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UNIVERSITY OF TORONTO

Faculty of Arts and Sciences

April Examinations 2013

ECO 204 Y1Y

Duration: 3 hours Total Points: 100 points

Examination Aid Allowed: Calculator.

Instructions:

- This exam consists of 7 questions in 32 pages, single-sided.

Please Write Your Name and ID # as these appear in ROSI Last Name:First Name:9-Digit ID #:

YOU CANNOT LEAVE THE EXAM ROOM DURING THE LAST10 MINUTES.

PLEASE REMAIN SEATED UNTIL THE PROCTOR ANNOUNCES THAT YOU CAN LEAVE THEROOM.

PLEASE DONT DETACH PAGES. IF YOU DO, THEN ITS YOUR RESPONSIBILITY TO RE-STAPLE DETACHED PAGES BACK TO THE EXAM

KEEPANSWERS ASBRIEF ASPOSSIBLE

For Graders Use Only: Maximum Possible Points Score

Short Questions

Question 1 3Question 2 3Question 3 12Question 4 6Question 5 4

Long QuestionsQuestion 6 30Question 7 42

Total Points = 100

In case of F grade, Final Exam c hecked by Instructor/Course Coordinator?Yes No

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Q UESTION1 [3 POINTS]A recent study assumed that firms in U.S. manufacturing sectors produce output according to the Cobb-Douglasproduction function . The following table contains estimates of for some sectors:

Sector Tobacco Products 0.18 0.33 0.51

Food and Kindred Products 0.43 0.48 0.91 Transportation equipment 0.44 0.48 0.92

Apparel and other textiles 0.70 0.31 1.01 Furniture and fixtures 0.62 0.40 1.02 Electronics and electric equipment 0.49 0.53 1.02

Paper and allied products 0.44 0.65 1.09 Petroleum and coal products 0.30 0.88 1.18

Primary metal 0.51 0.73 1.24

Which of these sectors have strictly convex cost functions (i.e. ( ) )? Briefly explain the basis of your argument.

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Q UESTION2 [3 POINTS]The following graph for L-1011 aircraft production is reproduced from Learning and Forgetting: The Dynamics ofAircraft Production (The American Economic Review , 2000):

True or fa lse: this graph shows that there was learning by doing in the production of L -1011 aircrafts? The wavy lineis measured on the left scale while the step line is measured on the right scale. Give a brief explanation.

http://www.jstor.org/stable/117324http://www.jstor.org/stable/117324http://www.jstor.org/stable/117324http://www.jstor.org/stable/117324http://www.jstor.org/stable/117324http://www.jstor.org/stable/117324http://www.jstor.org/stable/117324

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Q UESTION3 [12 POINTS]The following table is reproduced from the HBS Case The Aluminum Industry in 1994 (AL = Aluminum):

Average Primary Aluminum Smelter (1993) All cost figures $/metric ton Capacity (000s tpy) 133.02

Electricity usage (kWh/t) 15,800 Electricity price ($/kWh) $0.02

Alumina usage (t/t Al) 1.94 Alumina price ($/t Alumina) $190

Other raw materials $125 Plant power and fuel $10

Consumables $70 Maintenance $50

Labor $150 Freight $45

General and Administrative $75

(3.1) [2 Points] What is the difference between primary and secondary aluminum?

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(3.2) [2 Points] According to the case, which primary aluminum smelters are irrational producers and why? Explainbriefly.

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(3.3) [3 Points] This part is independent of all other parts below. Suppose the current price of AL is $1,100/ton. What isthe breakeven output of the rational average primary AL smelter? Show all important steps.

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(3.4) [5 Points] The following table contains actual and projected figures for Western consumption of AL, Rest of theWorld consumption of AL, and secondary production of AL. Suppose that in 1996, 0.75m tons of AL inventory wasunloaded onto the AL market and from thereon inventory was unloaded at a compound annual growth rate of 5%.Calculate the demand for primary AL in 1998. Show all important steps.

