterly quantity of syrup sold P = price of syrup (1986 dollars) A = square root of quarterly advertising expenses (1986 dollars) S = equals 1 if spring or summer, equals 0 if winter or fall 1 2 For example: the Chase and Chemical Bank merger and the Fleet Boston and Bank of America merger. Coke and Pepsi, the corporations, produce syrup or concentrate which is sold to (typically) independent bottlers. The bottlers carbonate the concentrate, bottle and distribute the soft drinks. These demand equations are for the concentrate, i.e. bottlers' demand. 5 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain I = real income (1986 dollars) Average values from data: QC = 30.22, QP = 22.72, PC = 12.96, PP = 8.16, AC = 5.89, AP = 5.28, I = 20.63 In this question, you will practice analyzing actual demand equations as these contain a plethora of information. (a) Examine the demand equation for Coke syrup: do the coefficients make economic/intuitive sense? Answer Firstly, notice how the authors of the paper chose a specific functional form. That said, does the equation make sense? You should always perform such a check because if something is amiss, it's a clue that either the functional form is incorrect and/or some variables (say, price of Sprite) have been omitted from the model. Look at the "signs" of each coefficient in the equation: Qc = 26.17 3.98Pc + 2.25Pp + 2.60A c 0.62A p + 9.58S + 0.99 I Observe these tell you that when each of these variables increases, then sales of Coke syrup are impacted as follows: An increase in: Pc PP AC AP S I Impact on Qc: Qc Qc Qc Qc Qc Qc Does this make sense? Yes. As the price of Coke syrup , sales of Coke syrup Yes. As the price of Pepsi syrup , sales of Coke syrup Yes. As advertising for Coke , sales of Coke syrup Yes. As advertising for Pepsi , sales of Coke syrup Yes. In spring and summer, sales of Coke syrup Yes. As income , sales of Coke syrup (b) Examine the demand equation for Pepsi syrup: do the coefficients make economic/intuitive sense? Answer Look at the "signs" of each coefficient in the equation: 6 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Qp = 17.48 + 1.40Pc 5.48Pp 4.81A c + 2.83A p + 11.64S + 1.92 I Observe these tell you that when each of these variables increases, then sales of Coke syrup are impacted as follows: An increase in: Pc PP AC AP S I Impact on Qp: Qp Qp Qp Qp Qp Qp Does this make sense? Yes. As the price of Coke syrup , sales of Pepsi syrup Yes. As the price of Pepsi syrup , sales of Pepsi syrup Yes. As advertising for Coke , sales of Pepsi syrup Yes. As advertising for Pepsi , sales of Pepsi syrup Yes. In spring and summer, sales of Pepsi syrup Yes. As income , sales of Pepsi syrup (c) Calculate the elasticity of Coke sales with respect to Coke price, Pepsi price, Coke advertising, Pepsi advertising and income. Answer: The demand equation is: Qc = 26.17 3.98Pc + 2.25Pp + 2.60A c 0.62A p + 9.58S + 0.99 I Because we have average values for each variable, we can use the point elasticity formula: E of y with respect to x = (% y) / (% x) = (dy/dx)(y/x) We can calculate the derivatives from the demand equation and use the average values of y and x in the ratio (y/x). The average values were: QC = 30.22, QP = 22.72, PC = 12.96, PP = 8.16, AC = 5.89, AP = 5.28, I = 20.63 Thus: 7 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain E of Qc wrt Pc E of Qc wrt Pp E of Qc wrt AC E of Qc wrt Ap E of Qc wrt I (dQc/dPc)(Average Pc /Average Qc ) (dQc/dPp)(Average Pp /Average Qc ) (dQc/dAc)(Average Ac /Average Qc ) (dQc/dAp)(Average Ap /Average Qc ) (dQc/dI)(Average I /Average Qc ) (3.98)(12.96/30.22) = 1.71 (2.25)(8.16/30.22) = 0.61 (2.60)(5.89/30.22) = 0.51 (0.62)(5.28/30.22) = 0.11 (0.99)(20.63/30.22) = 0.68 Here's the interpretation: A 1% in Pc will lower sales of Coke by 1.71% A 1% in Pp will increase sales of Coke by 0.61% A 1% in Ac will increase sales of Coke by 0.51% A 1% in Ap will lower sales of Coke by 0.11% A 1% in I will increase sales of Coke by 0.68% (d) Calculate the elasticity of Pepsi sales with respect to Coke price, Pespi price, Coke advertising, Pepsi advertising and income. Answer: The demand equation is: Qp = 17.48 + 1.40Pc 5.48Pp 4.81A c + 2.83A p + 11.64S + 1.92 I Because we have average values for each variable, we can