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UNIVERSITY OF TORONTO

Faculty of Arts and Sciences

August Examinations 2013

ECO 204 Y1Y

Duration: 3 hours Total Points: 100 points Examination Aid Allowed: Calculator.

Instructions:

- This exam consists of 3 questions in 19 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 ROOM DURING THE LAST 15 MINUTES OF THE EXAM

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

KEEP ANSWERS AS BRIEF AS POSSIBLE

Question Maximum Possible Points Score

1 50

2 30

3 20

Total Score out of 100 =

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QUESTION 1 [50 POINTS]

“204 Cupcakes” owns and operates shops across the city of Two-ronto (“TwO”) and it is the only company that

sells cupcakes in TwO. All stores are identical and each store has ample capacity.

(1.1) [3 POINTS] The quantity of cupcakes that can be produced at shop per day is given by the production function:

( )

Here “Technological Level of shop ”; “Number of workers per day at shop ”; “Number of cash registers

per day at shop ”, and are store-specific parameters. Calculate: the optimal number of workers and cash

registers required to process an (exogenously given) target “output” per day and derive store cost function

Show all necessary calculations.

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(1.2) [3 POINTS] [THIS PART IS INDEPENDENT OF ALL PARTS BELOW] True or false: an individual store has constant returns to

scale but diseconomies of scale. Show all necessary calculations.

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(1.3) [3 POINTS] [THIS PART IS INDEPENDENT OF ALL PARTS BELOW] Calculate store ’s marginal cost due to a small increase in

the wage rate (i.e. the change in due to a change in ). Show all necessary calculations.

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(1.4) [3 POINTS] Use these parameter values in all parts below: and at each store, a cash

register is staffed by two workers. Show that each store’s 20 and use this figure in all parts below. Show all

necessary calculations and state all assumptions.

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(1.5) [10 POINTS] Let price of a cupcake sold at any store and number of cupcakes sold at store (where

). Suppose that the demand curve facing the “204 Cupcakes” chain is:

∑

⏟

∑

⏟

Here are exogenously given parameters. Suppose that all stores act independently and compete with each

other as Cournot rivals in a one-shot “game”. Calculate the profit maximizing output and price at each store; the total

quantity of cupcakes sold across all stores; the gross profit at each store; and the gross profit across all stores. Show all

necessary calculations and state all assumptions and don’t forget to use

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(1.6) [3 POINTS] [EXCEPT FOR PART 1.7 THIS PART IS INDEPENDENT OF ALL OTHER PARTS BELOW] Calculate the for the case

when all stores are competing as Cournot rivals. How many stores must there be for the cupcakes market (at store-level)

to be characterized as “competitive”? Do not use this value of in later parts. Show all necessary calculations and don’t

forget to use

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(1.7) [5 POINTS] Now suppose that each store produces cupcakes as if it’s a “monopoly”. Assuming this is a “one-shot”

game, calculate the profit maximizing output and price at each store; the total quantity sold across all stores; and the

gross profit at each store as well as across all stores. Show all necessary calculations and state all assumptions and don’t

forget to use

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(1.8) [3 POINTS] Consider a hypothetical scenario when there “atomistic competition” in TwO’s cupcake market (i.e. as

). Calculate the profit maximizing output and price at each store as well as the total quantity sold across all

stores. Is “atomistic competition” the same thing as “perfect competition”? Show all necessary calculations and state all

assumptions and don’t forget to use

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(1.9) [3 POINTS] Now suppose that the “204 Cupcakes” Head Quarters chooses the output of each store to maximize

total profits across all stores. Assuming there are stores and that this is a “one-shot” game, calculate the profit

maximizing output and price at each store, the total quantity sold across all stores, and the gross profit at each store as

well as across all stores. Show all necessary calculations and state all assumptions and don’t forget to use

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(1.10) [10 POINTS] Suppose that the “204 Cupcakes” chain has 2 stores and that the price of cupcakes at store is:

∑

Recall that Solve for the pure strategies Nash Equilibrium in a simultaneous move “one shot” game where

each store can produce either the “Cournot” output or the “Cartel” output. Please enter your answers in the matrices

below. Show all necessary calculations and state all assumptions

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(1.11) [4 POINTS] Suppose that the simultaneous move game in part (1.10) is played repeatedly forever. “Solve” this

dynamic game. Show all necessary calculations and state all assumptions.

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QUESTION 2 [30 POINTS]

In Project 3 you used the Supermarket Scanner Data Set containing various data on “reg” and “lit” varieties of two

brands of soda (“X” and “Y”) sold in seven stores over 52 weeks.

The following table contains a portion of the regression output for the supermarket’s demand function for Brand Y: the

quantity of brand Y was regressed on a constant, the price of brand X, the price of brand Y and a dummy variable

which takes the value 1 if there was an “in-store” promo (i.e. not a “price” promo) on brand Y (and 0 otherwise):

Dependent Variable = Coefficient

Constant 40091.17132

207252.3658

-1427678.133

16719.61367

The following table contains a portion of the regression output for the supermarket’s function for Brand Y: the

of brand Y was regressed on the quantity of brand Y:

Dependent Variable = Coefficient

Constant 0

0.01803

Throughout this question assume that the supermarket has ample capacity and answer all parts up to 4 decimal places.

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(2.1) [5 POINTS] Suppose that currently: and there are no “in-store” promos on Brand Y.

Without deriving the utility function calculate the change in the “representative” Brand Y customer’s utility due to a 1%

decrease in across all stores. Show all necessary calculations.

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(2.2) [10 POINTS] Suppose that currently: and there are no “in-store” promos on Brand

Y. Derive the utility function of the “representative Brand Y consumer” and calculate the change in the “representative”

Brand Y customer’s utility due to a 1% decrease in without computing and using the new output. Show all necessary

calculations. Note: Due to rounding errors your answer in part (2.2) may be slightly different from the answer in part

(2.1) – this is OK.

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(2.3) [10 POINTS] Suppose that currently: and there are no “in-store” promos on Brand

Y. Calculate the price, income and substitution effects from a 1% decrease in . Show all necessary calculations.

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(2.4) [5 POINTS] Suppose that currently: and there are no in-store promos on Brand Y.

Does the current price of brand Y maximize profits? If not, calculate the optimal uniform price of brand Y. Show all

necessary calculations.

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Question 3 [20 POINTS]

(3.1) [10 POINTS] Under what conditions will a company with market power charging a uniform price produce at full

capacity? Then derive the optimal price rule for the case when the company is producing at full capacity. Answer this

question in general form (i.e. without using numerical values). Hint: Solve the PMP:

( ) ( )

And only examine the case when the company produces at full capacity. Show all necessary calculations.

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(3.2) [10 POINTS] Suppose that the solution to this PMP is:

( ) ( ) ( )

You are told that at the optimal solution:

What’s the most this company should pay per unit of extra capacity? Show all necessary calculations and calculate all

numbers to 4 decimal places.