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Page 1 of 39
UNIVERSITY OF TORONTO Faculty of Arts and Science
APRIL 2016 EXAMINATIONS
ECO204Y1Y [Ajaz’s ECO 204 Sections only: L0101, L0201, L0301, L5101]
Duration - 3 hours
Examination Aids: Non-Programmable Calculator and one A4 (letter) sized aid sheet (both sides; no restrictions on content)
Total Points: 156 Points
______________________________________________________________________________
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.
PLEASE REMAIN SEATED UNTIL THE PROCTOR ANNOUNCES
THAT YOU CAN LEAVE THE ROOM.
PLEASE DON’T DETACH PAGES – IF YOU DO, THEN IT’S YOUR
RESPONSIBILITY TO STAPLE TOGETHER ALL PAGES OF THIS
EXAM. WE ARE NOT RESPONSIBLE FOR LOOSE PAGES.
TO EARN CREDIT, YOU MUST SHOW ALL NECESSARY
CALCULATIONS AND STATE ALL ASSUMPTIONS.
PLEASE KEEP ALL ANSWERS AS BRIEF AS POSSIBLE.
PROCTOR’S INITIALS:
This exam consists of 10 questions in 39 pages, single-sided.
QUESTION MAX
SCORE ACTUAL
SCORE
Question 1 (Long) 37
Question 2 (Long) 46
Question 3 (Short) 18
Question 4 (Short) 5
Question 5 (Short) 6
Question 6 (Short) 5
Question 7 (Short) 5
Question 8 (Short) 12
Question 9 (Short) 10
Question 10 (Short) 12
TOTAL SCORE OF OUT 156 POINTS:
Page 2 of 39
Question 1 [37 Points]
(a) [15 Points] Consider a “rational” competitive firm with a linear 𝑇𝑉𝐶 function. Suppose the firm must
produce at least zero units and at most 𝑐 > 0 units. Setup and solve this firm’s profit maximization
problem (PMP), derive the various production “cases”, and derive the equation of and graph the “supply
curve”. To earn full credit you must derive – not state – the cases by solving the PMP (you’ll lose 10
points if you simply state the cases). Show all necessary calculations and state all assumptions.
Answer
Page 5 of 39
Please use the information in the following table for parts (b) and (c) of this question. The following
table shows key figures for the average Primary Aluminum (PAL) smelter in 1993:
Source: HBS case, Primary Aluminum Industry in 1994 All cost figures $/metric ton
“Variable” cost components in bold italics
Capacity (‘000s tpy) 133
Electricity usage (kWh/t) 15,800
Electricity price ($/kWh) 0.02
Total electricity cost: 316
Alumina usage (t/t Al) 1.94
Alumina price ($/t Alumina) 190
Total Alumina cost: 369
Other raw materials 125
Plant power and fuel 10
Consumables 70
Maintenance 50
Labor 150
Freight 45
General and Administrative 75
(b) [4 Points] What is the difference between primary vs. secondary aluminum? Please provide a short
explanation.
Answer
Page 6 of 39
(c) [4 Points] Assume that the average PAL smelter in 1993 has a production function exhibiting constant
returns to variable inputs. Compute the total variable cost (𝑇𝑉𝐶) function, the marginal cost (𝑀𝐶) at full
capacity, write down the equation of its supply curve, and graph its supply curve. Show all necessary
calculations and state all assumptions.
