eco204y final 2010w

8/12/2019 Eco204y Final 2010w

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UNIVERSITY OF TORONTO

Faculty

of

Arts

and

Sciences

April

Examinations

2010

ECO 204 Y1Y

Duration:

3

hours

Total

Points:

200

points

Examination Aids: Single 8.5” by 11” (Size A4) Double sided paper and calculator.

Instructions:

‐ This test consists of 5 questions in 28 pages, single‐sided.

Please give your name as it appears in ROSI

Last

Name:

____________________

First

Name:

______________

Student Number:

_______________________________

Question Points Scores

1 35

2 40

3

404

55

5 30

TOTAL (200 Points)

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All questions in this exam are based on the information in Question 1

Please read and do Question 1 before doing other questions

In case you can’t solve question 1 note that it gives information required for other questions

Question 1 [35 points]

Founded in January 2010, Dulce & Havana (D & H) designs and manufactures high end men’s jackets right

here in Toronto. The inputs for D & H jackets are fixed labor (tailors), fixed capital (machines), and variable

materials. Once

manufactured,

the

jackets

are

sold

at

a uniform

price

to

10

individual

customers

in

NYC;

at

a

uniform price to 5 individual customers in Boston; and at a uniform price to the Harry Boor‐son store on

Bloor Street in Toronto.

The marginal cost of distribution to NYC is $300; the marginal cost of distribution to Boston is $100; and the

marginal cost of distribution to Toronto is $0. The following graph depicts D & H’s business model:

Toronto

Factory

Jackets

Manufactured

Inputs

MCDistribution = $300

MCDistribution = $100

MCDistribution = $0

NYC

Boston

T. O.

Fixed Labor

Materials

Fixed Capital

D & H manufactures jackets according to the production function:

Here is number of jackets manufactured, is fixed labor, is materials, and is fixed capital. Currently, in

2010, the Toronto factory currently employs 32 tailors ( 32) who work on 8 machines ( 8). D & H

hires tailors and purchases materials from competitive markets. D & H purchased the machines in January

2010 for

$100

each

and

the

machines

have

a lifetime

of

20

months.

$10, $10, $100

In each month:

D & H has signed a 1 year contract with Harry Boor‐son: in each month of 2010 D & H will sell Harry Boor‐

son 20 jackets a month at a fixed price of $100. This contract expires in December 2010.

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Label the NYC market “market 1”, the Boston market “market 2” and the Toronto market “market 3”. The

following exhibit contains some key figures for January – March 2010:

Dolce & Havana: January – March 2010

January February

March

Units Sold in NYC:

10 30

20

Units Sold in Boston: 20 10

10

Units Sold in Toronto: 20 20

20

NYC Revenues: $9,000 $21,000

$16,000

Boston Revenues: $5,000 $3,500

$3,500

Toronto Revenues: $2,000 $2,000

$2,000

Available (Unused)

Capacity

50

40

50

Number of individual

customers in NYC

10 10

10

Number of customers

individual customers in

Boston

5 5

5

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(a) [5 points] Show that the NYC market demand curve is 1,000 10

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and from this calculate the

price elasticity in March 2010. Show all calculations and state any assumptions.

[You will need this demand curve for other questions in this exam].

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(b) [5 points] Show that the Boston market demand curve is 450 10 and from this calculate the

price elasticity in March 2010. Show all calculations and state any assumptions.

[You will need this demand curve for other questions in this exam].

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(c) [10 points] Show that the monthly cost function for manufacturing the target output is:

400 25

[You will need this cost function for other questions in this exam. From the cost function above note that the

total variable cost of serving the NYC market is 300 25 , the total variable cost of

serving the Boston market is 100 25 and the total variable cost of serving the Toronto

market is

25

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].

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(e) [10 points] Recall that D & H owns machines and that in each month:

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(d) [5 points] Does D & H have increasing, constant, or decreasing returns? Provide an argument for your

answer.

