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 3 of 39

Page 4 of 39

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 13 of 39

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 24 of 39

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 26 of 39

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 36 of 39

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