Problem Set- Econ Intermediate Microeconomics

1. Suppose that your neighbor owns an old tree, with branches that extend over yourlawn. He enjoys having the tree, getting utility of $100, and incurring $65 ofcleanup costs on his own lawn. However, the tree drops leaves and crabapples onyour lawn, which cost you $40 to clean up. The cost of having the tree removedwould be $20.

a. What is the efficient outcome? (Should the tree be taken down or not? Comparethe social net utility of leaving the tree up vs. taking it down.)

b. Suppose the law stated that your neighbor was liable for damages (orequivalently, that you have the right to have the tree taken down). Also, assumenegotiating is costless for both you and your neighbor. What would the actualoutcome be? (Is a compensatory payment paid? From whom to who? How muchis it? Is the tree taken down?)

c. Suppose the law stated that your neighbor was not liable for damages. Also,assume negotiating is costless for both you and your neighbor. What would theactual outcome be?

d. Now, suppose that another option is to build a fence for $15. The fence wouldprevent any leaves from falling on your lawn, saving you $40, but would alsoincrease your neighbor's cleanup costs by $30. Either person can build the fenceof his own accord, regardless of the liability law. Repeat parts a - c.

e. Now, suppose that entering negotiations would cost $200 to both people. What would the actual outcome be in each legal regime? (Remember that either personcan choose to build the fence.)

Note: You may want to fill out a table like the ones in the textbook, once for partsb & c, once for part d, and once for part e.

2. Suppose a monopoly firm with the long run total cost function LRTC(Q) = 1/30Q^3-1/2Q^2+4Q faces a market demand curve P(Q)=4-1/30Q^2.

a. Find the firm's LRMC, LRAC, and MR as functions of Q. (Use a graphingcalculator, Grapher, Wolfram Alpha, etc. to verify your equations match thegraph.)

b. What is the firm's profit-maximizing output, Q∗? Mark it on the horizontal axison the graph.

c. What price will the firm charge? Mark it on the vertical axis on the graph.

d. Calculate the firm's profit, and shade in the rectangle with area representing thefirm's profit on the graph. (Hint: π(Q∗)= TR-TC= P(Q∗)Q∗- SRTC(Q∗)=(P(Q∗)-ATC(Q∗))*Q∗ so you want the rectangle of height P(Q∗)-ATC(Q∗) and width Q∗. You should also estimate the area of the rectangle to check yourwork.)

e. Does this outcome result in deadweight loss? Shade in the area of the graphrepresenting it. You do not have to calculate it.

f. Suppose other investors observe this firm's abnormal profit and decide to enterthe industry. Also, suppose the new firm has the same production function as thisone. Will the profits of the 2 firms be positive, zero, or negative? (There aremultiple ways to approach this problem, you can assume it is a perfectlycompetitive market, or assume the firms will collude to maximize the sum of theirprofits, or apply one of the duopoly models.)

g. What term do we have to describe a situation like this? (There is more than onecorrect answer.

h. Propose a government policy that will result in greater total surplus than themonopoly outcome.

3. Suppose a firm in a monopolistically competitive industry has the following coststructure. (For the purposes of this problem, we will ignore the short-run / longrundistinction. If you want something more concrete, we are assuming that thefirm can change its level of capital more quickly than new firms can start up. Foreach part, use the graph to estimate Q∗ and P∗. Do not try to find equations forany of the curves. Round each answer to the nearest whole number.)

a. Suppose the Demand curve facing this firm (the "dd" curve in the textbook) and its MR curve are as shown in Graph I. What is the firm's profit-maximizingoutput, Q∗? Mark it on the horizontal axis on the graph.

b. What price will the firm charge? Mark it on the vertical axis on the graph.

c. Is the firm's profit positive, negative, or zero? Shade in the rectangle with arearepresenting the firm's profit on the graph. (Hint: π(Q∗)= TR-TC= P(Q∗)Q∗- SRTC(Q∗)=(P(Q∗)-ATC(Q∗))*Q∗ so you want the rectangle of height P(Q∗)-ATC(Q∗) and width Q∗. You should also estimate the area of therectangle to check your work.)

d. Will there be a tendency for firms to enter this industry? Go out of business?Neither?

e. Does this outcome result in deadweight loss? Shade in the area of the graphrepresenting it. You do not have to calculate it.

f. Repeat parts a-e for Graphs II & III. (Only the Demand curves, and as a result, the MR curves, change each time.)

Graph I

Graph II

Graph III

4. Efficiency in a single industry can be described as there being no "forgoneopportunities for trade," or deadweight loss. What this means is that the sum ofconsumer & producer surplus is maximized. This means that we want P*x =MC(Q∗), otherwise, there are units for which people are willing to pay more thanthe marginal cost, but they are not produced. For each of the following models,show graphically or explain why P*x=MC(Q∗) or P*x ≠MC(Q∗).

a. Perfect competition (short-run)
b. Perfect competition (long-run equilibrium)
c. Monopoly
d. Monopolistic Competition (short-run)
e. Monopolistic Competition (long-run equilibrium)
f. Bertrand Duopoly
g. Stackelber
g Duopoly
h. Cournot Duopoly
i. Externality (and zero transaction costs)
j. Externality (and high transaction costs)
k. Use of a public resource (commons)