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UNIVERSITY OF TORONTO Faculty of Arts and Science
APRIL 2017 EXAMINATIONS
ECO204Y1Y [Ajaz’s Sections Only: L0101, L0201, L0301, L0401]
Duration - 3 hours
Examination Aids: Non-Programmable Calculator
Total Points: 225 Points
This exam consists of 6 questions in 34 pages, double-sided
PLEASE WRITE YOUR LAST NAME, FIRST NAME, AND STUDENT ID # BELOW:
LAST
NAME:
FIRST
NAME:
STUDENT ID #:
____________________________________________________________________________________________
YOU CANNOT LEAVE THE ROOM DURING THE LAST 15 MINUTES OF THE EXAM.
TO EARN CREDIT, YOU MUST SHOW ALL NECESSARY CALCULATIONS AND STATE ALL ASSUMPTIONS.
QUESTION MAX SCORE POSSIBLE ACTUAL SCORE
1 15
2 30
3 25
4 30
5 45
6 80
TOTAL 225
Page 2 of 34
QUESTION 1 [TOTAL 15 Points]
Suppose a market consists of 𝑇 > 0 firms. Denote the 𝑖𝑡ℎ firm’s percentage share of market revenues
as:
𝑠𝑖 =Firm 𝑖′s revenues
Total Market Revenues× 100
(a) [5 Points] What is the maximum value of the 𝐻𝐻𝐼 (Herfindahl-Hirschman Index)? According to the
𝐻𝐻𝐼 when is a market characterized as being “concentrated”?
Answer
(b) [5 Points] Under current US and Canadian anti-trust regulations, the government must challenge any
proposed horizontal merger of two companies if the merger will change the 𝐻𝐻𝐼 by more than 200
points. How does one know the change in 𝐻𝐻𝐼 in advance of the merger? State salient assumptions and
show essential calculations.
Answer
Page 3 of 34
(c) [5 Points] The following table is from an article published in the Wall Street Journal and shows the
number of “light vehicles” (cars and light trucks) sold in the U.S. as well as market shares of all
automakers (by units sold) in February 2017:
Company # Cars Sold in Feb 2017 % MARKET SHARE
By Units Sold in Feb 2017
General Motors Corp. 237,232 17.8
Ford Motor Company 207,464 15.6
Chrysler 165,738 12.4
Toyota Motor Sales USA Inc. 174,339 13.1
American Honda Motor Co Inc. 121,686 9.1
Nissan North America Inc. 135,740 10.2
Hyundai Motor America 53,020 4
Mazda Motor of America Inc. 22,824 1.7
Mitsubishi Motors N A, Inc. 10,924 0.8
Kia Motors America Inc. 42,673 3.2
Subaru of America Inc. 45,500 3.4
Mercedes-Benz 27,035 2
Volvo 4,651 0.3
Volkswagen of America Inc. 25,145 1.9
Audi of America Inc. 13,741 1
BMW of North America Inc. 22,558 1.7
Porsche Cars NA Inc. 3,637 0.3
Fiat 2,145 0.2
Tesla 3,700 0.3
Jaguar 3,484 0.3
Land Rover 5,747 0.4
Alfa Romeo 443 ...
Mini 2,154 0.2
Smart 348 ...
Ferrari 270 ...
Maserati 1,087 0.1
Bentley 155 ...
Lamborghini 71 ...
Rolls Royce 126 ...
Maybach ... ...
TOTAL LIGHT VEHICLE SALES 1,333,637 100
Source: http://online.wsj.com/mdc/public/page/2_3022-autosales.html#autosalesE
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True, false, or “cannot answer this question”: a (hypothetical) Chrysler-Toyota USA merger in February
2017 would’ve been automatically been challenged by the US government on anti-trust grounds? Give a
maximum three sentence explanation.
Answer
Page 5 of 34
QUESTION 2 [TOTAL 30 Points]
Consider our analysis of the “The Aluminum Industry in 1994” case.
