ECONOMICS OF BUSINESS 2
SPRING 2022
PRACTICE IN-COURSE EXAM
Version I (Updated on 2022, Jan. 11)
Exam Instructions:
Please ensure that EACH problem is written in a SEPARATE scriptbook.
Calculators may be used.
If an electronic calculator is used, appropriate intermediate steps should
be shown.
Mobile phones CANNOT be used as calculators.
Any misconduct during the exam will be subject to the university code of
conduct without exception.
For these practice questions, very partial answers will be provided.
Note: Please carefully read the descriptions of the in-course exam posted on
Moodle for the details of exam specifications/formats.
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Section A
Problem A1: Return on (Variable) Cost (ROC) Regulation with
Incentive to Waste
References: Lecture Note 2, Train Ch. 2 (Specifically, pp. 81-88)
The following figure from Train p. 87 could be helpful to solve this problem.
This Problem is the sequel to Problem Set II, Problem 1.
Somewhere in the Caribbean, there is the (fictional) Econo Kingdom Island.
On the island, there is only one bus transportation supplier, Yellow Banana-
Marine Bus, that supplies bus transportation service with yellow buses to the
island citizens. It is known that the weekly inverse demand for bus service is
P = 7 Q on the island, where P is a bus-ticket price (unit is in pounds) and
Q is the number of passenger rides (unit is in tens of thousand of rides [i.e.
10,000 rides]). The Yellow Banana-Marine Bus has the production function
of transportation service Q(K,L) = 10 · K · L, where K is the value of bus
vehicles (unit is in tens of thousands of pounds [i.e. ￡10,000]), and L is the
bus driver working hours (unit is in tens of thousands of hours [i.e. 10,000h]).
For simplicity, we assume that L = 0.1 and w = 10 (so a bus driver’s wage
is 10 pounds per hour) and are fixed due to the unchangeable labor contract.
In addition, the Yellow Banana-Marine Bus’s fixed cost is F = 4 (unit is in
tens of thousands of pounds [i.e. ￡10,000])1. Under these assumptions, the
production function becomes Q(K) = K, and the total cost function becomes
TotalCost(K) = rK+wL+F = K+ 10 ·0.1 + 4 = K+ 5. (Note: based on this
cost function, we can re-interpret the fixed cost as F ′ = 5, instead of F = 4,
in this question. (The unit of fixed cost is in tens of thousands of pounds [i.e.
￡10,000]) Also, the interest rate (rental rate) is r = 1 on the island. The king
1For example, buying insurance, making a (fixed payment) contract with bus maintenance
engineers, etc.
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appreciated your previous economic consultation and has asked you again to
investigate this monopolized bus market.
1.1 Derive the marginal cost function. Then, draw the figure of inverse de-
mand, marginal revenue, marginal cost, and average cost functions. On
the figure, separate the elastic and inelastic portions of demand. FYI, the
inverse demand and average cost functions intersect at (Q,P ) = (5, 2).
Then, calculate the monopolistic quantity QM and price PM .
Answer:
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1.2 Calculate the consumer surplus CSM , profit piM , and total surplus TSM
under this monopolization.
Answer:
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Now, the king introduces the Return on (Variable) Cost (RoC) regulation
that restricts a firm’s allowed profit to be
pi(Q) ≤ kRoC · V ariableCost,
or it is equivalently written in this problem as
pi(Q) ≤ kRoC · (MC ·Q).
The king sets the allowed profit per unit of output at kRoC = 15/14. The
figure below depicts the feasible and allowed profits.
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1.3 How much does the monopolist earn (piRoC) under this RoC regulation
In addition, how much is the consumer surplus (CSRoC) and total surplus
(TSRoC)
Answer:
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1.4 Now, the king revises the allowed profit per unit of variable cost to be
knewRoC = 9/20. you instinctively could see that this revision would cre-
ate waste. Describe why Yellow Banana-Marine Bus has the incentive to
waste (that means renting buses and not using some of them) under this
new situation. Then, calculate how much the monopolist earns (pinewRoC)
under this RoC regulation Also, how much is the consumer surplus
(CSnewRoC) and total surplus (TS
new
RoC)
Answer:
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1.5 Shortly (within 150 words) describe the economic insights behind the fol-
lowing statement.
