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UNIVERSITY OF TORONTO

Faculty of Arts and Sciences

April Examinations 2012

ECO 204 Y1Y

Duration: 3 hours Total Points: 100 points

Examination Aid Allowed: Calculator.

Instructions:

- This exam consists of 6 questions in 39 pages, double-sided.

Please give your name and ID # as it appears in ROSI

Last Name: First Name:Student ID #

_____________________________________________________________________________

Question Points Scores1 (10 Short questions) 40

2 103 104 15

5 206 5

TOTALSCORE=

YOU MUST STAY SEATED DURING THE LAST10 MINUTES OF THE FINAL EXAM

WAIT UNTILALL EXAMS ARE COLLECTED

KEEP ANSWERS BRIEF

TO EARN CREDIT YOU MUST SHOW CALCULATIONS AND GIVE ARGUMENTS TO SUPPORT YOUR ANSWERS

FOR YOUR CONVENIENCE, THERE IS A WORKSHEET AT THE END OF THIS EXAM

Good luck!

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Q UESTION1 [40 POINTS] ALLSHORTQ UESTIONSSHOULDBE ANSWEREDINDEPENDENTLYOF EACHOTHER.

(1.1) [4 POINTS] Write down the Lagrangian objective function the first order conditions and (any)Kuhn-Tucker conditions for the following profit maximization problem (do NOT solve the problem):

( ) ( )

What are the possible sign s of the Lagrange multipliers (i.e. positive, zero, negative)?

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(1.2) [4 POINTS] Write down the Lagrangian objective function the first order conditions and (any)Kuhn-Tucker conditions for the following profit maximization problem (do NOT solve the problem):

( ) ( )

What are the possible signs" of the Lagrange multipliers (i.e. positive, zero, negative)?

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(1.3) [4 POINTS] True or false: if a firm with market power is producing the revenue maximizing output ata uniform price then the absolute value of the price elasticity must be equal to 1 (i.e. | | )? Give abrief explanation and use graphs to illustrate your answer. Do NOT solve the Revenue MaximizationProblem.

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(1.4) [4 POINTS] True or false: a firm with ample capacity and market power charging optimal 1 st degreeprice discrimination prices will produce the same total output as if it were charging the perfectlycompetitive uniform price? Do NOT solve any profit maximization problems and use graphs to illustrateyour answer.

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(1.5) [4 Points] Give three ways to characterize (define) the following attitude towards risk in decisionmaking under uncertainty corresponding to the last digit of your ID# (use graphs to illustrate youranswer):

If your ID # ends in 0, 2, 4, 6, or 8 Risk averse attitude towards risk

If your ID # ends in 1, 3, 5, 7, or 9 Risk neutral attitude towards risk

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(1.6) [4 Points] True or false: solving a CMP with the production function will yield identicalanswers for ( ) as solving the CMP with the production function ( ) ?Give a very brief explanation. Do NOT solve the Cost Minimization Problem.

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(1.7) [4 Points] Consider the following profit maximization problem:

( ) ( ) What can be said about the firms capacity if at the optimal solution ? Give a brief explanation

and use graphs to illustrate your answer. Do NOT solve the Profit Maximization Problem.

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(1.8) [4 Points] The following table shows the as a % of market demand for some U.S. sectors.What is the theoretical number of companies in each sector that can operate at the lowest cost perunit? Show your calculations in the table below.

Industry as % of Market Demand

Commercial Aircraft 10%Beer 1.37%

Mineral water 0.08%Source: Sutton, Sunk Costs and Market Structure, MIT Press

Industry

as %

of MarketDemand

Theoretical # of Companies Operatingat lowest cost per unit (show calculations)

CommercialAircraft

10%

Beer 1.37%

Mineral water 0.08%

http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=8351http://mitpress.mit.edu/catalog/item/default.asp?ttype=2&tid=8351

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(1.9) [4 Points] Consider a company that has purchased (not leased) capital to produce a target output

. Assume straight line depreciation, zero salvage value, and constant opportunity cost rate ofreturn. What are: the lowest and highest values of owned capital the lowest and highest prices ofowned capital? Give a brief explanation and show all necessary calculations.