(a) [10 Points] Explain why, despite the fact that demand for aluminum (AL) was growing between 1994
and 1998, that the price of primary AL in 1998 was almost equal to the price of primary AL in 1994.
Answer
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(b) [10 Points] True or false: Based on our final selection of the Primary AL supply model, the following
graph shows that primary AL prices will exhibit extreme price volatility when the PAL spot price is
between $1,500 - $2,000 per ton and quantity traded is between 5 – 8 mtpy? Give a brief explanation:
$/t
‘000 tpy
Answer
Page 7 of 34
(c) [10 Points] Based on our final selection of the Primary AL supply curve, use the table below (which
lists every PAL producer in 1994) to calculate the demand for PAL for the spot price of $900/ton. Provide
a brief explanation below the table:
Smelter Country Company Cumulative capacity
‘000 tpy AVC $/t
Zaporozhye Ukraine CIS 100.00 594.68
Sumgait Azerbaijan CIS 160.00 622.93
Sayansk Russia CIS 483.00 700.97
Irkutsk Russia CIS 743.00 707.33
Novokuznetsk 1H Russia CIS 828.00 730.35
Tursunzade (Regar) Tajikistan CIS 1348.00 736.65
Nadvoitsy Russia CIS 1408.00 742.35
Novokuznetsk 1V Russia CIS 1573.00 746.89
Kandalaksha Russia CIS 1638.00 751.63
Bratsk Russia CIS 2488.00 752.31
Uralsky Russia CIS 2558.00 757.08
Volgograd Russia CIS 2726.00 780.45
Krasnoyarsk Russia CIS 3476.00 792.14
Bogoslovsk Russia CIS 3636.00 814.93
Volkhov Russia CIS 3656.00 871.51
Belem Brazil State 4001.00 696.10
Alba 3 Bahrain State 4231.00 739.08
Asahan Indonesia State 4456.00 755.92
Alba Bahrain State 4677.00 777.70
Porto Vesme Italy State 4807.00 834.89
Fusina Italy State 4843.00 871.88
Venalum Venezuela State 5243.00 878.88
Guizhou China State 5403.00 910.36
Nag Hammadi Egypt State 5583.00 955.00
San Ciprian Spain State 5773.00 958.75
Qinghai China State 5923.00 965.20
Renukoot A India State 6058.00 1007.02
La Coruna Spain State 6136.00 1014.03
Zhengzhou China State 6166.00 1023.43
Shandong China State 6201.00 1043.71
Lian Cheng China State 6266.00 1044.36
Jebel Ali Dubai (UAE) State 6511.00 1052.09
Lanzhou China State 6601.00 1053.82
Orissa India State 6819.00 1067.87
Podgorica (Titograd) Yugoslavia State 6929.00 1074.60
Baiyin China State 7004.00 1108.02
Qingtonxia China State 7089.00 1111.55
Baotou 2 China State 7141.00 1138.25
Fushun 2 China State 7181.00 1150.57
Page 8 of 34
Smelter Country Company Cumulative capacity
‘000 tpy AVC $/t
Baotou 1 China State 7209.00 1175.56
Fushun 1 China State 7279.00 1176.40
Inota Hungary State 7312.65 1244.44
Konin Poland State 7360.65 1261.75
Alwaye India State 7380.65 1279.30
Ziar nad Hronom 1 Slovakia State 7449.65 1303.85
Hirakud India State 7473.65 1387.58
Talum Slovenia State 7548.65 1433.23
Korba India State 7648.65 1515.92
Slatina Romania State 7913.65 1578.12
Arak Iran State 8033.65 1631.29
Seydisehir Turkey State 8093.65 1740.75
Renukoot B India State 8123.65 2043.17