$ 1 0 . What is D & H’s monthly

opportunity cost

rate

of

capital?

Show

all

calculations

and

state

any

assumptions.

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[For this question, use information from Question 1 only] Recall that D & H has 10 individual customers in

NYC (“market 1”).

(a) [5 points] Recall from question 1 (a) that e mand curve is: th NYC market de

1,000 10

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Assuming all NYC customers are identical, use this market demand curve to derive the individual NYC

customer’s demand curve. Show all calculations and state any assumptions.

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(b) [5 points] [This part should be answered independentl of par (a)] Suppose each individual NYC

customer has the utility function:

y t

,

2

Here is savings in dollars and is the number of D & H jackets. Denote income by and the price of good

1 (D & H jackets) by . Solve the UMP and derive expressions for and in terms of the parameters

,, and

(i.e.

don’t

use

numbers

for

).

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(c) [5 points]

Use your answers in parts (a) and (b) to deduce the parameters and in the utility function.

Does this consumer have monotonic preferences over D & H jackets (good 1)? Show all calculations and

state any assumptions.

(d) [5 points] For what price of D & H jackets will a NYC customer maximize or minimize savings? Prove

whether savings are maximized or minimized. Show all calculations and state any assumptions. Hint: Use the

expression for

from part (b).

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(e) [10 points] Suppose in April 2010, D & H sells jackets in NYC through a two part tariff where each

customer pays an access fee for the right to buy jackets and a “usage” price for each jacket. Use the

individual demand curve in part (a) and calculate the optimal and (answers with decimal places are OK).

Graph your solution below. Hints: Allow for the possibility , and choose and to max Π

. [Do two part tariff pricing in this part only].

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$

q

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(f) [5 points] Now suppose that in April 2010 D & H sells jackets in NYC through 1st degree price

discrimination. Use the individual demand curve in part (a) to calculate the optimal prices and number of

$

q

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jackets (answers with decimal places are OK). Graph your solution below. [Do 1st degree price discrimination

in this part only].

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(g) [5 points] [This part assumes uniform prices] Suppose that in April 2010, $800. Consider a typical

NYC consumer with the utility function:

,

2

Here is savings in dollars and is the number of D & H jackets. Suppose this consumer has an income of

$5,000. Using values for and from part (c), solve the UMP for the optimal , and (any) Lagrange

multipliers given that $2,600. Calculate the marginal utility of relaxing the savings limit constraint. Show

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all calculations and state any assumptions.

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[For this question use information from question 1 only]

(a) [10 points] Use the Kuhn‐Tucker/Lagrangian method to calculate D & H’s profit maximizing outputs,

prices and (any) Lagrange multipliers for all 3 markets in April 2010. Show all calculations and state any

assumptions. Hints: Don’t forget the constraint that total output capacity, and that $100,

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2 0 .

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(b) [15 points] Now suppose there is a possibility of arbitrage between (i) NYC and Boston and (ii) between

Boston and Toronto. Assume the cost of arbitrage between NYC and Boston is $300, and the cost of

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arbitrage between Boston and Toronto is $200. Use the Kuhn‐Tucker/Langrangian method to calculate the

optimal outputs, prices and (any) Lagrange multipliers for all 3 markets in April 2010.

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(c) [10 points] [This part is based on your answer to part (b)] Suppose D & H can choose to raise the cost of

arbitrage either between NYC‐Boston or between Boston‐Toronto. Which one would D & H choose? Show all

calculations and state all assumptions.

(d) [5 points] Give two examples of how companies in prevent or inhibit arbitrage.

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[For this question, use information from question 1 only] D & H jackets have become a prized fashion item ‐‐

everyone wants one. Seeking to cash in on D & H’s success, another company, Canadian Moose (CM), sets

up a manufacturing facility in Toronto and starts producing jackets identical to D & H’s jackets. CM

competes with D & H in the Boston market only. The two companies have identical cost functions and the

marginal cost of distribution. For this question assume both companies have ample (unlimited) capacity.