use the point elasticity formula: E of y with respect to x = (% y) / (% x) = (dy/dx)(y/x) We can calculate the derivatives from the demand equation and use the average values of y and x in the ratio (y/x). The average values were: QC = 30.22, QP = 22.72, PC = 12.96, PP = 8.16, AC = 5.89, AP = 5.28, I = 20.63 Thus: 8 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain E of Qp wrt Pc E of Qp wrt Pp E of Qp wrt AC E of Qp wrt Ap E of Qp wrt I (dQp/dPc)(Average Pc /Average Qp ) (dQc/dPp)(Average Pp /Average Qp ) (dQc/dAc)(Average Ac /Average Qp) (dQc/dAp)(Average Ap /Average Qp ) (dQc/dI)(Average I /Average Qp ) (1.40)(12.96/22.72) = 0.80 (5.48)(8.16/22.72) = 1.97 (4.81)(5.89/22.72) = 1.24 (2.83)(5.28/22.72) = 0.65 (1.92)(20.63/22.72) = 1.74 Here's the interpretation: A 1% in Pc will increase sales of Pepsi by 0.80% A 1% in Pp will lower sales of Pepsi by 1.97% A 1% in Ac will lower sales of Pepsi by 1.24% A 1% in Ap will increase sales of Pepsi by 0.65% A 1% in I will increase sales of Pepsi by 1.74% (e) Use your answers in parts (c) and (d) to compare and contrast Coke and Pepsi sales. For example, which product reacts more to own advertising? What about rival advertising? Answer: Let's consolidate the two tables above: Variable Pc Pp A C Ap I Pepsi sales are more sensitive (E = 1.97) than Coke sales (E = 1.71) to changes in own prices Pepsi sales are more sensitive (E = 0.80) than Coke sales (E = 0.61) to changes in the rival's prices Pepsi sales are more sensitive (E = 0.65) than Coke sales (E = 0.51) to own advertising 9 Coke Elasticity 1.71 0.61 0.51 0.11 0.68 Pepsi Elasticity 0.80 1.97 1.24 0.65 1.74 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Pepsi sales are more sensitive (E = 1.24) than Coke sales (E = 0.11) to rival's advertising (i.e. Pepsi is impacted more by "negative" advertising). Both Coke and Pepsi are normal good (i.e. Y and Q ). Pepsi sales are more sensitive (E = 1.74) than Coke sales (E = 068) to income. In fact in every dimension, Pepsi is more sensitive than Coke. (f) Derive a simple demand equation for Coke and Pepsi (i.e. sales as a function of price) and graph the demand curve (i.e. price versus sales). Answer: The general demand function for Coke is: Qc = 26.17 3.98Pc + 2.25Pp + 2.60A c 0.62A p + 9.58S + 0.99 I To obtain the simple demand curve, use the average values to give a value to all variables except Coke prices (i.e., we are doing ceteris paribus: holding all other variables constant) Qc = 26.17 3.98Pc + 2.25(12.96) + 2.60(5.89) 0.62(5.28) + 9.58S + 0.99(20.63) Qc = 77 3.98Pc + 9.58S But now we have a problem: what to do about S? In fact, there will be two equations, corresponding to the case S = 0 and S = 1. Here are the demand equations and demand curves: Coke Demand Curve (Spring/Summer) Qc = 86.5 3.98Pc Pc = 21.73 0.25Qc Coke Demand Curve (Fall/Winter) Qc = 77 3.98Pc Pc = 19.34 0.25Qc Observe how the Spring/Summer demand is up and to the right of the Fall/Winter demand curve: 10 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain In fact notice how the intercept encompasses all the "other" variables (crossprice, advertising, crossadvertising, season, and income). This is why in ECO 100 changes in "other" variables would lead to shifts in the demand curve: Change in other variables Change in demand intercept Shifts in demand curve Turning to Pepsi: the general demand function for Pepsi is: Qp = 17.48 + 1.40Pc 5.48Pp 4.81A c + 2.83A p + 11.64S + 1.92 I To obtain the simple demand curve, use the average values to give a value to all variables except Pepsi prices (i.e., we are doing ceteris paribus: holding all other variables constant) Qp = 17.48 + 1.40(12.96) 5.48Pp 4.81(5.89) + 2.83(5.28) + 11.64S + 1.92 (20.63) Qp = 61.85 5.98Pp + 11.64S As before, there will be two equations, corresponding to the case S = 0 and S = 1. Here are the demand equations and demand curves: Pepsi Demand Curve (Spring/Summer) Qp = 73.49 5.98Pp Pp = 12.28 0.16Qp Here are the demand curves: 11 Pepsi Demand Curve (Fall/Winter) Qp = 61.85 5.98Pp Pp = 10.3 0.16Qp University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Note how the Pepsi demand curve is steeper and has a smaller intercept than the Coke demand curve. In fact if you graph either the Spring/Summer or Fall/Winter curves, the Pepsi demand curves are inside the demand curves for Coke that is, the curves do not cross: Question 4 Give some cost drivers for airline (horizontal) mergers. In particular, discuss the role of fleet composition. Answer: Airlines, especially US airlines, frequently merge with one another. There are two main cost drivers for mergers: economies of scale and economies of scope. 