Sorocaba A Brazil Other 8245.65 581.02
Grand Baie Canada Alcan 8425.65 591.69
Arvida 2 Canada Alcan 8572.65 607.52
Kitimat Canada Alcan 8844.65 643.18
Badin A USA Alcoa 8902.15 662.07
Arvida 1 Canada Alcan 8987.15 664.70
Portland Australia Other 9307.15 666.26
Shawinigan Falls Canada Alcan 9391.15 677.05
Beauharnois Canada Alcan 9439.15 679.71
Alcoa Tennessee A USA Alcoa 9549.15 679.75
Alouette Canada Other 9764.15 684.01
Tomago Australia Pechiney 10119.15 684.51
Dunkirk France Pechiney 10334.15 692.16
Wentachee A USA Alcoa 10411.15 694.28
Saramenha A Brazil Alcan 10421.15 702.60
Sunndalsora 2 Norway Hydro 10492.15 706.35
Becancour Canada Reynolds/Alumax 10852.15 707.00
Point Henry B Australia Alcoa 10958.15 708.88
Ardal 2A Norway Hydro 11044.85 710.97
Isle Maligne Canada Alcan 11117.85 716.10
Laterriere Canada Alcan 11321.85 722.56
Deschambault Canada Alumax 11533.85 731.76
Kinlochleven UK Alcan 11544.85 741.78
Kambara A Japan Alcan 11564.85 746.47
Ardal 1A Norway Hydro 11598.15 755.76
Sunndalsora 1 Norway Hydro 11665.15 769.81
Lochaber UK Alcan 11703.15 772.36
Hoyanger 1A Norway Hydro 11719.15 775.30
Baie Comeau 1 Canada Reynolds 11878.15 775.57
Hamburg Germany Reynolds/VAW 11998.15 781.90
Kurri Kurri Australia Alcan 12148.15 790.84
Page 9 of 34
Smelter Country Company Cumulative capacity
‘000 tpy AVC $/t
Alcoa Massena USA Alcoa 12273.15 791.18
Boyne Island Australia Comalco 12517.15 796.69
Karmoy 1 Norway Hydro 12624.15 800.80
Karmoy 2 Norway Hydro 12737.15 802.47
Mosjoen 1 Norway Alcoa/Elkem 12782.15 806.63
Ferndale USA Alumax 13054.15 810.45
Baie Comeau 2 Canada Reynolds 13174.15 811.47
Paranam Surinam Alcoa 13204.15 814.76
Hoyanger 2A Norway Hydro 13237.15 817.14
Tiwai Point New Zealand Comalco 13496.15 830.03
Point Henry A Australia Alcoa 13570.15 833.63
Baie Comeau 3 Canada Reynolds 13690.15 838.88
Puerto Madryn Argentina Other 13864.15 838.96
Mead USA Kaiser 14064.15 846.08
Ardal 2B Norway Hydro 14107.45 847.90
Mosjoen 2 Norway Alcoa/Elkem 14182.45 848.04
Sao Luis Brazil Other 14539.45 861.14
Lista Norway Alcoa 14619.45 866.88
Holyhead UK Kaiser 14746.45 873.50
Valco Ghana Kaiser 14946.45 873.63
Bell Bay Australia Comalco 15066.45 879.83
Wentachee B USA Alcoa 15209.45 883.95
Warrick A USA Alcoa 15464.45 892.62
Columbia Falls USA Other 15632.45 894.07
St.Jean France Pechiney 15752.45 894.54
Husnes Norway Hydro 15832.45 896.96
Hoyanger 1B Norway Hydro 15839.45 902.23
Straumsvik Iceland Alusuisse 15939.45 903.46
Norf Germany VAW 16149.45 904.04
New Madrid USA Noranda 16364.45 907.39
Badin B USA Alcoa 16421.95 908.67
Edea Cameroon Pechiney 16505.95 909.29
Ardal 1B Norway Hydro 16522.65 918.35
Hoyanger 2B Norway Hydro 16535.65 921.46
Alcasa Venezuela CVG 16745.65 925.25
Tacoma USA Kaiser 16819.65 926.38
Reynolds Massena USA Reynolds 16942.65 927.94
Frederick USA Other 17116.65 931.74
Hannibal USA Other 17361.65 935.22
Longview USA Reynolds 17565.65 937.27
Rockdale A USA Alcoa 17725.65 954.30
