final exam 2022 - answer key (1)
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STR401 - Managerial Economics
Final Exam - answer key
Wednesday, August 24, 2022
Directions:
This is a closed-book exam.
You will have three hours to complete the exam.
Answer all
questions as clearly and legibly as possible, using the supplied exam booklets. Do not answer your
questions in this exam booklet.
In order to get full credit, you need to show your work.
The exam has a total of 400 points, and the length of exam is 180 minutes.
The number of
points are indicated for each question. This exam consists of 9 pages, including this cover sheet.
You are expected to work alone. To con°rm this, please complete and submit with your exam
this cover sheet to the exam
I understand the Simon code of academic integrity and agree that I have completely abided by
it will continue to do so. In particular, I have not discussed the contents of this exam with anyone
else while completing it, and I will not discuss the contents of this exam with anyone who will take
it later.
Signed: ________________________________________
Print your name: __________________________________
1
Basic formulas
Optimality: "
MB
=
MC
"
Elasticity of
Q
with respect to
X
:
dQ
dX
X
Q
inverse elasticity rule:
P
°
MC
P
=
1
j
E
d
j
competitive market equilibrium:
Q
d
(
p
) =
Q
s
(
p
)
pass-through:
E
S
j
E
d
j
+
E
S
markets with externalities:
SMC
(
Q
) =
PMC
(
Q
) +
EMC
(
Q
)
and
SMB
(
Q
) =
PMB
(
Q
) +
EMB
(
Q
)
Two-part tari/s:
T
=
A
+
pq
Nash Equilibrium: "Everybody is playing a best response"
Derivative of a quadratic function: If
y
=
a
+
bx
+
cx
2
;
then
dy
dx
=
b
+ 2
cx
Area of a rectangle:
height
°
width
area of a triangle
1
2
°
height
°
width
Net Present Value:
1 +
°
+
°
2
+
°
3
+
:::
= 1 +
°
1
°
°
=
1
1
°
°
2
PART (A) - SHORT ANSWERS (200 points / 20 each):
(a) Brie±y de°ne the concept of cross-price elasticity of demand and discuss how it is useful
in both describing relationships across various products and in measuring the competitiveness of
markets.
Cross-price elasticity of demand measures how sensitive the demand for good X is with respect
to the price of good Y, de°ned as
dQ
x
dP
y
P
y
Q
x
(the percentage change in the demand for good X divided
by the percentage change in the price of good Y). Positive cross price elasticities indicate that the
two products are substitutes, while negative cross price elasticities indicate that the products are
complements. The higher cross-price elasticities suggest that the products are more substitutable
in the eyes of the consumers and thus making the market more competitive.
(b) A market for widgets is currently served by a single °rm (with market power). The current
market price of the widgets is $40, and the monthly sales are 1000 units.
The government is
currently taxing the sales of widgets at the rate of $5 per unit, so that for the sale of each unit, the
°rm receives $35 and the government receives $5. The °rm is currently pro°table. An economic
advisor comes to you and suggests replacing the $5/unit speci°c tax with a $5,000/month operating
fee. Evaluate the e/ects of the proposal on the °rm, the consumers and the overall e¢ ciency of the
market. Should you implement the proposal and why?
Eliminating the tax would lower the market price while raising the price received by the °rm
while expanding sales, so both the consumers and the °rm would be better o/, and the e¢ ciency
of the market would be improved. So the proposal makes perfect sense since the government still
gets its $5,000. While no °gure was needed for this question, below is an illustration of the solution
to highlight the basic e/ects.
Figure 1: illustration of solution to q1(b)
3
(c) Suppose there are two goods, X and Y, the markets for which can be characterized as
perfectly competitive (and the goods are independent, so there are no cross-price e/ects, and there
are also no externalities). The supply of both goods is in°nitely elastic, while the own-price elasticity
of demand for good X is
±
2
:
3
and the own-price elasticity of demand for good Y is
±
4
:
1
. If the
government wants to raise a °xed amount $A dollars in tax revenue from the two markets while
minimizing the deadweight loss associated with the tax, which market should the government tax
relatively more and why?
Recall that the deadweight loss caused by a tax is ampli°ed by the elasticity, so the optimal
strategy is to tax the less elastic market relatively more. Thus, the market for good X should be
taxed relatively more than the market for good Y.
(d) Suppose your (inverse) demand curve is given by
P
(
Q
) = 15
±
1
4
Q
while your total cost of
production is given by
TC
(
Q
) = 10+
Q
+
1
4
Q
2
. Solve for your pro°t-maximizing price and whether
you want to continue operating in the business.
Marginal cost of production is
MC
(
Q
) = 1+0
:
5
Q;
while the total revenue is
(15
±
1
4
Q
)
Q
, giving
marginal revenue of
15
±
0
:
5
Q:
Thus, the optimal output level is given by
1 + 0
:
5
Q
= 15
±
0
:
5
Q
!
Q
= 14
and so the price is
P
= 15
±
0
:
25
°
14 = 11
:
5
. Your pro°ts are
(15
±
0
:
25
°
14)
°
14
±
10
±
14
±
0
:
25
°
14
2
= $88
>
0
so it is worthwhile to stay in business.
