   # Problem Set

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Problem Set #2
The US College Enrollment and the “Third Law of Demand” A theorem proposed by Professors Alchian and Allen in their text, University Economics (1964) has had several rebirths of interest in the literature. The so-called “third law of demand,” or “relative price theorem,” holds that a fixed cost added to a good of varying quality causes the consumer to prefer the category considered of higher quality to the lower.
Recently a number of studies, keeping this theorem in mind have looked into a relationship between the ratio of public to private enrollment and unemployment in cross-sectional as well as in time series data. Part of the full cost of participating in higher education is foregone employment income. In their regression model, these studies have regressed the public/private ENROLLMENT RATIO (as an indicator of relevant demand) against UNEMPLOYMENT RATES (as an indicator of cost) as well as a number of variables designed to account for “other things” which tend to vary at the same time, such as income, financial aid and tuition ratios. Tuition ratio is typically specified as the ratio of the full cost (including forgone employment income) of public higher education (Pa) to private higher education (Pb), where Pa is less than Pb.
In Table 1, below, a cross-sectional model reveals the relationships between relative education demands by public and private university students (as measured by state level ENROLLMENT RATIO) and education price (as measured by the state level UNEMPLOYMENT RATE). The data source permits the introduction of a number of relevant ceteris pariabus variables, such as INCOME, FINANCIAL AID and TUITION RATIO and POPULATION.

Table 1
Dependent Variable: Enrollment Ratio
(t values in Parentheses)
State Level Data

Repressors Coefficient Estimates
CONSTANT -0.5905
-(0.135)
UNEMPLOYMENT 7.0689**
(3.264)
UNEMPLOYMENT SQUARED -1.4551*
-(2.584)
INCOME 0.1146
(0.2318)

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