代做Economics of Business 2 Spring 2024 Tutorial III帮做R程序

Economics of Business 2

Spring 2024

Tutorial III

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

Read the following materials and answer the questions:

Problem 1*: Lecture Note 4, Train Ch.4

Goal - Understanding the Ramsey Prices: Linear Independent Demands Problem 2**: Lecture Note 4, Train Ch. 4

Goal - Understanding the Ramsey prices with positive marginal costs Problem 3**: Lecture Note 5, Train Ch. 5

Goal - Understanding the Vogelsang-Finsinger Mechanism

Problem 4*: Lecture Note 6, Train Ch. 6 (Specifically, Section 6.2)

Goal - Understanding the Loeb-Magat Mechanism

Problem 5**: Lecture Note 6, Train Ch. 6 (Specifically, Section 6.3) Goal - Understanding the Sappington-Sibley Mechanism

* Answers are provided in Tutorials.

** Online answers are provided.

Office 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, office 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. Ramsey Prices with Linear Independent Linear Demands

On the (fictional) Econo Kingdom Island, gas markets are monopolized by only one gas supplier, WhattaGas, that supplies gas to the island citizens. On the island, there are only two types of gas buyers: (H) Household buy- ers that have the demand function QH   = 1 ✁ sH  . PH , and (B) Business buyers that have the demand function QB   = 1 ✁ sB  . PB   where sH   = 1 and sB   = .   See the footnote.    It turns out that the island has in- exhaustible natural gas resources from the underlying volcano, and the marginal cost of gas production is zero (MC = 0). However,  WhattaGas incurs the fixed cost of F = 0.48 (unit is in hundreds of millions of pounds [i.e.  $100,000,000]) for the maintenance of island-wide gas pipeline sys- tem. Currently, WhattaGas  charges monopolistic prices in each market. To avoid explosive gas prices, the king has asked you to investigate the introduction of the Ramsey Prices so that they maximize the total surplus without a negative profit.

(a) Draw the two figures of inverse demand functions, one for Household buyers (H) and the other for Business buyers (H). Separate the elastic and inelastic portions of demand for each buyers. At PH  = PB  = , which market has higher elasticity? (i.e. which market is more price sensitive?)

(b) Calculate the (unregulated) monopolistic prices (PH(M)  and PB(M)) and quantities (QH(M)  and QB(M)) for each market.

(c) If the king enforces WhattaGas to charge P = MC (first-best price) in each market, how much will the sales quantities in each marekt

(QH(F)B  and QB(F)B ) be?

(d) By using the demand functions, show that consumer surplus is CSi  =

.s(Q) where i  ∈ {H, B}.   Then, by using the results in (b) and

(c), calculate aggregate consumer surpluses under monopolistic prices

CSM  = CSH(M) + CSB(M) and under first-best prices CSFB  = CSH(F B) +

CSB(F B) .

(e) The aggregate consumer surplus/welfare is defined by CS = CSH (QH )+ CSB (QB ).  An isowelfare contour is a combination of QH   and QB

that gives the same level of CS. Graph five diferent levels of isowel- fare contours on the Q1-Q2  plane.