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ECON 2001 Assignment 2

2022

1 G o ve r n m e n t I n t e r ve n t i on on M onopo l y

Gasfrom(a counterfactual ﬁrm) is a monopolist in the Liqueﬁed Natural Gas(LNG) market in Freezeland. Freezeland government is worried about overly strong market power Gasfrom has. In order to ﬁx the problem, the minister orders you to compare diﬀerent government policies.

Before making a comparison, you found out that the true demand for LNG in Freezeland is P = 26 - qd and supply (or marginal cost) of production is P = 2 + 2qs . Based on this results, answer the following questions. (5 point for each, total 30 points)

1 . 1 E qu ili b r i u m

Derive the equilibrium price and quantity. After then, compute consumer, producer, and total surplus in equilibrium.

1 . 2 M onopo li s t i c ou t c o m e

Based on the demand function, the computed marginal revenue of the monpolist is P = 26 - 2qd . Find out the proﬁt maximizing quantity and price of the monopolist. After then, compute consumer surplus, producer surplus, and deadweight loss.

1 . 3 P r i ce F l oo r

Government thinks that setting price ﬂoor cannot be eﬀective since Gasfrom is making too huge proﬁts. Compute Gasfrom’s proﬁt if government sets (ﬁxed) price ﬂoor to Pf = 19 and explain why the price ﬂoor cannot ﬁx the problem.

1 . 4 P r i ce C e ili ng

Government can implement the price ceiling the price ceiling to beneﬁt the consumers. Compute consumer surplus, proﬁt, and deadweight loss with price ceiling of 19. Do consumers, monopo- list, and society as a whole beneﬁts with the policy (compared to monopoly)? Explain based on computed surpluses.

1 . 5 T ax

Government thinks that the problem would be abated by penalizing monopolist on generating too high proﬁt. Suppose government adds tax of 2 for each unit of production to Gasfrom, leading to the increase in supply function to P = 4 + 2qs . What would be collected tax revenue and changed consumer/producer surplus? How the deadweight loss would change?

1 . 6 Subs i dy

Government thinks that the real problem is underprovision of goods. To encourage the supply, government now provides a subsidy of 2 to all purchasing buyers, thus making market demand P = 28 - qd and marginal revenue P = 28 - 2qd . Compute a new monopolistic outcome price and quantity. After then, compute consumer and producer surplus, the amount of subsidy.

2 E x t e r n a li t y

Two cities, Upcity and Downton, are individually located at upstream and downstream of the Ohio River. Citizens in Upcity make their living on ﬁsh-farming or dyeing. The demand and supply information to each market is the following:

Fish-farming Upcity operates multiple ﬁsh-farms for Salmon and ﬁrms in UpCity are perfectly competitive. The market demand for Salmon is P = 200 - 0.1 * qd in dollar price and in ton quantity unit. The market supply for Salmon is P = 120 + 0.9 * qs .

Dyeing Upcity also operates multiple and perfectly competitive Dyeing yards. The market demand for dyed cloths is P = 200 - 0.1 * qd and and supply is P = 10 + 0.4 * qs . Dollar is a price unit and pounds cubic feet are quantity unit for demand and supply.

Using the above information, answer the following questions. (10 points for each, 40 points in total)

2 . 1 P o s i t i ve E x t e r n a li t y

Fish farms in Upcity feed their ﬁsh on the river, which also feeds Trouts caught by ﬁshers in Downton. In that sense, amount of feeds provides a positive externality to Downton by 50$ per ton of raising their ﬁsh. What would be the equilibrium price and quantity in the Salmon market? What would be the socially optimal price and quantity of Salmon if the positive externality to Downton is accounted for?

2 . 2 N e g a t i ve E x t e r n a li t y

Dyeing in Upcity contaminates the river thus reduces the amount of Trouts caught by ﬁshers in Downton. More precisely, each production of dyed cloth(in cubic inch units) provides negative externality to Downton by 100$. What would be the equilibrium price and quantity in the dying industry in Upcity? What would be the optimal price and quantity if negative externality to Downton is accounted for?

From question (2.3), consider only the impact of dyeing industry.