Answer
Page 7 of 39
Please use the following table for all remaining parts of this question. The following table (split over
several pages) shows the 𝐴𝑉𝐶 of all CIS smelters (sorted from the most to the least efficient CIS
smelter), followed by the 𝐴𝑉𝐶 of all state owned smelters (sorted from the most to the least efficient
state owned smelter), followed by the 𝐴𝑉𝐶 of all privately owned smelters (sorted from the most to the
least efficient privately owned smelter), and the cumulative capacity:
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
Page 8 of 39
Smelter Country Company Cumulative capacity
‘000 tpy AVC $/t
Fushun 2 China State 7181.00 1150.57
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
Page 9 of 39
Smelter Country Company Cumulative capacity
‘000 tpy AVC $/t
Kurri Kurri Australia Alcan 12148.15 790.84
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
Page 10 of 39
Smelter Country Company Cumulative capacity
‘000 tpy AVC $/t
Goldendale USA Other 18098.65 968.08
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
Page 11 of 39
(d) [4 Points] Assume that all CIS and state owned smelters are irrational producers and that all privately
owned smelters are rational producers. What is the current spot price of PAL if the current total market
supply of PAL is 11.99815mtpy? How much of this total output is supplied by irrational producers? Show
all necessary calculations and state all assumptions
Answer
Page 12 of 39
(e) [10 Points] Assume that all CIS and state owned smelters are irrational producers and that all
privately owned smelters are rational producers. Suppose that in 1993 (time “0”):
Western Demand for Aluminum (AL) = 20.4mt expected to grow at 2% CAGR over the next 5 years
Rest of World Demand for Aluminum (AL) = 4.1mt expected to grow at 3% CAGR over the next 5 years
Secondary production of Aluminum (AL) = 6mt expected to grow at 3.7% CAGR over the next 5 years
Traders will start unloading 1mtpy of PAL starting in 1994.
Produce a forecast range of PAL spot prices in 1995. Show all necessary calculations and state all
assumptions. You will need to use the preceding table. Compute all figures to 2 decimal places.
Answer
Page 14 of 39
Question 2 [46 Points]
This question is based on the HBS case The Prestige Telephone Company. Recall that the commercial
price was 𝑃𝑐 = $800/hour, the intercompany price was 𝑃𝑖 = $400/hour and that PDS is required to
have intercompany billing be less than or equal to $82,000/month on average. For your convenience,
key figures of the case are shown in the following tables:
Table 1
January February March
Intercompany Hours = 𝑞𝑖 206 181 223
Commercial Hours = 𝑞𝑐 123 135 138
Total Revenue $190,584 $181,584 $212,285
Service Hours = 𝑞𝑠 32 32 40
Available Hours 223 164 143
Total Hours 584 512 544
Total Expenses $231,513 $229,925 $233,723
Net Income (Loss): $(41,472) $(40,341) $(21,438)
Table 2
January February March Type of Input/Cost
Space costs:
Rent 8,000 8,000 8,000 Fixed
Custodial services 1,240 1,240 1,240 Fixed
Equipment costs
Computer leases 95,000 95,000 95,000 Fixed
Maintenance 5,400 5,400 5,400 Fixed
Depreciation
Computer equipment 25,500 25,500 25,500 Fixed
Office equipment and fixtures 680 680 680 Fixed
Power 1,633 1,592 1,803 Fixed & Variable
Wages and salaries
Operations 29,496 29,184 30,264 Fixed & Variable
Systems development and maintenance 12,000 12,000 12,000 Fixed
Administration 9,000 9,000 9,000 Fixed
Sales 11,200 11,200 11,200 Fixed
Materials 9,031 8,731 10,317 Ignore
Sales promotions 7,909 7,039 8,083 Assume Fixed $8,000
Corporate services 15,424 15,359 15,236 Assume Fixed $15,000
Page 15 of 39
(a) [4 Points] Is PDS complying with the regulatory requirement that average monthly intercompany
billing should not be more than $82,000 a month on average? Give a brief explanation and show all
necessary calculations:
Answer
Page 16 of 39
(b) [4 Points] According to the case, a manager believes that the company can increase profits by raising
the commercial price by $200/hour in March 2003 (resulting in 30% lower demand for commercial data
services). Without deriving/using the commercial demand curve or cost equations, explain the logic of
why this manager believes that profits will increase under her proposal. Provide a brief explanation and
show all necessary calculations:
Answer
Page 17 of 39
(c) [4 Points] Explain why power and operations expenses encompass both a fixed cost and a variable
cost. Provide a brief explanation and show all necessary calculations:
Answer
Page 18 of 39
(d) [4 Points] Recall that the commercial demand curve and PDS power, ops, and total cost functions
were, respectively:.
