代写Economics of Business 2 Spring 2024 Tutorial II代写C/C++程序

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Economics of Business 2

Spring 2024

Tutorial II

Initially posted on Jan. 04, 2024 (VERSION 1)

Read the following materials and answer the questions:

Problem 1**: Lecture Note 1, Train (1991) Ch.1

Goal - Understanding the Rate of Return (RoR) regulation Problem 2*: Lecture Note 2, Train Ch.2 (Speciﬁcally, pp. 72-81)

Goal - Understanding Return on Output (RoO) and Return on Sales/Revenue (RoS) regulations

Problem 3**: Lecture Note 2, Train Ch.2 (Speciﬁcally, pp. 81-88) Goal - Understanding Return on Cost (RoC) regulation

Problem 4**: Lecture Note 2, Train Ch.2 (Speciﬁcally, Section 2.5) Goal - Understanding Perfect Price Discrimination

Problem 5*: Lecture Note 3, Train Ch.3 (Speciﬁcally, Section 3.2)

Goal - Understanding a proﬁt maximization problem under uncertainty Problem 6**: Lecture Note 3, Train Ch.3

Goal - Understanding the Rate of Return regulation under uncertainty

* Answers are provided in Tutorials.

** Online answers are provided.

O ce Hours:

- Hisayuki YOSHIMOTO: Wed. 9:00-9:55am, Thu. 9:00-9:55am (during the Semester 2 teaching period, except vacation and traveling periods), Zoom on- line room (link posted on Moodle)

Note that office hours are for students who have studied materials and have some detailed/clarifying questions. Thus, o伍ce hours are not for solving prob- lems together with students or for re-explaining rudimentary concepts already addressed in the lecture but are for clarifying students’ speciﬁc/intellectual ques- tions (often with useful hints and tips to enhance students’ understandings). Questions related to tutorial problems are welcome. Use the office hours wisely to obtain better comprehension over the course materials.

Motto: Let’s get many economic insights behind equations and numbers.

Tip: Suggested to organize a student-studying group to solve and discuss prob- lems well.

1. Rate of Return (RoR) Regulation

On the (ﬁctional) Econo Kingdom Island, there is only one parcel de- livery service Parcels-of-the-Caribbean that supplies the delivery service to the island citizens. The daily (single-day) demand function of par- cel service on the island is given by Q(P) = 100 ✁ P (Quantity unit is in parcels), and the production function of Parcels-of-the-Caribbean is known as Q(K, L) = KL, where K is measured by the number of delivery vans and L is measured by the number of delivery workers. On the island, the wage of the postal labor is w = £168, and the rental fee of van is r = £168 (See footnote). For simplicity, there is no ﬁxed cost. The current mo- nopolistic price of parcel service is PM = £64 per shipment. The king is concerned about the expensive price of parcel service on the island and has asked you to start the investigation for government regulation.

(a) Calculate the inverse demand function and the marginal revenue function.

(b) Draw the ﬁgure of the inverse demand function and the marginal revenue function.

Separate the inverse demand function into the portions of elastic and inelastic demands on the ﬁgure. (Note: In Problem 1, we have learned MR = 0 divides elastic and inelastic portions of demand). Answer:

(d) Given the information that the monopolistic price is PM = £64 per shipment, how many parcels (QM ) does Parcels-of-the-Caribbean de- liver? Calculate the monopolistic quantity of delivery service (QM ).

(e) Based on Parcels-of-the-Caribbean’s production function Q(K, L) = KL, draw the ﬁgure of isoquant curves. Also, based on the cost func- tion Cost = rK + wL, draw the cost-minimizing isocost lines.

(f) In the previous problem, we have learned that the cost-minimizing condition (the kissing condition) is

Use this condition to derive the cost-minimizing input choices of cap-

ital (K * ) and labor (L* ) to produce QM .

Table 1: Summary Table

(g) Calculate the proﬁt (πM ), consumer surplus (CSM ), and total sur- plus (TSM ) under the (unregulated) monopolization. Then, ﬁll out the column of “unregulated optimal” in the summary table.

(h) How much is the capital labor ratio (L*/K*) under the (unregulated) monopolization of parcel service?

(i) The king has now asked you to apply the Rate of Return regulation. Your assistant creates the ﬁgure of the isoproﬁt contours as below.