Aratu 2 Brazil Alcan 17755.65 961.48
Vlissingen Netherlands Pechiney 17930.65 961.79
Goldendale USA Other 18098.65 968.08
Page 10 of 34
Smelter Country Company Cumulative capacity
‘000 tpy AVC $/t
Rockdale B USA Alcoa 18258.65 970.04
Distomon Greece Pechiney 18406.65 970.84
Alcoa Tennessee B USA Alcoa 18501.65 973.77
Vancouver USA Other 18616.65 974.71
Sundsvall 1 Sweden Other 18693.15 979.25
Stade Germany VAW 18763.15 980.78
Sebree USA Alcan 18943.15 981.23
Sorocaba B Brazil Other 19031.15 984.09
Hawesville USA Other 19217.15 991.25
Warrick B USA Alcoa 19262.15 996.56
Ravenswood USA Other 19430.15 997.74
Sundsvall 2 Sweden Other 19453.65 998.83
Richards Bay 2 South Africa Alusuisse 19538.65 1001.30
Aviles Spain Inespal 19618.65 1007.23
Auzat France Pechiney 19662.65 1009.40
Mount Holly USA Alumax 19844.65 1009.50
The Dalles USA Other 19926.65 1011.65
Lynemouth UK Alcan 20056.65 1012.72
Lannemezan France Pechiney 20099.65 1020.82
Valesul Brazil Billiton 20192.65 1024.16
Voerde Germany Hogal 20270.65 1024.26
Richards Bay 1 South Africa Alusuisse 20355.65 1026.71
Venthon France Pechiney 20385.65 1030.35
Steg Switzerland Alusuisse 20433.65 1042.51
Delfzijl Netherlands Aldel 20531.65 1088.61
Toging A Germany VAW 20605.65 1118.03
Essen Germany Other 20740.65 1125.87
Pocos de Caldas Brazil Alcoa 20830.65 1169.31
Saramenha B Brazil Alcan 20871.65 1175.85
Toging B Germany VAW 20884.65 1503.18
Answer
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QUESTION 3 [TOTAL 25 Points]
A study published in McFadden, Urban Travel Demand, Journal of Public Economics estimated the utility
function of an average “commuter” (who could walk/drive/take public transportation) to be:
𝑈 = −0.147(Total walking time to public tranport or car) − 0.0411(Total trip time) − 2.24(Cost of trip)
Here, “walking time” and “total trip time” are measured in minutes, while “cost of trip” is measured in
dollars.
(a) [15 Points] How many more additional minutes is the average commuter willing to spend commuting
by car/public transport in order to reduce “walking time” by a minute? State all salient assumptions and
show all essential calculations.
Answer
Page 12 of 34
(b) [10 Points] Holding walking times constant, what is the “value” of a minute of commuting time?
Explain how this information would be useful to (say) the TTC (Toronto Transit Commission). State all
salient assumptions and show all essential calculations.
Answer
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QUESTION 4 [TOTAL 30 Points]
(a) [5 Points] Show that 𝑑𝑥
𝑥100 = the percentage change in 𝑥 arising from an ‘infinitesimally’ small
change in 𝑥 can be expressed as (𝑑 ln 𝑥) × 100. Show all essential steps.
Answer:
Page 14 of 34
(b) [15 Points] An analyst proposes the following demand model for beef (lbs. per capita):
𝑞𝑏𝑒𝑒𝑓 = 𝛽0 × 𝑃𝑐ℎ𝑖𝑥𝛽1 × 𝑃𝑏𝑒𝑒𝑓
𝛽2 × 𝑌𝛽3
Here: 𝑃𝑐ℎ𝑖𝑥 = (real) price of chicken per lb.; 𝑃𝑏𝑒𝑒𝑓 = (real) price of beef per lb.; and, 𝑌 = (real) income.
