Problem Set 4

**Due 3/17/96 In Class--NO EXCEPTIONS!**

Theory

Nicholson Problems 6.1, 6.8, 7.4, 7.10.

Hint for problem 6.8: "Homogeneous" is defined in the glossary. There are several ways to attack part (a), but perhaps the most direct is to argue directly from the first order conditions for expenditure minimization. It is easy to see why it must hold in the two good case by simply drawing a graph.

Hint for 7.4 (c): you don't necessarily need to use the Slutsky equation here.

Applications

1. Suppose that one economist wishes to study the effects of abortion restrictions on the abortion rate, that is, the number of abortions as a percentage of the number of pregnancies. The economist finds that restrictions on medicaid funding and increases in the average distance to an abortion clinic both decrease the abortion rate for counties in the United States. You then present this economist with Figure VI of Kane and Staiger's article (discussed on pp. 76-77 of the reader).

(a) Interpret Figure VI. What is the estimated effect of a decrease in the average distance to a clinic on the teenage birth rate (that is, the number of births as a percentage of the number of teenagers?)

(b) There might seem to be an inconsistency between these two findings. Carefully describe a theoretical model of decision-making by teenagers which produces both predictions.

2. Kane and Staiger wish to study how changes in abortion access affect birth rates. They examine the effects of changes in regulations in different counties over time. They are thus able to look at the average (over counties) change in birth rates. In several places in their article, Kane and Staiger argue that it is important to observe changes in birth rates over time in a given county, rather than the following alternative: simply look "cross-sectionally" at different counties at a single point in time, and compute the correlation between restrictions and birth rates. We are interested in whether or not a finding of a negative correlation between restrictions and birth rates is evidence that restrictions on abortions cause a decrease in birth rates.

(a) Explain why such cross-sectional studies might in general produce misleading results. Provide a specific example of a scenario where you would not be able to interpret a negative correlation between abortion restrictions and birth rates as evidence that such restrictions reduce birth rates. Explain precisely what could cause the negative correlation in your example.

(b) Are there any assumptions (about the way restrictions are determined) under which you could interpret the negative correlation as evidence of causality?

3. Consider the Phelps' article.

(a) What is the "formula" used to determine the optimal tax in the Phelps article (what two quantities are set equal)?

(b) Before you looked at the article, how much would you have thought the risk of death would change as a result of driving after consuming no drinks versus 3-5? According to the article, what are the actual numbers?

(c) Consider a model of sequential decision-making about drinking, so that youths decide on the next drink only after having consumed the last one. How much, and in what direction, do you believe this would affect the estimate of the elasticity of demand of beer? Explain how this assumption would (qualitatively) change the analysis of the optimal tax on alcohol.