BA 210 Final Exam Version A Questions
BA 210
Dr. Jon Burke
Final Exam Version A
This is a 150-minute exam (2hr. 30 min.). There are 9 questions (about 16
minutes per question). The exam begins exactly as scheduled. To avoid
the temptation to cheat, you cannot take this exam if you arrive more than
10 minutes late, and you cannot (without permission) leave the room and
re-enter during the exam.
Exam Grading
Each individual question on the following exam is graded on this 4-point scale:
4 points if all is correct --- or there is only a small error.
3 points for missing or doing wrong part of a problem, but the rest is correct.
2 points for a reasonable and substantive attempt.
1 point if there is at least something of value in the attempt.
After all individual questions are graded, I sum the individual scores, and then compute
that total as a percentage of the total of all points possible.
I then apply a standard grading scale to determine your letter grade:
90-100% A; 80-89% B; 70-79% C; 60-70% D; 0-59% F
Finally, curving points may be added to letter grades for the entire class (at my
discretion), and the resulting curved letter grade will be recorded on a standard 4-point
numerical scale:
A = 4; A- = 3.7; B+ = 3.3; B = 3.0; B- = 2.7; C+ = 2.3; C = 2.0; C- = 1.7; D+ = 1.3; D =
1.0; F = 0
Tip: Pace yourself. When there is only ½ hour left, spend at least 5
minutes outlining an answer to each remaining question.
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BA 210 Final Exam Version A Questions
Question 1: Consider the following linear production
possibilities of dresses and cans food each month from
the U.S., Honduras (home to well known sweat shops),
and the Congo (the poorest country in the world).
Dresses
Food
U.S.
100 dresses
200 cans
Honduras
10 dresses
10 cans
Congo
4 dresses
2 cans
If each country needs 3 dresses each month and if the competitive-market
price of a can of food is $2, then what will be the competitive-market price
of a dress?
Answer to Question 1:
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BA 210 Final Exam Version A Questions
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BA 210 Final Exam Version A Questions
Question 2: Consider the following demand curves for
labor by Abby, Betty, Carla, Doug, Ernest, Frank:
Potential buyers of labor
Willingness to pay
Abby
$16
Betty
$14
Carla
$12
Doug
$10
Ernest
$8
Frank
$6
And consider supply curves for labor by Gail, Heidi, Ingrid, Jim, Kyle, and
Leo:
Potential sellers of labor
Cost to sell
Gail
$1
Heidi
$3
Ingrid
$4
Jim
$6
Kyle
$8
Leo
$11
a. Compute the competitive equilibrium wage and employment.
Compute consumer surplus and producer surplus (that is worker
surplus).
Now consider a minimum wage of $13 designed to help workers.
b. Show the lost producer surplus from the inefficient allocation of
employment. Specifically, suppose Kyle successfully competes to
sell labor instead of Heidi.
c. Show the lost total surplus as minimum wages reduce employment.
d. Show the wasted resources from potential workers competing for
employment. Specifically, suppose potential workers compete for
jobs by waiting in line.
Answer to Question 2:
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BA 210 Final Exam Version A Questions
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BA 210 Final Exam Version A Questions
Question 3: Consider the market below for pizza in
Chicago, where Giordano’s, Gino’s East, and Pizzeria
Duo are just a few of the competitors. Chicago officials
decide to impose an excise tax of $4 per pizza.
Price of pizza
$10
$9
$8
$7
$6
$5
$4
$3
$2
$1
Quantity of pizza
demanded
0
1
2
3
4
5
6
7
8
9
Quantity of pizza
supplied
8
7
6
5
4
3
2
1
0
0
a. What is the quantity of pizza bought and sold after the imposition of the
tax? What is the price paid by consumers? What is the price received by
producers?
b. Calculate the consumer surplus and the producer surplus after the
imposition of the tax. By how much has the imposition of the tax reduced
consumer surplus? By how much has it reduced producer surplus?
c. How much tax revenue does Collegetown earn from this tax?
d. Calculate the deadweight loss from this tax.