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(1.10) [4 POINTS] From The Aluminum Industry in 1994 case , recall that at the end of 1993 (AL =Aluminum): Western consumption of AL = 20.4m tons; Rest of the world consumption of AL = 4.1mtons; Production of secondary AL = 6m tons. Here are portions of Exhibit 4 from that case with 5 yearand 10 year CAGR (Compound Annual Growth Rate) forecasts:

5 year CAGR forecast 10 year CAGR forecastPrimary AL production 1.4% 3.6%

Secondary AL production 3.7% 3.4%Western consumption of AL 2.0% 3.3%

Rest of the World consumption of AL -3.5% 0.2%

Assume that 1m/tpy of AL inventories will be unloaded onto the London Metal Exchange in each yearbeginning with 1994. Predict the total supply of (new) primary AL in 1996 (up to 2 decimal places) byusing the following CAGRs corresponding to the last digit of your ID#:

If your ID # ends in 0, 2, 4, 6, or 8 use the 5 year CAGR forecast

If your ID # ends in 1, 3, 5, 7, or 9 use the 10 year CAGR forecast

State all assumptions and show all calculations.

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2011 2010 2009 2008 2007

Unit sales 42,620,000 50,312,000 54,132,000 54,828,000 51,630,000 Price/unit ($) $174 $164 $149 $167 $161

Source: Source: Apple 10-K Annual Reports (2011 and 2009)

An analyst uses the data above to estimate the following demand function for iPods (here 000s ofunits of iPods and price/unit):

(2.1) [1 Points ] According to the demand function above, what is the elasticity of iPods? Give a briefexplanation.

(2.2) [1 Points ] According to the demand function above what are the revenue maximizing uniform

price and output of iPods in 2011? Assume any number you like for capacity. State all assumptions andshow all calculations.

http://investor.apple.com/sec.cfmhttp://investor.apple.com/sec.cfm

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(2.3) [2 Points ] Assuming Apple chose the profit maximizing price and output in 2011, what was the

(upto 2 decimal places) of an iPod in 2011? State all assumptions and show all calculations.

(2.4) [2 Points ] How would the price of an iPod in 2011 have changed due to a $5 quantity tax on iPods?Assume Apple is charged with collecting the tax. State all assumptions and show all calculations.

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(2.5) [2 Points ] Derive the utility function of the representative consumer for Apple iPods andcalculate the marginal utility of everything else. State all assumptions and show all calculations.

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(2.6) [2 Points ] Use the demand curve for iPods to calculate the change in the representativeconsumers utility from consuming iPods and everything else due to a $5 quantity tax on iPods in 2011.State all assumptions and show all calculations.

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Q UESTION3 [10 POINTS](3.1) [3 Points ] This morning ( ), the government of Geece issued a bond that will startingtomorrow morning ( ) pay bondholders $100/day forever (the payment is made at the start of eachday). The price of the bond is $1,000 and the current (daily) interest rate is 5%. Will you buy this Geecebond at ? Show all calculations and state all assumptions.

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(3.2) [2 Points ] What is the internal rate of return at of the Geece bond in part (3.1) ? Given thecurrent interest rate of 5% , will you buy this Geece bond? Show all calculations and state allassumptions.

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Suppose that you have purchased the Geece bond on the morning of . Immediately afterwards,you read a Boom-berg.com article on how Geece might default on its bonds: according to the article, themarket believes that there is a 20% chance that Geece will default on payments to bondholders, such as

yourself. In the following questions, assume you have the utility function .(3.3) [5 Points ] Right after you read the Boom-berg.com article on Geece bonds, you hop on to your redtricycle and dash off to buy a credit default swap (CDS) policy on Geece bonds from Baldman Sucks , aninvestment bank. Suppose you want to buy a CDS on Geece bonds which fully insures you against thetotal present value of the outstanding Geece bond payments. What is the maximum dollar amountyoud pay to purchase this credit default swap policy? Assume CDS issuers are competitive. State allassumptions, show all calculations, and you are strongly urged to draw a graph to illustrate your answer.