Using data from the USDA the analyst estimates the parameters of the demand model by transforming
the above model into:
ln 𝑞𝑏𝑒𝑒𝑓 = ln𝛽0 + 𝛽1 ln 𝑃𝑐ℎ𝑖𝑥 + 𝛽2 ln 𝑃𝑏𝑒𝑒𝑓 + 𝛽3 ln 𝑌
And then regressing ln 𝑞𝑏𝑒𝑒𝑓 on a constant, ln 𝑃𝑐ℎ𝑖𝑥 , ln 𝑃𝑏𝑒𝑒𝑓 , and ln 𝑌 to obtain:
ln 𝑞𝑏𝑒𝑒𝑓 = 8.86 + 0.7 ln𝑃𝑐ℎ𝑖𝑥 − 0.83 ln𝑃𝑏𝑒𝑒𝑓 − 0.33 ln𝑌
Is beef an “Ordinary” or a “Giffen” good? Are beef and chicken “Complements” or “Substitutes”? Is beef
a “Normal” or an “Inferior” good? Prove your answers by calculating demand, cross-price, and income
elasticities. State salient assumptions and show essential calculations.
Answer:
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(c) [10 Points] True or false: beef is an “inferior” good it must therefore be a “Giffen” good? Provide a
brief explanation (no need for proofs).
Answer:
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QUESTION 5 [TOTAL 45 Points] The following table was compiled from the Netflix 2016 Annual Report:
Domestic streaming segment (US) 2015 2014 2013
Memberships (‘000s) 43,401 37,698 31,712
Monthly membership price $8.50 $8.14 $7.97
Gross Margin to Revenue Ratio 33% 27% 23%
International streaming segment 2015 2014 2013
Memberships (‘000s) 27,438 16,778 9,722
Monthly membership price $7.48 $8.34 $8.26
Gross Margin to Revenue Ratio -17% -12% -39%
Domestic DVD segment (US) 2015 2014 2013
Memberships (‘000s) 4,787 5,668 6,765
Monthly membership price $10.30 $10.29 $10.25
Gross Margin to Revenue Ratio 50% 48% 48%
Note: As of 2017, Netflix continues to operate in all three “segments” listed above.
Assume Netflix has constant returns in the short run and be sure to read the “note” at the bottom of the table. (a) [15 Points] True or false: In 2015, Netflix operated as a “rational producer” in all three segments (domestic streaming, international streaming, and domestic DVD)? State salient assumptions and show essential calculations. Answer
Page 18 of 34
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(b) [10 Points] True or false: the sole reason that in 2015 the domestic DVD membership was priced higher than the domestic streaming plan was because Netflix’s cost of providing the domestic DVD plan was more than its cost of providing a domestic streaming plan? Justify your answer. State salient assumptions and show essential calculations. Answer:
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(c) [15 Points] Suppose an analyst uses the 2013 – 2015 data to estimate the following demand model
for international streaming:
ln 𝑃 = 3.48 − 0.14 ln 𝑞
Assume Netflix’s minimum output is zero and that it has ample capacity. What should’ve been Netflix’s 2015 profit maximizing price and contribution margin in the international streaming segment? Explain why the actual price in 2015 was higher/lower than the one you calculate below. State salient assumptions and show essential calculations. Answer:
