Economics $333$: Problem Set $2$

Winter $2024$

Please write neatly or type your answers to the following questions. Answers that cannot be read

may lose points. This assignment is due on Sunday, February $4$ at $11$:$59$pm$.$ Please upload your

single pdf or doc file on Canvas. No late submission is accepted. A full solution key will be

provided after the due date.

Consider a factory that gains a benefit from being able to generate pollution and a

nearby farmer that suffers costs because of that pollution. Suppose that the marginal

benefits to the factory and the marginal costs to the farmer are given by:

Factory: $MB=500-5Q$

Farmer: $MC=200+10Q$

a$.$ Solve for the optimal level of pollution that maximizes net social benefits. Show

mathematically and graphically. $(4$ points$)$

b$.$ If the farmer owns the property rights, how much will the factory pay for the

right to pollute? Show mathematically and graphically. $(4$ points$)$

c$.$ Calculate the net benefits for the farmer. Please show your work. Show

mathematically and graphically. $(4$ points$)$

d$.$ Calculate the net benefits for the factory. Please show your work. Show

mathematically and graphically. $(4$ points$)$

e$.$ Suppose that instead of one farmer, there is a larger neighborhood affected by

the factory's pollution. Explain the implications this has for Coasian bargaining.

$(2$ points$).$

Note: Graphical work for parts a$-$d may easily be shown on the same graph.