License auctions with exit (and entry) options: Alternative remedies for the exposure problem

Inspired by some spectrum auctions, we consider a stylized license auction with incumbents and one entrant. Whereas the entrant values only the bundle of several units (synergy), incumbents are subject to non-increasing demand. The seller proactively encourages entry and restricts incumbent bidders. In this framework, an English clock auction gives rise to an exposure problem that distorts efficiency and impairs revenue. We consider three remedies: a (constrained) Vickrey package auction, an English clock auction with exit option that allows the entrant to annul his bid, and an English clock auction with exit and entry option that lifts the bidding restriction if entry failed

Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals

We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and sub-Gaussian estimates for the heat operator, and the other using the analytic theory for p.c.f. fractals and a fixed point argument. The heat semigroup (probabilistic) method is applicable to a more general class of metric measure spaces with Laplacian, including certain infinitely ramified fractals, however the cut off technique involves some loss in smoothness. From the analytic approach we establish a Borel theorem for p.c.f. fractals, showing that to any prescribed jet at a junction point there is a smooth function with that jet. As a consequence we prove that on p.c.f. fractals smooth functions may be cut off with no loss of smoothness, and thus can be smoothly decomposed subordinate to an open cover. The latter result provides a replacement for classical partition of unity arguments in the p.c.f. fractal setting.Comment: 26 pages. May differ slightly from published (refereed) versio

The Poverty of Wealth and Income in the United States

An alternative poverty rate was calculated using poverty thresholds from the U.S. Census Bureau to assess income poverty and a similar set of thresholds at four months’ of the poverty threshold for annual income to assess wealth (i.e. net worth) poverty. Using point estimates derived from the multiple imputations of the Survey of Consumer Finances (SCF) between the years of 1989 and 2007, the findings revealed the percentage of households in poverty by both measures was 6% in 2007 compared to 11.1% of households experiencing poverty of income only and 22.4% experiencing a poverty of at least one of the measures. The author assessed the demographics of the households experiencing poverty of both income and wealth and found a larger racial gap for African Americans and Hispanics than income poverty alone, support for the lifecycle hypothesis, and the importance of home ownership in lower poverty rates among other factors