Answer to Question 3:
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BA 210 Final Exam Version A Questions
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BA 210 Final Exam Version A Questions
Question 4: Two companies, one based in
Albuquerque and the other in Boston, are using the
same Chicago-based lawyer. Each firm needs the
lawyer’s services in May, June, July, August, and
September. As a result of coordinating schedules, the lawyer could each
month make a triangle route (Chicago- Albuquerque -Boston) rather than
making two separate trips. The airfares each month are:
Triangle $1200, Chicago-Albuquerque roundtrip $800, Chicago-Boston
roundtrip $600
Before the May trip, Albuquerque (the Albuquerque company) confronts
Boston (the Boston company) over its share of the triangle airfare.
Albuquerque presents its offer. Boston either accepts it for each of the five
trips, or rejects it and returns after the May trip with a counteroffer. After the
May trip, Albuquerque either accepts that counteroffer for each of the
remaining four trips, or rejects it and returns after the June trip with a
counteroffer. And so on, with alternating counter-offers before each of the
remaining trips.
What cost should Albuquerque agree to pay for each trip? Should Boston
accept that initial offer?
Answer to Question 4:
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BA 210 Final Exam Version A Questions
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BA 210 Final Exam Version A Questions
Question 5: Sam’s Club and Costco both sell emergency
food supplies in a weather-proof bucket that provides 275
delicious easy-to-prepare meals, including potato soup and
corn chowder. The unit cost to both retailers is $50. The
retailers compete on price: the low-price retailer gets all the market and
they split the market if they have equal prices. Suppose they consider
prices $60, $70, and $80, and suppose market demands at those prices
are 80, 50, and 20. Determine optimal prices and profits in that Price
Competition Game.
Sam’s Club and Costco consider modifying the price competition game
described above with the following low-price guarantee: “We guarantee
lower prices than any other store, and we do everything in our power to
ensure that you’re not paying too much for your purchase. That’s why we
offer our Low Price Guarantee. If you find a lower advertised price, simply
let us know and we’ll gladly meet that price!” Determine optimal prices and
profits in that Price Competition Game modified by the Low Price
Guarantee, and compare with the original Price Competition Game above.
Answer to Question 5:
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BA 210 Final Exam Version A Questions
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BA 210 Final Exam Version A Questions
Question 6: R.J. Reynolds Tobacco Corp. (Player A) and
Philip Morris Corp. (Player B) must decide how much money
to spend on advertising each year. They consider spending
either $20,000 or zero each year. If one advertises and the
other does not, the advertiser pays $20,000, then takes
$60,000 profit from the other. If each advertises, each pays $20,000 but
the advertisements cancel out and neither player takes profit from the
other. Suppose the yearly interest rate is 20%.
What strategies (AOne,BOne) should each player choose if they expect this
game to last only one time period? Are there mutual gains from
cooperative strategies (ACoop,BCoop) rather than (AOne,BOne)? If they expect
this game to repeat indefinitely, would Player A cooperate each period and
choose ACoop if Player B followed the Grim Strategy of punishing noncooperation? and would B cooperate each period and choose BCoop if A
followed the Grim Strategy of punishing non-cooperation?
Answer to Question 6:
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BA 210 Final Exam Version A Questions
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BA 210 Final Exam Version A Questions
Question 7: To understand how to discourage antisocial
behavior, consider Grandma’s demand for cigarettes.
$ price per
pack
0.00
0.20
0.40
0.70
1.00
1.60
2.30
2.40
3.50
Packs
demanded
9
8
7
6
5
4
3
2
1
Suppose each pack Grandma smokes hurts 3 other senior citizens $0.25;
that is, you would have to compensate each of them $0.25 for them to
voluntarily let Grandma smoke a pack of cigarettes. Suppose the unit cost
of supplying cigarettes is $1.50 per pack, and cigarette producers are
perfect competitors.
Assuming there are no taxes or subsidies, compute total surplus.
Assuming the government imposes the optimal tax, compute the number of
packs of cigarettes that are consumed.
Assuming the government imposes the optimal tax, compute total surplus.
Compare total surplus before and after the tax, and comment about the
effect of the tax.
