economics questions

Final Exam Preparation, Public Economics

David Benjamin

December 7, 2015

1. One question each from the final two clusters and a selection of:

2. Let Joe and Mojo have preferences a0.5i b 0.5 i . Assume each agent has an

equal endowment of ale and bread of five units.

(a) Calculate Joe’s excess demand as a function of the price of ale.

(b) Compute the equilibrium by setting setting the excess demand functions equal to zero. Could you have taken a short cut?

(c) Compute Joe’s equilibrium Marginal Rate of Substitution.

(d) What happens to the equilibrium if Joe has instead 15 units of ale?

3. Assume a firm can generate 5q1 units of profit for each unit of output

q1. Assume that each unit of production produces q21 5

units of pollution. Suppose the firm is endowed with one emission permit and can purchase additional permits at price p.

(a) Find the demand for permits as a function of p. What is the corresponding output level?

(b) Assume a second firm whose permit excess demand is 1−p. What is the equilibrium permit price?

4. Describe an environment in which permit trading can contribute to eco- nomic efficiency. How do permits make such a contribution? Why in a traditional model are permits and Pigouvian taxes considered equiva- lent in implementation? Give a reason that in practice they may not be.

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5. Assume a static common resource problem with benefits from fishing equal to y(s, b) = (s. ∗ b)0.5 and cost of fishing equal to 5b.

(a) What is the unregulated outcome of this economy? Explain through a graph and an argument why this is the case.

(b) What is the Pareto Optimal quantity. Can you show it on the same graph? What is the welfare gain?

6. Suppose a permit case like in textbook with m1 > m2 and the cost of reducing emissions equal to m1

2 e2. Suppose also that the firms must

borrow to pay for permits at firm specific interest rates r1 and r2. Give a condition for the benefits to pollution reduction to entirely disappear.

7. Suppose the government does not know the level of the marginal dam- ages, but that the neighbors themselves can effectively petition the government to impose a Pigouvian tax of any size after a failed nego- tiation. What will the set of outcomes of these negotiations include? Lets say the government wanted to implement the efficient quantity but with this feedback mechanism, how might the government implement a reporting scheme (with possible fines on both sides) to insure an effi- cient outcome if the original model does not. What if the government has access to a costly auditing technology?

8. Assume a Total damage function of D = 3q2, a demand function con- stant with price 200 and a supply function of TC = 4q3 + q + 4.

Find the equilibrium quantity and set of possible transfers both with and without negotiations and with property rights that either belong to the firm or the neighbors. What is the Pigouvian tax that would have produced the same outcome in terms of quantity?

9. Show through a graph how a tax on a second good can increase welfare. What are the policy implications of this result? How does it apply to capital taxation?

10. From a policy point of view, does the evidence in Adults Adrift support a screening or or human capital model of education. How would the answer to this question affect any policy prescriptions you have? If schools are not sufficiently endowing human capital to their students, is there an identifiable externality that is responsible for this?

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11. Assume UG = z 0.333x0.667g . Assume George is endowed with 10 units of

the private good which he can convert to public goods at a one for one ratio.

(a) Take the other agents donations of private goods to be converted to public goods as given and equal to zero. Write down George’s utility as a function of his donation.

(b) How much of the private good will George donate in equilibrium.

12. Describe the procedure necessary to solve for an equilibrium analyti- cally. Show how this translates in an economy with an Edgeworth box. If you have a demand curve as part of your solution method you should explain how it is derived from consumer and/or firm maximization.

13. Explain graphically the difference between the the equilibrium in a dynamic unregulated common’s problem and one controlled by either myopic or farsighted regulation.

14. What does it mean for a good to be non-excludable? In theory one may worry that such a problem could completely shut down private markets. How did we deal with that in designing a private environment for the public goods case so that this doesn’t happen? How and why did we use game theory in this design?

15. Explain how permits can improve economic efficiency over a policy of one-size-fit all regulations. Be sure to define efficiency for this environ- ment.

16. Traditionally we look at the distribution of consumption as a fairness concern, not an efficiency concern. Why is that the case? Is there a perspective from which income distribution looks like a public good? [Hint: the book offers one and public discourse offers a second.] Why can education be considered a public good?

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