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Port Price ($/TEU) High Season Demand (TEU) % in 20 Containers Japan 940 320 30China 878 68 40

Hong Kong 766 737 42Indonesia 840 68 40

India 790 340 40Korea 710 35 46

Malaysia 643 138 54Singapore 649 43 39

Taiwan 702 41 41Thailand 663 9 20

Please answer the following parts for the port corresponding to the last digit of your ID #:

If your ID # ends in 0, 1, or 2 Hong Kong

If your ID # ends in 3, 4, or 5 India

If your ID # ends in 6, 7, or 8 Malaysia

If your ID # ends in 9 Taiwan

(4.1) [2 POINTS] Calculate the num ber of 40 containers destined for the port corresponding to the lastdigit of your ID # (see above). State all assumptions and show all calculations.

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(4.4) [3 POINTS] Which type of demand curve (linear or constant elasticity) should CTC use to solve forthe optimal total revenue maximizing prices and outputs? Give a brief explanation.

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(4.5) [3 POINTS] From the CTC case, recall the following three constraints in the high season:

( ) ( ) (tons)

The following table contains portions of the sensitivity report for CTCs high season total revenuemaximization problem:

CONSTRAINT FINALVALUE LAGRANGEMULTIPLIER

1,547.46 0 22,800 30.11TOTAL40' TEU : TOTAL20' TEU 1.514 0

TOTAL40' TEU : TOTAL20' TEU 1.514 0

Interpret the Lagrange multipliers on the TEU and weight constraints (you are expected to providenumbers and recommendations in your explanation). State all assumptions and show all calculations.

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(4.6) [3 POINTS] Use the sensitivity report above to compute the optimal ratio in thehigh season. Show all calculations.

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Q UESTION5 [20 POINTS]

PARTA

(5.1) [4 POINTS] A company with market power has constant returns. Setup, solve, and derive theconditions for the various Kuhn-Tucker cases of the following general Profit Maximization Problem giventhat the company can charge a uniform price or 1 st degree price discrimination prices:

( ) ( )

You must express all first order conditions and the conditions for the Kuhn-Tucker various cases in termsof marginal revenue and marginal cost only. State all assumptions and show all calculations.

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PARTB

In the paper Econometric Analysis of Collusive Behavior in a Soft-Drink Market published in the Journalof Economics and Management Strategy (Summer 1992), Gamsi, Laffont and Vuong (GLV) estimated thefollowing demand functions for Coke and Pepsi concentrate syrup based on quarterly data 1968 1986:

The subscript is for Coke and is for Pepsi where:

= quarterly quantity of syrup sold

= price of syrup (1986 dollars)

= square root of quarterly advertising expenses (19 86 dollars){

= real income (1986 dollars)

The average values of the variables in the data set (except season) were:

GLV also estimated Coke and Pepsis average variable cost to be (these are constant across seasons):

Assume Pepsis and Cokes costs stem from manufacturing concentrate syrup only (think of Pepsi and

Coke as producing syrup for gate delivery).

(5.2) [2 POINTS] What type of returns to variable inputs do Pepsi and Coke have? Give a briefexplanation.

http://www.wiley.com/bw/journal.asp?ref=1058-6407http://www.wiley.com/bw/journal.asp?ref=1058-6407http://www.wiley.com/bw/journal.asp?ref=1058-6407http://www.wiley.com/bw/journal.asp?ref=1058-6407http://www.wiley.com/bw/journal.asp?ref=1058-6407http://www.wiley.com/bw/journal.asp?ref=1058-6407

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Answer the questions below for Pepsi and the season corresponding to the last digit of your ID # below:

If the last digit of your ID # ends in 0, 2, 4, 6, or 8 Pepsi in spring/summer

If the last digit of your ID # ends in 1, 3, 5, 7, or 9 Pepsi in winter/fall

(5.3) [2 POINTS] Derive Pepsis demand curve for the season corresponding to the last digit of your ID #(see above). State all assumptions, show all calculations, and derive all figures up to two decimal places .