𝑃𝑐 = 1,466.66 − 4.83𝑞𝑐
𝐶𝑝𝑜𝑤𝑒𝑟 = 179.51 + 4(𝑞𝑖 + 𝑞𝑐 + 𝑞𝑠)
𝐶𝑜𝑝𝑠 = 21,600 + 24(𝑞𝑖 + 𝑞𝑐)
𝐶𝑃𝐷𝑆 = 𝑇𝐹𝐶𝑃𝐷𝑆 + 𝑇𝑉𝐶𝑃𝐷𝑆 = 212,800 + 28𝑞𝑐 + 28𝑞𝑖 + 4𝑞𝑠
Why is 𝑞𝑠 a part of 𝐶𝑝𝑜𝑤𝑒𝑟 but not 𝐶𝑜𝑝𝑠? Provide a brief explanation and show all necessary calculations.
Use these demand and cost functions in all remaining parts below.
Answer
Page 19 of 39
(e) [4 Points] True or false: there are decreasing returns to the variable “inputs” of power and
operations? Provide a brief explanation and “prove” your answer.
Answer:
Page 20 of 39
(f) [8 Points] Calculate the breakeven output of a company with a single division (say division “1”). Then
calculate the breakeven output (for division 1) of a company with two divisions “1” and “2” (same
𝑇𝐹𝐶 as when the company consists of a single division). True or false: the breakeven output of division 1
(when the company consists of just division 1) is always lower than the breakeven output of division 1
(when the company consists of divisions 1 and 2)? Show all calculations and state all assumptions.
Assume constant returns, fixed price(s), and that division 1 has a positive contribution margin.
Answer:
Page 21 of 39
(g) [4 Points] Assume PDS bills the maximum allowable intercompany hours (on average). Calculate the
commercial breakeven output (for the PDS to breakeven). Assuming PDS’s total capacity and service
hours are equal to the March 2003 capacity and service hours, indicate whether the commercial
breakeven output is feasible. Show all calculations and state all assumptions.
Answer:
Page 22 of 39
(h) [4 Points] Derive the commercial demand curve in that month when PDS breaks even (i.e. based on
your answer to part (g)). Show all calculations and state all assumptions. Use the March 2003
commercial demand curve here and below if you can’t solve part (h) [3 points will be deducted].
Answer:
Page 23 of 39
(i) [10 Points] Assume PDS bills the maximum allowable intercompany hours (on average). Use the
demand curve in part (h) to calculate the profit maximizing commercial uniform price and quantity, as
well as any Lagrange multipliers. Assume PDS’s total capacity and service hours are equal to the March
2003 capacity and service hours. Show all calculations and state all assumptions. You may state the
various “cases” (i.e. you don’t have to derive the cases).
Answer:
Page 25 of 39
Question 3 [18 Points]
The following tables show portions of the “Excel Solver solution” to a uniform pricing profit
maximization problem for a company with constant returns:
Demand Curve
P = a – bq
a
b 4.83
q
P 841.46
output = q
R
MC 28.00
TVC
Gross Profits 136999.80
capacity
Cell Name Cell Value Formula Status Slack
$B$8 output = q $B$8<=$B$13 Not Binding 130.58
$B$8 output = q $B$8>=0 Not Binding 168.42
Final Value
Lagrange Multiplier Cell Name
$B$8 output = q
$B$8 output = q
(a) [10 Points] What are the values of the following terms: 𝑞, 𝑎, 𝑅, 𝑇𝑉𝐶, gross profits, capacity, the two
“cell values” in the second table, the two “final values” in the third table, and the two Lagrange
multiplier values in the third table? Explain your reasoning.
Answer:
Page 27 of 39
(b) [4 Points] Based on your answer to part (a), for what value of capacity would the Lagrange multiplier
for the capacity constraint be positive and what would the value of the Lagrange multiplier tell us?
Explain your reasoning.
Answer
Page 28 of 39
(c) [4 Points] Based on your answer to part (a), for what value of the minimum output would the
Lagrange multiplier for the minimum output constraint be positive and what would the value of the
Lagrange multiplier tell us? Explain your reasoning.