12 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain By merging, airlines can purchase inputs as a larger entity ("scale") and arguably secure better prices for inputs 3 . Given that fuel costs are the biggest component of airline operating costs (see table below), one might be tempted to say that the greatest impact of a merger would be on fuel costs. Cost Per Available Seat Mile (cents/CASM) 3Q 2005 Crew Fuel Maintenance Other CASM Major (legacy) Carriers Northwest 1.2 3.1 0.9 0.9 6.2 American 1.1 3.0 1.2 0.8 6.1 US Air 0.8 2.7 1.0 1.1 5.9 America West 0.8 2.8 1.0 1.3 5.9 Alaska 1.1 2.8 0.9 1.1 5.9 Delta 1.1 2.9 0.8 1.0 5.8 Hawaii 0.7 2.6 0.9 1.5 5.7 Continental 0.8 2.8 0.9 1.1 5.6 United 0.8 2.9 1.0 0.8 5.5 Low Cost Carriers Air Tran 0.9 2.8 0.8 1.9 6.5 Spirit 0.9 2.6 1.0 1.5 6.0 Frontier 0.7 2.9 0.7 1.4 5.7 ATA 1.0 2.7 0.7 1.3 5.7 Southwest 1.1 1.7 0.8 0.6 4.3 Jet Blue 0.6 2.2 0.6 0.8 4.1 Source: CreditSights. Other expenses include cost of leasing aircrafts. In fact, a bigger airline will not be able secure lower fuel prices. This is because fuel is traded in competitive markets and as such all prices are uniform regardless of quantity. The merger therefore may lead to lower price of inputs other than fuel. This brings us to economies of scope. Recall the definition: there are economies of scope when the cost of "producing" goods jointly is lower than the cost of "producing" goods separately. Formally: C(Q1 + Q2) < C(Q1) + C(Q2). This is certainly the case with airlines. For example, as one airline, they will have a single reservation system (which generates revenue enhancements since passengers can "code share"; in this question however, we're focusing on cost drivers), single maintenance/catering facility etc. It's doubtful if labor costs will be lower unless redundant workers are laid off, which in a unionized industry is difficult. There is another cost Carrier 3 Recall that the long run AC curve can decline with volume either because of increasing returns to scale and/or lower input prices. 13 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain driver which has to do with composition of the airlines' fleet. For example (Sources: Fleet data from CreditSights, 3Q05 and Airliners.net. Range data from Airliners.net): Narrowbody Aircrafts in Major and National Carriers (3Q05) "Legacy" Aircraft "Newer" Generation Aircraft MD80 1564 737300 1815 DC9 770 737700 1540 737800 1900 A320 2615 A319 1831 717200 2060 Range (nautical miles) Fuel Cost (/mile) 3Q05 3.5 2.6 4.9 1.8 2.5 2.4 N/A 3.0 TOTAL Legacy Carriers American United Delta Continental Northwest US Air Sub total 334 117 451 65 21 50 65 201 127 36 239 127 36 69 94 78 24 199 74 65 194 76 97 55 0 410 217 207 180 279 154 Low Cost Carriers Aloha Hawaiian Southwest Jet Blue American West Alaska Frontier Air Tran ATA Spirit MidWest Sub total 26 10 13 49 194 37 231 0 252 24 138 77 3 21 2 22 3 41 218 79 59 34 9 11 77 20 108 9 11 412 79 130 51 41 80 21 12 33 14 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain Observe how there is variation across carriers in aircraft types and therefore aircraft range. This is because airlines networks target some "average" distance: some carriers focus on short haul routes while others focus on medium or long haul routes. If two airlines with different fleet composition (i.e. average route length) merge, they will collectively serve passengers on the merged (larger) network at a lower cost than two separate (larger) networks. Of course, the network range also expands, since each airline can now use the partner's routes and aircrafts to connect passengers to its own routes. This is useful information for an airline analyst as it predicts which airlines are likely to merge. 15 University of Toronto, Department of Economics, ECO 204. Summer 2009. S. Ajaz Hussain 16 ...
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