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PARTC

(5.4) [2 POINTS] Assume Pepsi is a profit maximizer and charges a uniform price. What i s Pepsis optimalcapacity in the season corresponding to the last digit of your ID # (see above)? State all assumptions,show all calculations, and derive all figures up to two decimal places . Hint #1: If Pepsi were to build the

production facility for the first time, what capacity would it choose? Hint #2: When is the value ofexpanding capacity zero?

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(5.5) [2 POINTS] Assume Pepsis actual capacity is 75% of the value you calculated in part (5.4) . Use youranswers to part (5.1) to solve for Pepsis optimal uniform price and output in the season correspondingto the last digit of your ID # (see above). State all assumptions, show all calculations, and derive all

figures up to two decimal places . Note: Only if you could not solve for optimal capacity in part (5.4) thenassume capacity of the maximum market size (this is not necessarily the optimal capacity and

you should only use this figure if you c ouldnt solve part (5.4) ).

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(5.6) [2 POINTS] Assume Pepsis actual capacity is 75% of the value you calculated in part (5.4) . What isPepsis optimal uniform price and output if the government requires Pepsi to behave as if it is perfectlycompetitive in the season corresponding to the last digit of your ID # (se e above)? State allassumptions, show all calculations, and derive all figures up to two decimal places . Note: Only if youcould not solve for optimal capacity in part (5.4) then assume capacity of the maximum

market size (this is not necessarily the optimal capacity and you should only use this figure if youcouldnt solve part (5.4) ).

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(5.7) [2 POINTS] Suppose that after Pepsi has produced but before any customers have purchased thetotal output in part ( 5.5 ), Pepsi management finds out that the maximum willingness to pay forconcentrate syrup has fallen by 50%. If Pepsi wants to dispose the total output produced in part ( 5.5) bycharging uniform prices, how much syrup should it sell? Assume there is no secondary market for unsoldsyrup. State all assumptions, show all calculations, and derive all figures up to two decimal places .

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PARTD

(5.8) [2 POINTS] Assume Pepsi is a profit maximizer and charges 1 st degree price discrimination prices.What i s Pepsis optimal capacity for the season corresponding to the last digit of your ID # (seeabove)? State all assumptions, show all calculations, and derive all figures up to two decimal places . Hint

#1: If Pepsi were to build the production facility for the first time, what capacity would it choose? Hint#2: When is the value of expanding capacity zero?

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(5.9) [2 POINTS] Assume Pepsis actual capacity is 75% of the value you calculated in part (5.8) . Use youranswers to part (5.1) to solve for Pepsis optimal 1 st degree price discrimination prices and total outputfor the season corresponding to the last digit of your ID # (see above). State all assumptions, show allcalculations, and derive all figures up to two decimal places . Note: Only if you could not solve for optimalcapacity in part (5.8) then assume capacity of the maximum market size (this is not necessarilythe optimal capacity and you should only use this figure if you couldnt solve part (5.8) ).

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Q UESTION6 [5 POINTS]Below is Exhibit 1 from the Prestige Telephone Company case:

Exhibit 1: HBS case The Prestige Telephone Company

January 2003 February 2003 March 2003

Intercompany Hours 206 181 223 Commercial Hours 123 135 138

Total Revenue Hours 329 316 361

Service Hours 32 32 40

Available Hours 223 164 143

Total Hours 584 512 544

Recall that the Prestige Data Services commercial demand curve in March 2003 was:

And that the total cost function of Prestige Data Services was:

( ) Here:

Price of commercial data services ($/hour)Hours of commercial data services/monthHours of intercompany data services/monthHours of services/month

Recall that in March 2003: price of intercompany data services ($/hour) = $400/hour and

$800/hour.Solve for the profit maximizing uniform price and output in that month when Prestige Data Servicesbreaks even. You are expected to derive the demand curve in the breakeven month, make plausibleassumptions about the commercial capacity, solve the problem with the constraint that capacity,and use appropriate constrained optimization method. For convenience , you can assume that

State all assumptions and show all calculations.

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WORK SHEET (DO NOT TEAR OFF)