Answer
Page 29 of 39
Question 4 [5 Points] The following graph for L-1011 aircraft production is reproduced from “Learning and Forgetting: The Dynamics of Aircraft Production” (The American Economic Review, 2000):
True or false: this graph shows that there was “learning by doing” in the production of L-1011 aircrafts?
The “wavy” line is measured on the left scale while the “step” line is measured on the right scale. Give a
brief explanation.
ANSWER
Page 30 of 39
Question 5 [6 Points]
Give two examples of non-price mechanisms used by companies to prevent/stop arbitrage in 3rd degree
price discrimination. Give a brief description.
ANSWER
Page 31 of 39
Question 6 [5 Points]
Do you agree with the statement that “Bier Market on King Street, an affluent area of Toronto, charges
higher prices than other Bier Market locations because of the high rents on King Street”? For the
purpose of this question, treat rent as a fixed cost, assume Bier Market is a profit maximizer, and explain
briefly why the Bier Market on King Street charges higher prices than other locations.
ANSWER
Page 32 of 39
Question 7 [5 Points] Your friend is a consultant with the Bad Consulting Group (BCG). As is the case with BCG consultants, your friend wants to “show off” her analytical skills. She tells you about the optimal price rule (which she learned while at HBS, aka Hogwash Business School) and wants to show you how it works. You show her the following table and ask her to demonstrate the optimal price rule on the “long haul international business segment”:
Segment Price Elasticity
Long-Haul International Leisure -0.265
Long-Haul Domestic Business -1.04
Long-Haul Domestic Leisure -1.15
Short Haul Business -1.104
Short Haul Leisure -0.7
Long-Haul International Business -1.520
Suppose the marginal cost of a seat is $10 and the current average fare of long-hail international leisure segment is $1,700 and supposedly the profit maximizing price. Show how your BCG friend should use the optimal price rule to determine/confirm if the “price is right” or “wrong”. Give a brief explanation. Answer
Page 33 of 39
Question 8 [12 Points]
(a) [6 Points] Develop a simple model to explain why car-manufacturers and dealerships don’t sell cars
at uniform prices but rather at 1st degree price discrimination prices. Assume constant returns and
ample capacity. Explain your answer (you’re encouraged to use graphs over math).
Answer
Page 34 of 39
(b) [6 Points] Suppose a company has the following demand and cost models:
𝑞𝑥 = 0.000024𝑃𝑥−5.25 , 𝑇𝑉𝐶𝑥 = 0.0186𝑞𝑥
Assuming ample capacity, calculate the profit maximizing uniform price and the profit maximizing 1st
degree total output. Show all necessary calculations. You don’t need to derive the cases. Calculate your
answer to 4 decimal places.
Answer
Page 35 of 39
Question 9 [10 Points]
Consider a consumer with the utility function 𝑈(𝑞1, 𝑞2) where both goods 1 and 2 are “good” goods and
𝑃1, 𝑃2, 𝑌 > 0. Show that in general, an income tax is no worse for consumers than an excise tax on good
1 (where the excise and income taxes raise the exact same amount of revenues). Show all necessary
calculations and state all assumptions.
Answer
Page 37 of 39
Question 10 [12 Points]
(a) [4 Points] In Project 3, explain the process for declaring whether (say) the development of the access
road was a success or a failure.
Answer
Page 38 of 39
(b) [4 Points] In Project 3, was the investor risk averse, risk neutral, or risk loving?
Answer
Page 39 of 39
(c) [4 Points] Below is the histogram of 𝑁𝑃𝑉 from a particular Monte-Carlo simulation of Project 3:
Here is the summary stats table for the 𝑁𝑃𝑉 histogram:
Summary Statistics of NPV Simulations
Average $ 222,179.41
Standard Deviation $ 1,221,227.71
Maximum $ 23,799,115.30
Minimum $ (314,971.15)
What is the investor’s certainty equivalence of facing uncertain 𝑁𝑃𝑉 in Project 3?
Answer
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