ALL FIGURES ARE MILLIONS OF METRIC TONS 1993 1994 1995 1996 1997 1998

Western Consumption of AL 20.4 21.1 21.8 22.5 23.2 24.0

Rest of World Consumption of AL 4.1 4.1 4.1 4.1 4.1 4.1

WRITE DOWN YOUR FINAL ANSWER HERE 1998 Demand for Primary AL (mtpy)

Secondary Production of AL 6.00 6.22 6.45 6.69 6.94 7.20

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Q UESTION4 [6 POINTS](4.1) [3 Points] Give two examples of non-price mechanisms that companies use to prevent/stop arbitrage in 3 rd degreeprice discrimination.

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(4.2) [3 Points] Below is a simplified Profit Maximization Problem for a company selling its product through 3 rd degreeprice discrimination to segments 1 and 2 and having to set the price differential equal to the cost of arbitrage per

unit because it cant stop arbitrage through non -price mechanisms:

( ) ( ) ( ) ( ) ( ) ( )

( ) ( ) ( ) ( ) [ ] [ ( ) ( ) ]

What is the interpretation of ? Explain briefly and show all important steps. Hint: You do NOT have to solve the PMP.

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Q UESTION5 [4 POINTS](5.1) [2 Points] Consider a firm with market power and a downward sloping demand curve ( ). Suppose the companysells its product by charging a uniform price. Provide expressions for its total revenue and marginal revenue.

(5.2) [2 Points] Consider a firm with market power and a downward sloping demand curve ( ). Suppose the companysells its product by charging 1 st degree price discrimination prices. Provide expressions for its total revenue and marginalrevenue.

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Q UESTION6 [30 POINTS] A-sad Inc. produces output by using variable labor and fixed capital according to the following production function:

[ ]

The parameter Let price of labor and price of capital.

(6.1) [2 Points] A-sad cost function exhibits constant average variable cost. Given this fact argue that the parameter

(and use throughout Question 6) . Show any calculations. Hint: You can answer this question without solving A-sads cost minimization problem.

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(6.2) [3 Points] This part is independent of all other parts below. Compute: the elasticity of output with respect tolabor the elasticity of output with respect to fixed capital the elasticity of output with respect to level oftechnology/management. Show all important steps. Hint: Elasticity can be calculated by two methods -- which methodis more convenient in this question?

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(6.3) [3 Points] Derive the equation, intercepts and slope of the iso-quant curve for an arbitrary output level andgraph the iso-quant curve below. Show all important steps.

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(6.4) [10 Points] Solve A-sads shor t run cost minimization problem. Show all important steps. You are expected to solvethis problem by using the appropriate constrained optimization method.

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(6.5) [3 Points] This part is independent of all other parts below. True or false: A- sads is proportional to the

(6.6) [3 Points] This part is independent of all other parts below. True or false: A- sads cost function exhibits constanteconomies of scale ? Briefly explain your answer.

amount of fixed capital (i.e. as does )? Briefly explain your answer.

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(6.8) [3 Points] True or false: learning by doing will lower A- sads and ? Show all important steps

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Q UESTION7 [42 POINTS]

THROUGHOUT THIS QUESTION YOU MUST ROUND ALL NUMBERS TO FOUR DECIMAL PLACES. THIS INCLUDES ROUNDING ALL FINAL ANSWEAND ALL NUMBERS DURING CALCULATIONS TO4 DECIMAL PLACES. MAKE SURE TO ROUND FIGURES TO4 DECIMAL PLACES AT EACH AND

EVERY STEP OF THE CALCULATIONS.

In Project 3 you worked with a super market scanner data set for two brands of soda X and Y sold in seven stores(62 through 68) over 52 weeks, and where each brand of soda had two varieties reg and lit . Let:

quantity sold (ozs./100,000), price ($ per oz.), Total variable cost ($)

Assume that each brand of soda is managed by its own pricing manager at this supermarket chain. These pricingmanagers do not cooperate with each other and choose optimal strategies to maximize their brands profits.