Answer to Question 7:
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BA 210 Final Exam Version A Questions
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BA 210 Final Exam Version A Questions
Question 8: Consider the Work-Shirk Game for an employee
and an employer. Suppose if the employee chooses to work, he
loses $130 of happiness from the effort of working, but he yields
$500 to his employer. Suppose the employer can monitor the
employee at a cost of $50. Finally, if the employee chooses to not work
and the employer chooses to monitor, then the employee is not paid, but in
every other case (“work” or “not monitor”), then the employee is paid $210.
Predict strategies or recommend strategies if this game is repeated daily.
Answer to Question 8:
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BA 210 Final Exam Version A Questions
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BA 210 Final Exam Version A Questions
Question 9: Suppose Employer Earl has use for two kinds of
employees. Skilled and hard working Type A employees
contribute $140,000 per year to profits. And Type B employees
contribute $70,000 per year to profits.
Suppose Type A workers have existing jobs paying $60,000 per year, and
Type B have existing jobs paying $50,000 per year. Suppose Type A
workers regard the cost of completing a hard college class as $2,000 a
year of salary, and Type B workers as $10,000 a year of salary. Suppose
there is no way for the employer to directly tell Type A workers from Type B
workers, but the employer can confirm the number of completed classes.
Finally, suppose potential employees can make a wage demand that the
employer must either accept or reject (but not counter).
Determine wage demands, the number of completed classes, and which
types work for Employer Earl.
Answer to Question 9:
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BA 210 Final Exam Version A Questions
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BA 210 Final Exam Version A Questions
Answers to Final Exam Version A (remember to
try each problem before looking at these
answers)
Answer to Question 1:
Step 1. Find who should make food. That is, who has the comparative
advantage. For each citizen of the U.S., each can of food takes up 1/200
of his month, during which time he could complete 1/200 × 100 = ½ dress.
For each citizen of Honduras, each can of food takes up 1/10 of his month,
during which time he could complete 1/10 × 10 = 1 dress. For each citizen
of the Congo, each can of food takes up 1/2 of his month, during which
time he could complete 1/2 × 4 = 2 dresses.
Conclusion: The U.S. has the lowest opportunity cost and the comparative
advantage in making food, then Honduras. And the Congo has the lowest
opportunity cost and the comparative advantage in making dresses, then
Honduras. Since you need 9 dresses, the Congo should produce only
dresses and Honduras should produce 5 dresses, which takes 5/10 of its
month, which leaves 5/10 for food.
Step 2. Find the price PD per dress. Given that the market price of food is
$2, here is what that price PD must satisfy to get the solution above:
For U.S. to choose food full time, potential income from dresses 100PD
must be no more than potential income from food, so 100 PD < 400.
Conclusion: PD < 4.
For Honduras to choose dresses part time, potential income from dresses
10PD must equal potential income from food, so 10PD = 20. Conclusion: PD
= 2.
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BA 210 Final Exam Version A Questions
For Congo to choose dresses full-time, potential income from dresses 4PD
must be no less than potential income from food, so 4PD > 4. Conclusion:
PD > 1.
Putting it all together, the competitive-market price is PD = 2.
(See how the non-specialist determines price, and that the specialists’
inequalities are satisfied at that price.)
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BA 210 Final Exam Version A Questions
Answer to Question 2:
a. At price $8, Abby, Betty, Carla, Doug, and Ernest buy labor from Gail,
Heidi, Ingrid, Jim, and Kyle. In particular, competitive equilibrium
wage is $8 and employment is 5. Consumer surplus from Abby,
Betty, Carla, Doug, and Ernest is the difference between their
willingness to pay and $8, which is $8 = $16-$8, $6 = $14-$8, $4 =
$12-$8, $2 = $10-$8, and $0 = $8-$8, making aggregate consumer
surplus $20 = $8+$6+$4+$2+$0. Producer surplus from Gail, Heidi,
Ingrid, Jim, and Kyle is the difference between $8 and their cost to
sell, which is $7 = $8-$1, $5 = $8-$3, $4 = $8-$4, $2 = $8-$6, and $0
= $8-$8, making aggregate producer surplus $18 =
$7+$5+$4+$2+$0. (There is a technical simplification we make to
work with integers when we assume someone will buy or someone
will sell even when they get surplus 0. Make the same simplification
on your homework and exams.)