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(d) [5 Points] According to Netflix Annual Report, in 2015, the value of Netflix’s “DVD operations equipment” was $88,471,000 with a remaining useful life of five years (including 2015). Making the plausible assumption that Netflix’s “DVD operations equipment” is firm-specific (i.e. cannot be used by/leased to other companies), calculate the “DVD operations equipment user cost of capital” in 2015, i.e. 𝑃𝐾 (price of using owned capital). Assume zero salvage value and use the straight line depreciation method. State salient assumptions and show essential calculations. Answer:
Page 22 of 34
QUESTION 6 [TOTAL 80 Points] The following tables are compiled from the lecture on The Prestige Telephone Company:
January 2003 February 2003 March 2003
Revenue Hours
Intercompany 206 181 223
Commercial 123 135 138
Service hours 32 32 40
Available hours 223 164 143
Total hours 584 512 544
All data for 2003 January February March
Revenues
Intercompany sales
82,400 72,400 89,200
Commercial sales
Computer use
98,400 108,000 110,400
Other
9,241 9,184 12,685
Total Revenue 190,041 189,584 212,285
Expenses
Space costs
Rent
8,000 8,000 8,000
Custodial services 1,240 1,240 1,240
Equipment costs
Computer leases
95,000 95,000 95,000
Maintenance
5,400 5,400 5,400
Depreciation:
Computer equipment 25,500 25,500 25,500
Office equipment and fixtures 680 680 680
Power
1,633 1,592 1,803
Wages and salaries
Operations
29,496 29,184 30,264
Systems development and maintenance 12,000 12,000 12,000
Administration
9,000 9,000 9,000
Sales
11,200 11,200 11,200
Materials
9,031 8,731 10,317
Sales promotions
7,909 7,039 8,083
Corporate services
15,424 15,359 15,236
Total expenses $ 231,513 $ 229,925 $ 233,723
Net income/(loss) $ (41,472) $ (40,341) $ (21,438)
Page 23 of 34
Use this information throughout question 6 Recall that the “commercial price” was $800/hour, the “intercompany price” was $400/hour, the average intercompany revenues were capped at $82,000/month, and the commercial demand curve in March 2003 was 𝑃𝑐 = 1,466.66 − 4.83𝑞𝑐 . Recall also from the Prestige Telephone Company case that:
𝐶𝑝𝑜𝑤𝑒𝑟 = 𝑇𝐹𝐶𝑝𝑜𝑤𝑒𝑟 + 𝑇𝑉𝐶𝑃𝑜𝑤𝑒𝑟 = 179.51 + 4(𝑞𝑖 + 𝑞𝑐 + 𝑞𝑠)
𝐶𝑜𝑝𝑠 = 𝑇𝐹𝐶𝑜𝑝𝑠 + 𝑇𝑉𝐶𝑜𝑝𝑠 = 21,600 + 24(𝑞𝑖 + 𝑞𝑐)
𝑇𝐹𝐶𝑃𝐷𝑆 = 𝑇𝐹𝐶𝑝𝑜𝑤𝑒𝑟⏟
179.51
+ 𝑇𝐹𝐶𝑜𝑝𝑠⏟ 21,600
+ 𝑇𝐹𝐶𝑎𝑙𝑙 𝑜𝑡ℎ𝑒𝑟⏟ 191,200
≈ $212,800
𝑇𝑉𝐶𝑃𝐷𝑆 = 𝑇𝑉𝐶𝑝𝑜𝑤𝑒𝑟 + 𝑇𝑉𝐶𝑜𝑝𝑠 = 28𝑞𝑐 + 28𝑞𝑖 + 4𝑞𝑠
𝐶𝑃𝐷𝑆 = 𝑇𝐹𝐶𝑃𝐷𝑆 + 𝑇𝑉𝐶𝑃𝐷𝑆 ≈ 212,800⏟
𝑇𝐹𝐶𝑃𝐷𝑆
+ 28𝑞𝑐 + 28𝑞𝑖 + 4𝑞𝑠⏟ 𝑇𝑉𝐶𝑃𝐷𝑆
Page 24 of 34
(a) [5 Points] What was the total cost of “Service Hours” in March 2003? What “activity” was this cost due to? State salient assumptions and show essential calculations. Answer: (b) [5 Points] Recall that a meeting has been arranged in which Susan Bradley (Prestige Data Services manager) has to explain to Daniel Rowe (President of the Prestige Telephone Company) how PDS intends to become profitable. Suppose that at this meeting, Susan Bradley says “Daniel, notice that while maintaining commercial price at $800/hour we’ve been billing more commercial hours over time which correlates perfectly with smaller losses over time. If this upward trend in commercial hours continues then eventually PDS will break even”. What must one assume in order for Susan’s statement to be correct (i.e. that the smaller losses can be attributed solely to the growth in commercial hours)? Answer:
Page 25 of 34
(c) [10 Points] Show that PDS must sell approximately 177 commercial hours for PDS to “breakeven”.