The top of the proﬁt hill is at (K * ; L* ) = (6; 6), as you have solved before. You suggest to the king to set the allowed rate of return on capital to be $27 per capital. Under this regulation, Parcels-of-the- Caribbean’s optimal input choices are known as (KROR ; LROR ) = (8; 5). The hill sihouette with L = 5 is plotted below.

How much is the output (QROR ), proﬁt (πROR ), consumer surplus (CSROR ), and total surplus (TSROR ) after this regulation? Does the total surplus increase under this ROR regulation, compared to the unregulated total surplus? State your economic insights (within 70 words). Then, complete the column of “regulated optimal” on the summary table.

(j) How much is the capital labor ratio ( ) after this ROR regu- lation? Does it increase or decrease, compared to the unregulated capital labor ratio ( )? State your economic insights with the phrase “ine伍cient input choices” (within 70 words).

(k) If Parcels-of-the-Caribbean is not regulated, what are the cost-minimizing

input choices that allow to produce the quantity of QROR? Use the

cost-minimizing condition derived before. Why doesn’t Parcels-of-

the-Caribbean use the cost-minimizing inputs under ROR regulation?

State your economic insights as a consultant (within 100 words).

2. Return on Output (RoO) vs Return on Sales/Revenue (RoS) Regulation

Somewhere in the Caribbean, there is the (ﬁctional) Econo Kingdom Is- land. 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 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) = KL, 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 thou- sands of pounds [i.e. $10,000]). Under these assumptions, the produc- tion 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 F1 = 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 appreciated your previous economic consultation and has asked you again to investigate this monopolized bus market.

(a) Derive the marginal cost function. Then, draw the ﬁgure of inverse demand, marginal revenue, marginal cost, and average cost func- tions. On the ﬁgure, separate the elastic and inelastic portions of demand. FYI, the inverse demand and average cost functions inter- sect at (Q, P) = (5, 2). Then, calculate the monopolistic quantity QM and price PM .

(b) Calculate the consumer surplus CSM , proﬁt πM , and total surplus TSM under this monopolization.

Now, the king introduces the Return on Output (RoO) regulation. The king sets the allowed proﬁt per unit of output at kRoO = 3/4. The ﬁgure below depicts the feasible and allowed proﬁts.

(d) How much does the monopolist earn (πRoO ) under this RoO regu- lation? Also, how much is the consumer surplus (CSRoO ) and total surplus (TSRoO )?

(e) Does Yellow Banana-Marine Bus have an incentive to waste its in- puts under RoO? Also, can the RoO regulation make the ﬁrm produce the output at which the demand becomes inelastic?

(f) If kRoO is inﬁnitesimally close to 0, can the island attain inﬁnitesi- mally the chose to second-best outcome? If so, how much will the total surplus be? If he does, what will happen to the ﬁrm’s proﬁt? State the economic insights as an economic consultant (within 100 words).

Alternately, the king considers introducing the Return on Sales/Revenue (RoS) regulation. Under the RoS regulation, the government regu-lates an allowed proﬁt to be

where the kRoS is the proportion of sales/revenue that can be retained as an allowed proﬁt. The king plans to set kRoS = .

(g) Derive the revenue and allowed proﬁt functions. Then, calculate the allowed proﬁt maximizing level of output and the maximum value of allowed proﬁt. (Note: the feasible proﬁt, revenue, and allowed proﬁt are plotted as below )

(h) How much output does Yellow Banana-Marine Bus choose under this RoS regulation? How much is the monopolist’s proﬁt (πRoS ), consumer surplus (CSRoS ) and total surplus (TSRoS )? Does the monopolist have an incentive to waste its inputs?

(i) Briefly state what will happen when the king sets kRoS inﬁnitesimally close to zero. Also, under this RoS regulation, can the king make the monopolist produce a quantity that falls into the inelastic portion of demand? As a consultant, state your economic insights (within 100 words).

3. Return on Cost (RoC) Regulation

Note: This problem is the sequel to the problem in Tutorial I.