2 . 3 P i gou v i a n T ax

An Ohio government thinks that, due to the externality, Upcity is over/under-producing compared to the optimal quantity of dyed cloths. Thus, the state government of Ohio investigates the situation and (misleadingly) overestimate the negative externality to be 150$ per ton production of dyed cloth and levies the environmental tax as much as negative externality. What would be the new equilibrium outcome? In new outcome, would total surplus increase or decrease (compared to the equilibrium in 2.2)?

2 . 4 C oase Theo r e m

Instead of ﬁxing the problem, the Ohio government invites the mayors of two cities and asks them to negotiate on the compensation on contamination occurred by dyeing cloths. What would be per unit compensation from Upcity to Downton? Accounting for compensation, how much dyed clothes would be produced? Would this outcome improve the total surplus compared to the tax policy in (2.3)?

	N o t E n t e r	E n t e r
N o t E n t e r	0 / 0	0 / 4
E n t e r	4 / 0	- 2 / - 2

Table 1: Entry Game

	Le ft	R i gh t
Le ft	2 / 3	2 / 2
R i gh t	2 / 2	3 / 2

Table 2: Bargaining

3 Sho r t A n s w e rs

Answer the following mini-questions. While writing down your answers, provide a d e t a il e d ex - p l ana t i on supporting your answer (”detailed” here means the level that a person who knows the concept but did not hear anything about the question can fully agree on your conclusion). If you just write down the answer, 0 point would be assigned. (5 points each, total 30 points)

3 . 1 G a m e 1 - E n t r y G a m e

There are two players, A(chooses the row) and B(chooses the column) in the game. Players are doing strategic game of entering the market or not. Each ﬁrm’s payoﬀ for each outcome are written in the (3.1) in the order of ﬁrm A’s/B’s proﬁt. Find out Best Responses of agent A and B and Nash Equilibrium. After then, consider an another game that increase monopolistic proﬁt from 4 to 6, i.e. payoﬀ of A if A enters but B does not enter. Would there be any change in equilibrium?

3 . 2 G a m e 2 - B a r g a i n i ng

There are two players, A(chooses the row) and B(chooses the column in the game. Players are doing strategic game of building houses on each side. Each player prefers the other player to build house on the side they prefer, A on the right and B on the left. The exact payoﬀ are written in the (3.2). Find out each player’s best response and all Nash Equilibria. What is the diﬀerence on the equilibrium outcome with the Bargaining model in the lecture note? (Hint: If payoﬀs between choices are the same, assume that all of them are best responses.)

3 . 3 E x p ec t e d U t ili t y I

Elon is a graduating student at UPenn and has a utility function u(x) = ,x based on his monthly income x thousand in dollars. He is weighing over two career paths, opening a new business and entering the government. Opening a new business is risky, having 1.5 percent of success and 98.5 percent of failure. If the business becomes successful he expects to earn 2.56 billion dollar per year or earn nothing. If he works in the government, he would gain 25,000$ per year. Compute expected utility for each of two options. Also, explain which career path he would take.

3 . 4 E xp ec t e d U t ili t y II

With the above example, suppose that Elon refused to join the government. Instead, assume that Elon got an oﬀer from the start-up which has 50 percent of success and 50 percent of failure. If the ﬁrms becomes successful, the startup will compensate him by y dollars and 0 if the ﬁrm fails. In this case, how big y should be for Elon to accept the job oﬀer? More precisely, compute the value y which makes the job oﬀer which gives the same expected payoﬀ with opening the business.

3 . 5 A dve r se S e l ec t i on

Suppose there are two potential types of driver, safe (S) or risky (R). Insurance company believes that it is equally possible to meet safe or risky driver, but does not know exactly which type of driver has visited. Safe type has valuation of 30$ for the insurance contract and risky type has valuation of 70$ for the insurance contract. Insurance company’s expected cost of providing insurance is 40$. Assume that the insurance company is a monopolist, thus it oﬀers the premium as much as an expected valuation of the agent. What is the premium that the insurance company would oﬀer? With that insurance premium, would both safe and risky type agent accept the contract?

3 . 6 M o r a l H a z a r d

An insurance company and an agent signed for the insurance contract of reducing the hospital cost from 10 to 6. A demand for the agent for the hospital service is P = 12 - qd . Find out 1) quantity demanded for the agent before and after the insurance contract, 2) Consumer surplus before and after the contract, and 3) the monetary amount that the insurance company has to pay to cover the medical cost. Assuming that 3) is the premium that the agent has to pay when she signs for the contract, argue whether she would like to sign for the contract.