One focus of the usual classroom discussion of consumer theory is the demonstration that the individual consumer's reaction to a change in the market price of a commodity can be usefully broken down into vectors of substitution effects and income effects. The Slutskv equation relating the price effect to the substitution and income effects can be simply nmotivated by J. R. Hicks' graphical presentation, p. 31, but the usual proof (see Paul Samuelson) is very tedious and nonintuitive. If the instructor includes a discussion of the expenditure function in his curriculum, however, he has available a concise, intuitively appealing proof of the Slutsky equation. 1 Suppose a consumer with income y faces a vector of commoditv prices p. His Marshallian demand curve for commodity j is given by xj = Dj(y, p). The minimum expenditure necessary for the consumer to achieve any utility level u is given by his expenditure function, y = m(u, p) (here y is in units of the jth good). His Hicksian income-compensated demand for commodity j is represented xj= hi(u, p); if m is differentiable, we have the well-known result that

Irreplaceable commodities, 144.—Insuring irreplaceable commodities, 148.—The value of collective protection, 151.—Appendix, 155.

The Net Effect of an Alcohol Tax Increase on Death Rates in Middle Age by Philip J. Cook, Jan Ostermann and Frank A. Sloan. Published in volume 95, issue 2, pages 278-281 of American Economic Review, May 2005

Improving academic outcomes for economically disadvantaged students has proven challenging, particularly for children at older ages. We present two large-scale randomized controlled trials of a high-dosage tutoring program delivered to secondary school students in Chicago. One innovation is to use paraprofessional tutors to hold down cost, thereby increasing scalability. Participating in math tutoring increases math test scores by 0.18 to 0.40 standard deviations, and increases math and nonmath course grades. These effects persist into future years. The data are consistent with increased personalization of instruction as a mechanism. The benefit-cost ratio is comparable to many successful early childhood programs. (JEL H75, I21, I24, I26, I32, J13, J15)