ECONOMICS OF BUSINESS 2 SPRING 2023
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ECONOMICS OF BUSINESS 2
SPRING 2023
PRACTICE IN-COURSE EXAM
Version I (Updated on 2023, Jan. 07)
Version I (Updated on 2023, Feb. 12): Problem A2 Simplified
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 .
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. f10,000]), 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. f10,000])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. f10,000]) Also, the interest rate (rental rate) is r = 1 on the island. The king 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 πM , 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
π(Q) ● kRoC . VariableCost,
or it is equivalently written in this problem as
π(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.
1.3 How much does the monopolist earn (πRoC ) 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 k 
= 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 (π
) under this RoC regulation? Also, how much is the consumer surplus (CS
) and total surplus (TS
)?
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
. SB = 
. SH
where SB = 
and SH = 
.
2.3 It is known that at Ramsey (R) Prices the quantity for the household customers is known to be QH(R) = 16. Find Ramsey Prices and quantities for both customers.
You may (or may not) use the following quadratic function formula: The solution of ax2 + bx + c = 0 is given by
_b 土^b2 _ 4ac
2a .
Answer:
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2.4 Why is PB(R) higher than PH(R)? 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 is MC = 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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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 , P1 = PM , and AC1 = ACM
in period 1. (Note: throughout this problem, the upper script is a period index)
Now, based on the observed information (that is Q1 , P1 , and AC1 ), the king decided to introduce the Vogelsang-Finsinger Mechanism. Explain the Vogelsang-Finsinger Mechanism. What price (P2 ) does the Reggae- Track chooses in period 2?
Answer:
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3.3 How much are the Q2 and AC2 ? What price (P3 ) would ReggaeTrack choose in period 3? In addition, Similarly, by setting P3 = AC2 , P4 = AC3 , and so on, will the prices eventually converge to the first-best or
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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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 Pt=1 = 20, how much subsidy and after-subsidy profit does it gain in period 1? Alternatively, if ReggaeTrack chooses Pt=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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2023-03-21