On the (ﬁctional) Econo Kingdom Island, there is only one parcel de- livery service, Parcels-of-the-Caribbean, that supplies the delivery service to the island citizens. The inverse demand function of parcel service on the island is given by P = 100 ✁ Q, and the production function of Parcels- of-the-Caribbean is known as Q(K, L) = KL, where K is measured by the number of delivery vans and L is measured by the number of delivery workers. On the island, the wage of the postal labor is w = £168, and the rental fee of van is r = £168. For simplicity, there is no ﬁxed cost. The current monopolistic price of parcel service is PM = £64 per shipment. The king is concerned about the expensive price of parcel service on the island and has asked you to start the investigation for government reg- ulation. The feasible proﬁt in this problem is plotted below. Note that the maximum of unregulated proﬁt is attained at (K, L) = (6, 6), and the units of variables are the same as previously deﬁned.

(a) Derive the revenue [Revenue(Q)], marginal revenue [MR(Q)], cost [Cost(K, L)], and proﬁt [π(K, L)] functions. Then, draw the ﬁgure of the inverse demand and marginal revenue functions. Furthermore, separate the inverse demand function into the portions of elastic and inelastic demands on the ﬁgure.

(b) Based on the Parcels-of-the-Caribbean’s production function Q(K, L) = KL and cost function Cost(K, L), draw the ﬁgure of isoquant curves and isocost lines. Also, by using the “kiss” condition (see Tutorial

I), derive the expansion path.

(c) Given the information that the monopolistic price is PM = £64 per shipment, how many parcels (QM ) does Parcels-of-the-Caribbean deliver? How much capital (KM ) and labor (LM ) are required to cost-minimizingly produce QM? In addition, derive the monopolistic proﬁt πM , consumer surplus CSM , and total surplus TSM .

Now, the king considers introducing the Return on Cost (RoC) regu- lation. Under the RoC regulation, the ﬁrm’s allowed proﬁt becomes

where kRoC is the proportion of costs that the ﬁrm is allowed to retain as proﬁt. After the regulation, (i) feasible proﬁt, (ii) allowed proﬁt, (iii) feasible and allowed proﬁts, and (iv) feasible and allowed proﬁt (viewed from a diferent angle) look as plotted below.

(d) The constraint curve (see Train Ch.2, Figure 2.12, pp. 83) has its top at (K; L; π) = (7; 7; 147). Calculate the kRoC in this regulation. Answer:

(e) Briefly discuss (within 100 words) if the monopolist has an incentive to e伍ciently use inputs under this RoC regulation. You may use the expansion path derived in (b).

(f) How much output does the monopolist produce under this RoC regu- lation? Also, calculate the (allowed) proﬁt (πRoC ), consumer surplus (CSRoC ), and total surplus (TSRoC ). Compared to the answer in

(c), how much increase in total surplus does the island gain?

(g) The king further considers reducing the kRoC toward 0 so that the monopolist produces a quantity that falls into the inelastic portion of demand. As his trusted economic consultant, discuss if this plan would work or not (within 200 words).

4. Perfect Price Discrimination and Full Surplus Extraction

This continues from Tutorial I, the cigarette monopolization by Smokes- A-Lot on the island. The demand for cigarettes on the island is Q(p) = 20 ✁ 2P (and the inverse demand function is P (Q) = 10 ✁ Q). The mo- nopolistic cigarette supplier Smokes-A-Lot has the marginal cost MC = 2 and ﬁxed cost F = 7.5. So, the average cost function is AC FYI, the average cost function and the demand function intersect at (Q, P) = (15, 2.5). The units of variables are the same as previously deﬁned.

(a) Re-draw the ﬁgure of inverse demand, marginal cost and average cost functions.

(b) One day, the CEO of Smokes-A-Lot visits the used-book store on the island and ﬁnds a book, “Willingness To Pay: The Secret of Island Smokers ,” that precisely describes, by name, each and every island citizen’s willingness to pay for cigarettes (i.e. individual demand function). The CEO immediately buys the book (the book price is almost free) and decides to implement perfect price discrimination in the cigarette market with the information given in the book. Accord- ing to this amazing (and magical) book, the CEO sells the ﬁrst box of cigarettes at £10 to a buyer who has the highest willingness to pay on the island. Then, he sells the second box at slightly lower than £10 to a buyer who has the second highest willingness to pay. He continues to sell more cigarette boxes at incrementally lower prices (perfect price discrimination).