Now consider a minimum wage of $13 designed to help workers.
b. Show the lost producer surplus from the inefficient allocation of
employment. Specifically, suppose Kyle successfully competes to
sell labor instead of Heidi. Kyle’s cost to sell is $8 and Heidi’s is $3,
so there is $5 lost producer surplus from Kyle selling rather than
Heidi.
c. Show the lost total surplus as minimum wages reduce employment.
Carla and Doug and Ernest no longer employ labor and, if only the
least cost workers get jobs, Ingrid and Jim and Kyle are no longer
employed. Carla and Doug and Ernest value labor at $12 and $10
and $8 and Ingrid’s and Jim’s and Kyle’s cost to sell are $4 and $6
and $8, so the minimum lost total surplus from reduced
employment is $12 = ($12+$10+$8)-($4+$6+$8).
d. Show the wasted resources from potential workers competing for
employment. Specifically, suppose potential workers compete for
jobs by waiting in line. Since only the first 2 potential workers will be
employed, only Gail and Heidi will work since they have the most to
gain from employment. They have to wait in line long enough so that
the cost of the line makes unemployment unattractive to Ingrid and
the rest of the potential sellers of labor. For Ingrid to find work
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BA 210 Final Exam Version A Questions
unattractive, her net wage must be below her cost of $4 to sell, so the
line must reduce wages from the minimum of $13 down to just below
$4. That is, $9 is wasted in line by Gail and Heidi as they compete
for employment.
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BA 210 Final Exam Version A Questions
Answer to Question 3:
a. The tax drives a wedge between the price paid by consumers and the
price received by producers. Consumers now pay $8, and producers
receive $4. So after the imposition of the tax, the quantity bought and
sold will be 2 pizzas.
b. Consumer surplus is now $1 (one consumer who buys a pizza at $8
has a willingness to pay of $9, so that the consumer surplus is $9 − $8 =
$1, and the other consumer has consumer surplus of $8 - $8 = $0).
Compared to the situation before the imposition of the tax, where the
equilibrium price was $6, consumer surplus has been reduced by $5 (from
$6 to $1). Similarly, producer surplus is now $1 (one producer who sells
a pizza at $4 has cost $3, so that the producer surplus is $4 − $3 = $1, and
the other producer has producer surplus of $4 - $4 = $0), so producer surplus has decreased by $5 (from $6 to $1).
c. Chicago earns a tax of $4 per pizza sold, which is a total tax revenue of
$8.
d. Total surplus has been decreased by $10. Of that $10, the town earns
$8 in revenue, but $2 of surplus is lost. That is the deadweight loss from
this tax.
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BA 210 Final Exam Version A Questions
Answer to Question 4:
Rounds to
End of
Game
Offer by
T otal Gain
to Divide
A's Gain
Offered
B's Gain
Offered
1
A
20
20
0
2
B
40
20
20
3
A
60
40
20
4
B
80
40
40
5
A
100
60
40
To consider all possible offers to split the gains from an agreement on
splitting the cost of the triangle route, consider a bargaining payoff table.
The game ends if an offer is accepted or if the five months end without an
accepted agreement, and gains are measured as a percentage of the gain
from using the triangle route for all five months.
Starting from the end of the bargaining game and rolling back to the
beginning, Albuquerque’s best acceptable offer leaves Albuquerque with 60
percent of the gains from trade, and Boston with 40 percent.
Recall, the airfares each month are: Triangle $1200, Chicago-Albuquerque
roundtrip $800, Chicago-Boston roundtrip $600. In particular, the gain from
five triangle trips is 5x(1400-1200) = 1000.
Albuquerque’s initial offer should be for Albuquerque to keep 60 percent of
the $1000 gain, or $600. So Albuquerque pays 5x800-600 = $3400 for
the five trips. Boston should accept that offer, and gain $400 and pay
5x600-400 = $2600 for the five trips.
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BA 210 Final Exam Version A Questions
Answer to Question 5:
The Price Competition Game has a dominance solution for each player:
First, eliminate $80 because it is weakly-dominated; then, choose $70
because it is weakly dominate. Conclusion: Both should choose $60.
