ECON 4465
Public Economics — Problem Set #1
Due: September 25th at 2:40pm (submit through the courseworks)
1. Consider a reform that changed welfare benefits in New Jersey and suppose that at the same time there was only a normal inflation adjustment to benefits in New York (note: even though there was no reform in NY, that does not mean that nothing in New York has changed — for example, the composition of the group of welfare recipients may have changed over time). The data for welfare recipients (per month) in the two states looks as follows:
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New Jersey
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New York
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|
Average hours of work
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Average benefit
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Average hours of work
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Average benefit
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|
Before the reform
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45
|
1000
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55
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1000
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|
After the reform
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55
|
600
|
60
|
1100
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(a) Explain what assumption(s) you need to make to rely on this data in order to estimate the effect of the reform.
(b) What is the difference-in-difference estimate of the effect of the reform on hours of work of welfare recipients?
(c) What is the corresponding estimate on the effect on welfare benefits?
(d) What is the implied elasticity of hours of work to the level of welfare benefits (ie., percentage change in hours of work per a one percent change in the level of benefits)? Note: the previous parts tell you what changes are, but the elasticity has to be evaluated at some reference point. It is obvious what the initial point is when one evaluates the elasticity theoretically — that’s where you take the derivative — but with real–life data one could use a lot of different points — before or after the reform, in New Jersey or New York or anything in between. One common choice is to take the mid–point between before and after reform values for the treated group.
2. The demand for smartphones is given by D(p) = 400 — p + 5/pT, where p is the price of a smartphone and pT is the price of a tablet (a substitute for smartphones). The supply is given by S(p) = 4 · p. The price of tablets is fixed and set at pT = 500.
Suppose that the government imposes two taxes on phones: a $20 tax to be paid by the consumers and $80 tax that producers have to pay.
(a) What is the economic incidence of this policy?
(b) What is the excess burden here?
(c) How would economic incidence change if government imposed instead a $80 tax on consumers and a $20 tax on producers
(d) Imagine that the tax on producers increases to $130, while the tax on consumers remains unchanged at $20. How does the excess burden change? Divide the change in excess burden into components coming from the surplus of each of the parties involved (demand, supply, government).
(e) Which component of the change in excess burden is the largest? Explain why.
3. The demand for food purchased in grocery stores is given by DG = 100 — PG + 2/1PT where PG is the price (index) of food in supermarkets and PT is the price of take-outs. Correspondingly, the demand for take-outs is DT = 100 — PT + 2/1PG . The supply functions are given by SG = 2/1PG and ST = 2/1PT respectively. The government imposes a tax of 40 on take-out food. Determine how the incidence of this tax is split between consumers and producers of the two types of food. Note: you have to find prices for both goods that yield an equilibrium in both markets simultaneously.
4. Suppose that the marginal private cost of providing higher education for n students is given by MPC(n) = n and that the marginal private benefit schedule is given by MPB(n) = 200 — n (ie, benefits decline with the number of students, presumably because additional students are less qualified and derive lower return from being educated). Imagine though that people with college education are more likely to vote and volunteer. Assume (on faith) that these behaviors benefit everyone. The additional social benefit from these activities is valued at
20 per person with college education.
(a) Plot a graph showing private marginal benefit, private marginal cost and social marginal benefit.
(b) Find the price and quantity that correspond to the private competitive equilibrium (i.e., with no intervention of any kind).
(c) Find the socially efficient quantity and the deadweight loss from being at the private competitive equilibrium instead.
(d) What value of a monetary subsidy to education would implement the efficient solution?
5. There are 4 firms in the industry that have the total costs of eliminating pollution given by P2 /4, P2 /3, P2 /2 and P2 respectively.
(a) Suppose that we want to reduce aggregate pollution in a way that minimizes the overall cost. Derive the marginal cost of doing so as a function of the overall reduction in pollution P*
(b) Suppose we want to reduce the overall pollution by 100 units. How much should each of the firms reduce pollution by in order to minimize the overall cost of doing so?
(c) Suppose that we require each firm to reduce pollution by 30 units. Firms are allowed to trade obligations to lower their pollution reduction requirements. What will be the competitive market price of a unit of pollution reduction and how many units will be traded?
(d) Suppose we do not allow firms to trade in part (c). What would be the deadweight loss compared to the solution in part (c)