(e) Suppose that the price of gasoline is currently
P
= $4
:
54
. Concerned over the impact of
such high gasoline prices on consumer welfare, the government imposes a price ceiling of
P
= $4
on
the gasoline market. Use the supply-and-demand framework to graphically and verbally illustrate
the e/ects of such regulation on the gasoline market. Who gains, who loses and what is the overall
impact on market e¢ ciency?
The solution is illustrated in the below °gure ²At ceiling of $4, the ceiling is binding and relative
to the market equilibrium, shrinks supply while creating excess demand. Given the quantity traded
shrinks, that creates a deadweight loss for the units that would be valuable to trade but no longer
get traded since suppliers are unwilling to supply them at price of $4. The producers are strictly
worse o/, producing less and receiving a lower price. Consumers may be worse o/ or better o/ ²
the lower price generates a surplus transfer (CS(2) area) from producers to consumers, but at the
same time the consumers also lose their share of the deadweight loss triangle. And recall that this
is the minimum ine¢ ciency, where we are still assuming that the good is getting allocated to those
who actually value it the most.
(f) Ann and Bob are working on a joint project and choosing how many hours to contribute
towards the project. The payo/ matrix is given by the table below. Solve for the Nash equilibrium
of the game where Ann and Bob choose their contributions simultaneously (and only once). Brie±y
describe the process how you got to your answer.
4
Figure 2: Graph for question 1(e)
We follow the logic of best responses ²with the best responses bolded in the table below. Then,
the Nash equilibrium is given by the cell where the two best responses meet so that neither player
wants to change what they are doing, giving the equilibrium as Ann contributing 1 hour and Bob
contributing 0 hours.
Bob
0
1
2
Ann
0
2,
2
4
,1
7
,1
1
4
,
3
3,2
5,1
2
3,5
2,
7
6,6
(g) You operate a Hampton Inn, franchised from Hilton. You have just completed an extensive
market research project to identify your demand curve and adjusted your pricing accordingly to
maximize your pro°ts. Right after this, however, Hilton informed you that the annual franchise
fee that you need to pay has increased from $100,000 to $125,000 per year. Your CFO comes and
says, "given the increase in the franchise fee, we should increase the price of our rooms to recoup
the increased cost." How would you respond?
The franchise fee is a °xed cost, and as a result should have no e/ect on the pricing decision.
Given that the pricing strategy is currently optimal, then changing prices would only decrease your
pro°ts further.
(h) Brie±y explain the impact of product di/erentiation (vertical or horizontal) on the intensity
of price competition and the pro°tability of the °rms involved.
The purpose of product di/erentiation is to decrease the intensity of price competition and thus
increase pro°tability, whether that di/erentiation is vertical or horizontal. In both cases, having
your loyal customers decreases your incentives to go after other customers.
5
(i) Brie±y explain the concepts of learning curves and economies of scale and how they di/er
from each other.
Economies of scale refers to the situation where your average costs are falling as you expand
the scope of your operations (say, output per month). The basic idea is that some scale is always
good to lower your average costs, whether it is due to specialization, ability to spread °xed costs
over a bigger number of units or maybe improved bargaining power with your suppliers. Learning
curves, in turn, also deal with decreasing average costs but deals with the idea of learning, i.e.
getting better at doing things over time. So the idea of learning curves is that it becomes cheaper
for you to produce
any
level of output the more experience you have, which we can measure by the
cumulative output you have produced up to today. That is, because you have already produced
100,000 cars over time, your average costs are lower for any output level than when you had only
produced 1,000 cars.
(j) A vertical merger, where two companies in a supply chain merge together, is di/erent from
a horizontal merger, where two competitors in the same market merge, because it does not have a
direct e/ect on the market by simply reducing the number of competitors. Such vertical mergers,
however, are still evaluated by the Department of Justice or the Federal Trade Commission for
their potential anti-competitive e/ects. Brie±y describe some of the ways how such a merger may
either help or hurt the °nal consumer and thus be either pro- or anti-competitive.
On the bene°t side, one of the main components is the elimination of double marginalization,
where the upstream supplier uses its market power to extract surplus from the downstream poducer,
which then increases prices to the °nal consumers and, as a result, lowers overall pro°ts for the
supply chain as a whole.
Then, a merger can actually lower prices to the consumers by making
the merged °rm worry about pro°ts in the whole supply chain.
One of the main concerns, on
the other hand, is the risk of what we call market foreclosure.
The merged entity may have an
incentive to prevent its competitors from having access to the upstream supply (e.g. AT&T could
be tempted to block other cable companies from having access to Time Warner content), thus
gaining a competitive advantage in the marketplace and being able to charge higher prices due to
the reduced competition (increased product di/erentation in the case of content, for example, since
only you can now sell the content), or simply skewing the competitive environment by charging
the competitors much higher prices for the input, thus weakening competition by increasing the
production costs of your competitors.
6
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I T Demand
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Graph Input Tool
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Chapter 4 HW Flashcards | Quizle X +
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Output
0
0
1
10
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30
3
60
4
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5
90
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