“The firm under RoC regulation will increase output beyond the unregu-
lated level only to the point that marginal revenue is zero. The attempt
of lowering kRoC further simply induces the firm to waste, and it never
produces output that falls into the inelastic portion of demand.”
Answer:
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Problem A2: Ramsey Prices
References: Lecture Note 4, Train Ch. 4 (Specifically, pp. 116-138)
Somewhere in the Caribbean, there is the (fictional) Econo Kingdom Island.
On the island, there is a garbage collection monopolist, Coast-Litter-Busters.
Coast-Litter-Busters serves two types of customers, business customers (B) and
household customers (H). The demand function of business customers is given
by QB = 30 PB and the demand function of household customers is given by
QH = 24 PH . For simplicity, we assume there is no marginal cost, yet the
monopolist has the fixed cost F = 328. So far, the monopolist is not regulated.
2.1 Draw the two figures of inverse demand functions, one for business cus-
tomers and the other for household customers. Then, calculate the mo-
nopolistic prices and quantities.
Answer:
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2.2 Calculate the consumer surplus and profit for each type of customers un-
der this unregulated monopolization. In addition, how much is the total
surplus under this unregulated monopolization
Answer:
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Now, the king considers setting Ramsey Prices to attain the second-best
outcome. The king knows the necessary condition of Ramsey Prices, that is
PB MCB
QB
· SB = PH MCH
QH
· SH
where SB =
dQB
dPB
and SH =
dQH
dPH
.
2.3 It is known that at Ramsey Prices (R) the quantity for the household
customers is either QRH = 4, Q
R
H = 8, Q
R
H = 12, or Q
R
H = 16. (Note: only
one of these prices can be a Ramsey Price for the household customers).
determine Ramsey Prices for both customers.
You may use the following quadratic function formula: The solution of
ax2 + bx+ c = 0 is given by
x =
b±√b2 4ac
2a
.
Answer:
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2.4 Why is PRB higher than P
R
H State the economic insights behind these
Ramsey Prices (within 50 words). Then, calculate the increase in total
surplus that the island will have after the introduction of Ramsey Prices.
Answer:
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2.5 Some claim that the king should set prices to be equal to the marginal
costs. If the king accepts and implements this claim, what will happen to
the monopolist Is this result first- or second-best outcome And is the
result feasible State the economics insights (within 100 words).
Answer:
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Section B
Problem B1: Vogelsang-Finsinger Mechanism
References: Lecture Note 5, Train Ch. 5
This problem is the sequel to Tutorial problem with a scaled-up market
Somewhere in the Caribbean, there is the (fictional) Econo Kingdom Island.
Based on your previous great performance, the king further keeps you as an
economic consultant to improve the island’s total surplus. In addition, the is-
land recently experienced population increase and inflation.
On the island, there is one rail service supplier, ReggaeTrack,2 that faces
the annual inverse demand function. However, due to the recent population
increase, demand and cost functions changed. Now, the inverse demand function
is P (Q) = 110 Q. The fixed cost is F = 900, and the marginal cost isMC = 10.
See the footnote.3
The CEO and employees of ReggaeTrack know the inverse demand, fixed
cost, and marginal cost, as they operate the business. However, island citi-
zens (including the king) do not have any information on the shapes of inverse
demand, fixed cost, and marginal cost functions. So, information asymmetry
exists.
However, the king is hoping to overcome this difficulty in asymmetric infor-
mation to attain the second-best outcome.
3.1 Draw the figure of the inverse demand function, marginal cost function,
and average cost function that ReggaeTrack faces. Note that the demand
function and average cost function intersect at (Q,P ) = (90, 20). Also,
note that the information (shapes) of these functions are only known by
the CEO and employees of ReggaeTrack. Also, calculate the (unregulated)
monopolistic quantity QM , price PM , and average cost ACM .
Answer:
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2For simplicity, let’s assume there are only two stations on the island, located at the north
and south ends of the island, and the trains do not stop at other locations. In addition, the
trains play non-stop Reggae music.