Costco
Sam's
$60
$70
$80
$60
400,400
0,800
0,800
$70
800,0
500,500
0,1000
$80
800,0
1000,0
300,300
To define the normal form for the Modified Price Competition Game, at
Sam’s price $70 and Costco price $60, Sam’s reduces price to $60 and
splits the market demand of 80; hence, both make $(60-50)x40 = $400.
And so on.
Costco
Sam's
$60
$70
$80
$60
400,400
400,400
400,400
$70
400,400
500,500
500,500
$80
400,400
500,500
300,300
The Price Competition Game modified by The Low Price Guarantee has a
$70 as a weakly dominate strategy for each player.
Conclusion: The “Low Price Guarantee” guarantees high prices and profits.
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BA 210 Final Exam Version A Questions
Answer to Question 6:
To begin, fill out the normal form for each month for this game of
simultaneous moves, with payoffs in thousands of dollars. For example, if
Reynolds advertises and Philip does not, Reynolds pays $20,000, then
takes $60,000 profit from Philip. Hence, Reynolds makes $40,000 and
Philip looses $60,000.
Philip
Reynolds
Ad
-20,-20
-60,40
Ad
No Ad
No Ad
40,-60
0,0
(Payoffs are in thousands of dollars.)
On the one hand, what strategies (AOne,BOne) should each player choose if
they expect this game to last only one time period? In that one-shot game,
each player should choose Advertise since it is the dominate strategy for
each player. Each player thus earns -20.
On the other hand, if the game continues indefinitely, then each player
should consider the Grim Strategy. The Grim Strategy has two
components. 1) The Cooperative action of No Advertise, which is mutuallybetter than the non-cooperative strategy of Advertise. 2) The Punishment
action of Advertise, which gives the other player the worst payoff after that
player chooses his best response to (makes the best of) his punishment.
The Grim Strategy is thus, in each month, Cooperate and choose No
Advertise, as long as the other player has Cooperated and chosen No
Advertise in every previous month. But if the other player ever chooses to
Not Cooperate and so to Advertise, then you punish by choosing Advertise
in the next month and in every month thereafter --- forever.
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BA 210 Final Exam Version A Questions
Suppose Player B followed the Grim Strategy. Would Player A cooperate
each period and choose No Advertise?
On the one hand, if Player A cooperated each period and chose No
Advertise, then the Grim Strategy says Player B will also cooperate each
period and choose No Advertise, and so Player A earns 0 each period.
On the other hand, if Player A cheated in any period, then consider the first
period when he cheats.
In that first period, the Grim Strategy says Player B will still cooperate and
choose No Advertise. Player A’s best response to cooperation is
Advertise, which earns 40 in that period, rather than earning 0 if he had
continued to cooperate. So the one period gain from cheating is 40.
But starting in the next period and continuing forever, the Grim Strategy
says Player B will punish by choosing Advertise. Player A’s best response
to Advertise is to Advertise, which earns -20 in each punishment period,
rather than earning 0 if he had continued to cooperate. So the eventual
loss from cheating is 20.
Summing up, if Player B followed the Grim Strategy, then Player A would
cooperate each period exactly if the one period gain of from cheating of 40
does not compensate for the eventual losses of 20 starting the next period.
Use the formula that $1 starting next month and continuing for each
subsequent period is worth $(1/r) today. Since the interest rate r = 20% =
0.20, the eventual losses of 20 is the same as loosing 20/0.20 = 100 today.
Therefore, the one period gain of from cheating of 40 does not compensate
for the losses of 100 (since 40 < 100), so Player A would cooperate and
would choose No Advertise each period.
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BA 210 Final Exam Version A Questions
Answer to Question 7:
Since the market is perfectly competitive, the sellers’ price is $1.50 per unit.
Assuming there are no taxes or subsidies, consumption = 4, producer
surplus = 0, consumer surplus
= 2.00+0.90+0.80+0.10 = $3.80, and external effects are - 3x0.25x4 = $3.00, so total surplus is $0.80
Assuming the government imposes the optimal tax = marginal external
effect = 3x0.25 per unit, the buyers’ price is 1.50+0.75 = $2.25 per unit, so
3 units are consumed.
