Type Ia supernovae are important cosmological distance indicators. Each of these bright supernovae supposedly results from the thermonuclear explosion of a white dwarf star that, after accreting material from a companion star, exceeds some mass limit, but the true nature of the progenitor star system remains controversial. Here we report the spectroscopic detection of circumstellar material in a normal type Ia supernova explosion. The expansion velocities, densities, and dimensions of the circumstellar envelope indicate that this material was ejected from the progenitor system. In particular, the relatively low expansion velocities suggest that the white dwarf was accreting material from a companion star that was in the red-giant phase at the time of the explosion.

This paper applies revealed preference theory to the nonparametric statistical analysis of consumer demand. Knowledge of expansion paths is shown to improve the power of nonparametric tests of revealed preference. The tightest bounds on indifference surfaces and welfare measures are derived using an algorithm for which revealed preference conditions are shown to guarantee convergence. Nonparametric Engel curves are used to estimate expansion paths and provide a stochastic structure within which to examine the consistency of household level data and revealed preference theory. An application is made to a long time series of repeated cross-sections from the Family Expenditure Survey for Britain. The consistency of these data with revealed preference theory is examined. For periods of consistency with revealed preference, tight bounds are placed on true cost of living indices.