[SOLVED] Econ 323 Comprehensive Problem Set CPS B1 Matlab

Econ 323

Comprehensive Problem Set (CPS) [Optional]

This problem set will be made up of three blocks.  Block 2 and 3 will be filled in later in the semester.  This block corresponds to material before MT1.

The CPS is optional.  If a student elects to do it, it may replace one of the three midterm exams.  That is, the CPS can replace a low midterm score, or if a student has not taken one of the exams for some reason, it can fill in for the missing test.

As described in the syllabus and in class, the CPS is intended to be incrementally more challenging than the “standard” practice problems or exam problems we do routinely.  You can think of it as a “stretch” assignment. All questions will have a small novelty or two that the student needs to work out on their own. The problems should then seem harder than our “standard” work.

Block 1:  Answer 2 of the following 3 questions. 50 points per problem.

1. A Monopsony is the lesser-known sibling of a Monopoly.  While a Monopoly is a market with only one seller of a good, a Monopsony is a market with only one buyer of a good.  This leads to its own kind of market failure.  

[Some context if you are interested: Monopsony comes up most frequently in labor markets.  As an interesting example, professional sports leagues have many characteristics of Monopsonies.  The NFL is the pretty much the only elite league for professional football.  If you want to play pro football at a high level, the NFL is the only entity that will buy your services.  This gives the NFL market power over players, and probably limits the amount the league pays for player salaries, through features like “salary caps” and other restrictions.  [As an aside, I speculate that, since European soccer has many elite professional leagues, this probably leads to higher player salaries in soccer.  Kylian Mbappe, for example, recently had a contract that paid $121 million per year over two years (with signing bonus) for PSG.  Cristiano Ronaldo supposedly is being paid $220 million to play in the Saudi pro league, though his particular high salary is probably due to other factors.  Meanwhile, Dak Prescott in the NFL is the highest paid player at “only” $60 million per year,]

A company/factory town would be another example of a Monopsony.  If there is only one significant employer buying labor in a local area, that employer will have a unique type of market power over its employees. Fewer jobs with lower salaries will be the result in a Monopsony, as you will discover.]

The analysis for market failure with a Monopsony is similar to that of a Monopoly, with one key difference.  Your goal in this problem, if you attempt it, is to figure out how that works.  If you study the notes from our class on Monopoly, and try to apply our method to the Monopsony case, that will hopefully provide some hints on how to analyze this situation.  Now for the problem:

A market for a good is characterized as a Monopsony.  There are many sellers and a single buyer of the good, the “Monopsonist”.

The Supply curve is: P_S(Q)= 100+1.8Q

The Marginal Benefit to the Monopsonist from buying the good is P_B(Q)= 2000-1.4Q

a.) What is the efficient quantity and price of the good?

b.) What is the equilibrium quantity and price of the good?

c.) What is the Marginal Benefit to the Monopsonist at the equilibrium?

d.) What is the deadweight loss created by the Monopsonist?

2. Beekeeping for the purpose of making honey provides external benefits to farmers located near the beehives, as bees pollinate their plants and improve crop yields.  Bees also produce negative externalities.  Being stung by bees is unpleasant.  The more bees in a certain area, the more likely it is that people will be stung. In addition to hurting, some people have alergic reactions to stings and thus it can clearly be costly.  Suppose we have the following situation.

Marginal Benefit to Honey Consumers from an additional beehive: MPB=5000-75Q

Marginal External Benefit to neighboring farmers from an additional beehive: M_EB=1000+.2Q

Marginal Cost to Honey Producers of an additional beehive: M_PC=500+5Q

Marginal External Cost to neighbors from additional beehives: M_EC=0+.1Q

a.) Find the market equilibrium Quantity and Price of hives.

b.) What is the M_SB at the Market equilibrium? M_SC?

c.) What is the socially optimal (Efficient) level for this society?

d.) What is the Deadweight loss at the Market equilibrium?

e.) What is the tax/subsidy that will lead to a new Market equilibrium at the Optimal quantity?

3. Suppose the government wishes to reduce the amount of methane gas, a waste product created from refining petroleum.  Suppose the marginal benefit to society from reducing (abating) methane from the current levels is constant at $6000 per gigaton.

Abatement levels will be on the x-axis and Costs on the y-axis.

Assume that there are four producers, named 1, 2,.3, 4.

The marginal abatement costs are:

Producer 1: M_AC,1 =.3A₁.

Producer 2: M_AC,2= .5A₂.

Producer 3: M_AC,3= .6A₃

Producer 4: M_AC,4= (1/3)A₄

The total amount that is ultimately abated is A=A₁+A₂ +A₃+A₄

a.) The Marginal Abatement Cost (MAC) for the whole market is the horizontal sum of the individual producers’ marginal abatement costs.  What is the market-wide MAC as a function of A? [Note, the coefficient on producer 4 is 1/3, which will give a beautiful clean answer in the end.  If you round 1/3 to .333 or something be aware that it will be slightly off, but you can probably guess what the number is suppose to be.]

b.) Given the answer to 1, what is the socially optimal level of methane abatement?

Prior to any abatement, Producer 1 produced 9000 gigatons of methane, Producer 2 produced 10000 gigatons, Producer 3 12000 gigatons,  Producer 4 produced 11000 gigatons.  The total methane is thus 42000 gigatons.

c.) The government wishes to use permits to achieve the optimal abatement.  Each permit will allow the owner to produce 1 gigaton of methane. How many permits must the government issue to achieve the optimal abatement level?

d.) If the permits were not tradeable, how much must each firm abate, and what are the Marginal abatement costs for each firm when they reduce their pollution to the permitted level?

e.) If the firms can buy/sell their permits with one another, how much abatement does each firm do in the equilibrium?