Assuming the government imposes the optimal tax, consumption = 3,
producer surplus = 0, consumer surplus
= 1.25+0.15+0.05 = $1.45
Since the tax revenue balances the external effect, the optimal tax
increased total surplus from $0.80 to $1.45
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BA 210 Final Exam Version A Questions
Answer to Question 8:
First, complete the normal form below for the Work-Shirk Game. For
example, if the employee chooses to work and the employer chooses to
monitor, then the employee loses $130 of happiness from the effort of
working but is paid $210, and the employer gains $500 from his employee
but pays $50 for monitoring and pays $210 to his employee.
Employer
Employee
Monitor
Trust
80,240
80,290
0,-50
210,-210
Work
Shirk
To predict actions or recommend actions, since the game has
simultaneous moves, first look for dominate or dominated actions. There
are none.
Then look for a Nash equilibrium in pure strategies. There is none. If the
Employee were known to Work, the Employer Trusts. But if the Employer
were known to Trust, the Employee Shirks. But if the Employee were
known to Shirk, the Employer Monitors. But if the Employer were known to
Monitor, the Employee Works. So there is no Nash equilibrium in pure
strategies.
Since the game is repeated, actions need to become unpredictable
because predictable actions can be exploited.
The Nash equilibrium strategy for the Employee is the mixed strategy for
which the Employer would not benefit if he could predict the Employee’s
mixed strategy. Suppose the Employer predicts p and (1-p) are the
probabilities the Employee chooses Work or Shirk. The Employer expects
240p - 50(1-p) from playing Monitor, and 290p - 210(1-p) from Trust. The
Employer does not benefit if those payoffs equal,
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BA 210 Final Exam Version A Questions
240p - 50(1-p) = 290p - 210(1-p), or -50 + 290p = -210 + 500p,
or p = 160/210 = 0.762
The Nash equilibrium strategy for the Employer is the mixed strategy for
which the Employee would not benefit if he could predict the Employer’s
mixed strategy. Suppose the Employee predicts q and (1-q) are the
probabilities the Employer chooses Monitor or Trust. The Employee
expects 80q + 80(1-q) from playing Work, and 0q + 210(1-q) from Shirk.
The Employee does not benefit if those payoffs equal,
80q + 80(1-q) = 0q + 210(1-q), or 80 = 210 – 210q,
or q = 130/210 = 0.619
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BA 210 Final Exam Version A Questions
Answer to Question 9:
The Worker is a
Type A
to Employer $140K
Value/Cost
of Self
$60K
of Courses
$2K
Type B
$70K
$50K
$10K
Consider finding an appropriate integer number N so the Employer should
accept a wage demand of $140K per year for workers that have completed
at least N courses, and a wage demand of $70K per year to the other
workers. There are two constraints on N, incentive compatibility and
participation.
Incentive compatibility constrains the number N of courses to be high
enough so Type B workers do not bother to meet it, and low enough so
Type A workers will meet it.
Incentive compatibility for Type B requires
$70,000 > $140,000 - $10,000 x N, or N > 7.
Incentive compatibility for Type A requires
$140,000 - $2,000 x N > $70,000, or N < 35.
Participation constrains the number N of courses so Type B and Type A
workers both accept the job offers of $70,000 to Type B workers and
$140,000 to Type A workers.
Participation for Type B requires
$70,000 > $50,000, which is true regardless of N.
Participation for Type A requires
$140,000 - $2,000 x N > $60,000, or N < 40.
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BA 210 Final Exam Version A Questions
Putting it all together, the Employer should pick any number N between 7
and 35 and accept a wage demand of $140K per year for workers that
have completed at least N courses, and accept a wage demand of $70K
per year for the other workers.
Comment: Those acceptances separate Type A from Type B workers, but it
comes at the communication cost of $2,000 x N per year paid by the Type
A workers. Even if the smallest number of courses were picked (N = 7),
the cost of the information asymmetry is $2,000 x 7 = $14,000 per year.
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