In this

question,

denote

D

&

H’s

output

by

and

CM’s

output

by

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. Calculate

and

give

all

answers

up

to

two decimal places. You can hold D & H’s NYC and Toronto prices and outputs constant.

(a) [10 points] Suppose D & H and CM compete as Cournot rivals. Calculate the optimal outputs and price in

April 2010. Show all calculations and state any assumptions.

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(b) [10 points] Suppose D & H and CM compete as Stackelberg rivals with D & H as the leader. Calculate the

optimal outputs and price in April 2010. Show all calculations and state any assumptions.

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(c) [10 points] Suppose D & H and CM secretly collude and act as a cartel. Calculate the optimal outputs and

price in April 2010. Show all calculations and state any assumptions. Hints: Do not assume that the firms in

the cartel will produce the monopoly profit maximizing output (instead, solve the cartel’s optimization

problem).

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Price

of

Jackets

in

the

Boston

Market

Cartel Output

=

Cournot Output

=

Monopoly Output

=

Cartel Output =

Cournot Output =

Monopoly Output =

Show all calculations below.

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(d) [15 points] Suppose D & H (player 1) and CM (player 2) play a one‐shot simultaneous game in April 2010

where each firm can produce the cartel output, Cournot output, or the profit maximizing monopoly output.

Fill the tables below and compute the pure strategy Nash equilibrium. Hint: Exploit the fact that the two

firms are symmetrical, so that to calculate the entries below you need to do 6 calculations, not 9.

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Revenues

Cartel Output

=

Cournot Output

=

Monopoly Output

=

Cartel Output =

Cournot Output =

Monopoly Output =


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Total Variable Cost

Cartel Output

=

Cournot Output

=

Monopoly Output

=

Cartel Output =

Cournot Output =

Monopoly Output =


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Payoffs (Total Gross Profits)

Cartel Output

=

Cournot Output

=

Monopoly Output

=

Cartel Output =

Cournot Output =

Monopoly Output =

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Show the pure strategy Nash equilibrium above. Indicate if this is a prisoner’s dilemma game.

(e) [10 points] True or false: “ A cartel of D & H and CM will eventually break down because each party has

an incentive to cheat ”? Show all calculations and state any assumptions.

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[For this question, use information from question 1 only] Recall that D &H has a contract to sell Harry Boor‐

son 20 jackets per month at a price of $100 per jacket. Harry Boor‐son is famous for its markdown policy:

over time the store drops the price of unsold items. On April 1st 2010, Harry Boor‐son has priced D & H

jackets 25% markup over cost.

Consider a customer who wants to buy one D & H jacket: he is willing to pay $120 for the jacket. He can buy

the jacket

today

(week

1)

or

wait

until

week

2 when

the

jacket

may

be

available

with

2/3

probability

and

marked down to $75. The customer can buy the jacket in week 2 or wait until week 3 when the jacket may

be available with 1/2 probability and marked down to $60. The customer can buy the jacket in week 3 or

wait until week 4 when the jacket may be available with 1/4 probability and marked down to $50. If the

jacket is not sold in week 4 it is removed from the shelf and given to Harry Boor‐son’s cousin Da Ali Gee. For

your convenience, the following table summarizes Harry Boor‐son’s policy:

Week 1 Week 2 Week 3 Week 4

Week 5 +

Probability

Jacket

is

available

1

2/3

1/2

1/4

0

Price 25% markup

over cost $75 $60 $50

Not for Sale

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Assuming the customer is risk neutral and decides on the basis of consumer surplus, what is the customer’s

optimal strategy ? What is Harry Boor‐son’s expected revenues and when does it expect to sell the jacket?

Show all calculations. Hint: Draw a decision tree.

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eco204y final 2010w

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