State salient assumptions and show essential calculations.
Answer
Page 26 of 34
(d) [5 Points] Suppose Susan Bradley was right in that commercial hours would trend up over time and
eventually reach the “breakeven commercial output” of 177 hours in the “breakeven month”. What is
the equation of the “commercial demand” curve in the “breakeven month”? State salient assumptions
and show essential calculations.
Answer
Page 27 of 34
(e) [5 Points] Suppose that we are in the “breakeven month”: is demand for commercial data services
price (in)sensitive? Based on your answer, would you recommend any immediate action vis a vis the
commercial price? State salient assumptions and show essential calculations. [Use the March 2003
demand curve only if you couldn’t answer part (d)]
Answer
Page 28 of 34
(f) [25 Points] Show that the solution to the following general Profit Maximization Problem (PMP) is:
max𝑞
Π = 𝑅 − 𝑇𝑉𝐶 − 𝑇𝐹𝐶 𝑠. 𝑡. 0 ≤ 𝑞 ≤ 𝑐
Case B Case C Case D
When 𝑀𝐶(0) ≥ 𝑀𝑅(0) When 𝑀𝑅(𝑐) ≥ 𝑀𝐶(𝑐) When neither cases B or C occur
𝑞 = 𝑞𝑚𝑖𝑛 = 0 𝑞 = 𝑐 𝑀𝑅(𝑞) = 𝑀𝐶(𝑞)
𝜆1 = 0 𝜆1 = 𝑀𝑅(𝑐) 𝜆1 = 0
𝜆2 = 𝑀𝐶(0) − 𝑀𝑅(0) 𝜆2 = 0 𝜆2 = 0
State salient assumptions and show essential calculations. Please answer this question in general terms
(i.e. derive the results in the above table).
Answer
Page 29 of 34
Use this space to answer question 6 part (f)
Page 30 of 34
Use this space to answer question 6 part (f)
Page 31 of 34
Use this space to answer question 6 part (f)
Page 32 of 34
(g) [15 Points] Suppose that we are in the period when PDS’s commercial demand has reached the
“breakeven output”. Now suppose that “commercial capacity” is 170 hours a month. Solve the following
problem:
max𝑞𝑐𝑅𝑐 − 𝑇𝑉𝐶𝑐 𝑠. 𝑡. 𝑞𝑐 ≥ 0, 𝑞𝑐 ≤ 𝑐 = 170
Indicate whether you’d recommend expanding capacity or reducing minimum output. State salient
assumptions and show essential calculations.
Answer
Page 33 of 34
(h) [10 Points] Once again suppose we are in that period where commercial demand has reached the
“breakeven output”. Please see the Solver output and sensitivity report for the following problem:
max𝑞𝑐𝑅𝑐 𝑠. 𝑡. 𝑞𝑐 ≥ 0, 𝑞𝑐 ≤ 𝑐 = 170
a = 1654.91
b = 4.83
c = 170
q = 170
P = $833.81
R = $ 141,747.80
MC = $28.00
TVC = $ 4,760.00
Profits = $ 136,987.80
Output = 170
Final Lagrange
Cell Name Value Multiplier
$C$19 𝑞𝑐 ≤ 𝑐 170 ???
$C$19 𝑞𝑐 ≥ 0 170 ???
True or false: PDS should not raise the minimum output constraint and should expand capacity by an
hour so long as the cost of adding another hour of capacity is less than $833.81 - $28 ≈ $805? State
salient assumptions and show essential calculations.
Answer
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