Under this perfect price discrimination, when will the CEO stop low- ering the price of another box of cigarettes? Does he stop selling at the average cost price or at the marginal cost price? State your economic insights (within 100 words).

Usually, the monopolist sets a single price for its products to maxi- mize its proﬁt (Law of Uniform Price). Contrarily, under the perfect information and under the perfect price discrimination, the monopo- list can set “many/numerous” prices to discriminate each consumer at each of his/her purchasing quantity. As a result, it is optimal to keep incrementally decreasing prices until the price is equal to the marginal cost, MC = 2. It is not proﬁt maximizing for the monopo- list to stop selling at the average cost (P = 2.5) as it can earn more proﬁt by selling products at prices above marginal cost and earn more proﬁt.

(c) How much proﬁt (πPPD ) does Smokes-A-Lot gain after this per- fect price discrimination? Also, how much is the consumer surplus (CSP PD ) and total surplus (TSP PD )? Is this result the ﬁrst-best or the second-best outcome?

The monopolist earns all surplus above the marginal cost with

T talSurplus = 2/1 . 8 . 16 - 7.5 = 56.5 (million pounds),

and this is the ﬁrst-best outcome.

(d) Does Smokes-A-Lot have incentive to minimize its cost under the perfect price discrimination? State your economic insight as a con- sultant (within 100 words).

(e) (Almost) Full Surplus Extraction: The king gets the idea to sell the monopoly right (exclusive right) of cigarette sales to Smokes-A- Lot to raise money. After purchasing this monopoly right, Smokes- A-Lot will be the o伍cial monopolistic cigarette supplier on the island with perfect price discrimination. The king asks you as an economic consultant to set the price on this monopoly right. What price would you suggest for this monopoly right? (Hint: What is the maximum amount of money the king can extract from Smokes-A-Lot without making the ﬁrm earn a zero or negative proﬁt?)

The king sets the monopoly right price inﬁnitesimally close to 56.5 million pounds. At this price Smokes-A-Lot can earn an inﬁnitesi- mally small proﬁt (that is higher than but close to zero proﬁt) and keep producing cigarettes. The king extracts the (inﬁnitesimally close to) full total surplus.

5. Monopolistic Firm's Proﬁt Maximization under Uncertainty

On the (ﬁctional) Econo Kingdom Island, there is one royal rugby team, Scrum Rummies, that is a member of the Caribbean international rugby league. It is well known that the performance of the team varies across seasons. The team has good performance with probability Pr(Good) = and bad performance with probability Pr(Bad) = . It is also known that the inverse demand for season tickets for the good performance season is P (Q) = 20 ✁ Q. (Note that the unit of price is in hundreds of pounds [i.e.$100] while that of quantity is in thousands [i.e. 1,000 season ticket]). Also, the demand for season tickets for the bad performance season is P (Q) = 10 ✁ Q. However, the island citizens, including the king, do not know the team’s performance before the season. Rugby is a major sport on the island, and the king’s agency, a for-proﬁt ﬁrm, sells the season tickets. For simplicity, there are no marginal or ﬁxed cost for selling tickets. Also, only season tickets are sold to the island citizens.

(a) If the island citizens and the king knew the team’s performance was going to be good, what would the king set the ticket price at to maximize proﬁt? Derive the proﬁt function, then solve for the proﬁt maximizing ticket quantity (QG ) and price (PG ). How much would the proﬁt (πG ) be?

(b) If the island citizens and the king knew the team’s performance was going to be bad, what would the king set the ticket price at to max- imize proﬁt? Derive the proﬁt function, then solve for the proﬁt maximizing ticket quantity (QB ) and price (PB ). How much would the proﬁt (πB ) be?

(c) In reality, the king does not know the team’s performance before the season, yet he needs to set a season ticket price. You, as a trusted economic consultant of the king, make a suggestion to the king to maximize the expected proﬁt. Derive the expected proﬁt function.

(d) Draw the proﬁt functions under good performance and bad perfor- mance. Also, draw the expected proﬁt function. (Note: The horizon- tal axis is the ticket sales quantity, and the vertical axis is [expected] proﬁts.)

(e) How much is the ticket price (PE ) that maximizes expected proﬁt? Is it higher or lower than the answers of (PG ) calculated in (a)? State your economic insights (within 50 words).