The following cost equations were estimated via regression analysis on all stores, all weeks, and both varieties of soda:

The following demand equations were estimated via regression analysis on all stores, all weeks, and both varieties ofsoda 1:

For your convenience, we have re-arranged demand models and to give you the following demand models:

HINT: WHICH DEMAND MODEL YOU WORK WITH DEPENDS ON THE QUESTION.

The following table contains average values of brand X and Y prices:

($/oz.) ($/oz.)Average 0.0283 0.0286

THROUGHOUT THIS QUESTION ASSUME THAT THE SUPERMARKET HAS AMPLE CAPACITY AND UNLESS STATED OTHERWISE, YOU DONT HAVETO PUT THE CONSTRAINTS

1 In actuality, these demand models were estimated by including Hval_150 as an independent variable. We then entered mean valuefor Hval_150 and added it to the regression intercept. As such, the intercepts in demand models and include Hval_150.

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(7.1) [3 Points] This part is independent of all other parts below. In Project 3, what assumption did you make whichallowed you to estimate the functions without intercepts? Give a brief explanation.

(7.2) [3 Points] This part is independent of all other parts below. True or false: the supermarkets production functionfor selling Brands X and Y has diminishing returns to variable inputs? Give a brief explanation.

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(7.3) [5 Points] This part is independent of all other parts below. If the last digit of your ID # ends in 0, 2, 4, 6, 8 thenplease answer this part for brand X, otherwise answer this part for brand Y. Suppose the supermarket carries your brandof soda but not the other brand (i.e. your brand of soda is a monopoly). Next, suppose the supermarket charges theaverage price of your brand of soda. How can the supermarket do a quick check to see if this (average) price is in fact theoptimal profit maximizing price? Show all important steps. Hint: You can answer this question without solving the ProfitMaximization Problem.

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(7.4) [5 Points] This part is independent of all other parts below. If the last digit of your ID # ends in 0, 2, 4, 6, 8 thenplease answer this part for brand X, otherwise answer this part for brand Y. Suppose the supermarket were to only sellyour brand of soda (i.e. your brand of soda is a monopoly). Calculate the profit maximizing output and price of yourbrand . Dont forget the hints about ample capacity and assume that output of your brand is . Show all importantsteps.

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(7.5) [5 Points] Now suppose the supermarket carries both brand X and brand Y products. Calculate the profitmaximizing outputs and prices for the case when brands X and Y compete as Cournot rivals . Dont forget the hints aboutample capacity and

. Show all important steps.

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(7.6) [5 Points] Now suppose the supermarket carries both brand X and brand Y products. Calculate the profitmaximizing outputs and prices for the case when brands X and Y compete as Bertrand rivals . Dont forget the hintsabout ample capacity and

. Show all important steps.

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Prices for each pricing strategy

Brand Y

Enter Bertrand Price below Enter Cournot Price below

Brand X

Enter Bertrand Price below

Enter Cournot Price below

Quantities for various pricing strategies Brand YBertrand Price Cournot Price

Brand XBertrand PriceCournot Price

Contribution margins for various pricingstrategies

Brand YBertrand Price Cournot Price

Brand XBertrand PriceCournot Price

Gross profits for various pricingstrategies

Brand YBertrand Price Cournot Price

Brand XBertrand PriceCournot Price

Please write down brand X and brand Ys pure strategies Nash equilibrium:

Brand Xs Pricing Strategy Brand Ys Pricing Strategy

(7.7) [10 Points] Conside r the following one -shot game. S uppose brand X and Y pricing managers can either charge theBertrand price or charge the Cournot price. Compute the pure strategies Nash Equilibrium of this one-shot game. Foryour convenience, we have inserted tables to guide your calculations and given you lots of space below for calculations.

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FOR PART7.7 CALCULATIONS

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FOR PART7.7 CALCULATIONS

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FOR PART7.7 CALCULATIONS

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(7.8) [6 Points] Is the one-shot game in part (7.7 ) a prisoners dilemma game? If so , what would you recommend to thepricing managers if the game in part (7.7) is played repeatedly forever? Hint: Do your recommendations require thepricing managers to value long term gains over short gains? If so, under what conditions will these managers value longterm gains over short term gains? Show all important steps.

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