3The units are defined as follows: Q is in the unit of millions of rides. P is in the unit of
pounds. F is in the unit of millions of pounds. Under these settings, profits and total surplus
are in the unit of millions of pounds.
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3.2 Now (in period 1), you as an distinguished economic consultant observe
only the (unregulated) monopolistic quantity QM and price PM . Further-
more, after the cost transaction record investigation, you know that the
monopolistic average cost is ACM . Thus, you observe
Q1 = QM , P
1 = PM , and AC
1 = ACM
in period 1. (Note: throughout this problem, the upper script is a period
index)
Now, based on the observed information (that is Q1, P 1, and AC1), the
king decided to introduce the Vogelsang-Finsinger Mechanism. Explain
the Vogelsang-Finsinger Mechanism. What price (P 2) does the Reggae-
Track chooses in period 2
Answer:
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3.3 How much are the Q2 and AC2 What price (P 3) would ReggaeTrack
choose in period 3 In addition, Similarly, by setting P 3 = AC2, P 4 =
AC3, and so on, will the prices eventually converge to the first-best or
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second best price
Answer:
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3.4 Describe briefly (within 100 words) why ReggaeTrack has the incentive
to lie (eg. reporting fake transaction records of costs) to inflate average
costs under the Vogelsang-Finsinger mechanism. In addition, if the king
enforces frequent audits and large/huge penalties on false cost reports,
will ReggaeTrack stop inflating costs
Answer:
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3.5 Describe briefly (within 100 words) why ReggaeTrack has the incentive
to lie (eg. reporting fake transaction records of costs) to inflate average
costs under the Vogelsang-Finsinger mechanism. In addition, if the king
enforces frequent audits and large/huge penalties on false cost reports,
will ReggaeTrack stop inflating costs
Answer:
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Problem B2: Finsinger and Vogenlsang Mechanism
References: Lecture Note 6, Train Ch. 6 (Specifically, pp. 187-190)
This problem is the sequel to the Tutorial III Problem 2, 3, and 4.
Somewhere in the Caribbean, there is the (fictional) Econo Kingdom Island.
On the island, there is one rail service supplier, ReggaeTrack, that faces the
annual inverse demand function P (Q) = 55 Q. The fixed cost is F = 225, and
the marginal cost is MC = 5. See the footnote.4
The CEO and employees of ReggaeTrack know the inverse demand, fixed
cost, and marginal cost, as they operate the business. However, island citi-
zens (including the king) do not have any information on the shapes of inverse
demand, fixed cost, and marginal cost functions. So, information asymmetry
exists. However, the king is hoping to overcome this difficulty in asymmetric
information to attain the second-best outcome.
4.1 Draw the figure of the inverse demand function, marginal cost function,
and average cost function that ReggaeTrack faces. Note that the demand
function and average cost function intersect at (Q,P ) = (45, 10). Also,
note that the information (shapes) of these functions are only known by
the CEO and employees of ReggaeTrack.
Answer:
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4.2 Calculate the (unregulated) monopolistic quantity QM , price PM , and av-
erage cost ACM . Assume that ReggaeTrack charges PM in period 0.
Answer:
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4The units are defined as follows: Q is in the unit of millions of rides. P is in the unit of
pounds. F is in the unit of millions of pounds. Under these settings, profits and total surplus
are in the unit of millions of pounds.
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4.3 Now, at the end of period 0, the king decides to introduce the Finsinger and
Vogelsang Mechanism without advance notice to improve the total surplus.
Concisely describe the Finsinger and Vogelsang Mechanism. Specifically,
write and interpret (1) subsidy formula and (2) after-subsidy profit. Does
the mechanism induce first- or second-best outcome Also, does the king
need to know the entire shape of demand function
Answer:
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4.4 If ReggaeTrack chooses P t=1 = 20, how much subsidy and after-subsidy
profit does it gain in period 1 Alternatively, if ReggaeTrack chooses
P t=1 = MC = 5, how much subsidy and after-subsidy profit dose it gain
in period 1
Answer:
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4.5 State the economic insights behind the following statement:
“Regardless of the discount rate, the speed of movement under Finsinger
and Vogelsang Mechanism is very slow when marginal cost is constant.”
Answer:
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