Negligible Variation and the Change of Variables Theorem

In this note we prove a necessary and sufficient condition for the change of variables formula for the HK integral, with implications for the change of variables formula for the Lebesgue integral. As a corollary, we obtain a necessary and sufficient condition for the Fundamental Theorem of Calculus to hold for the HK integral

2013 Annual Report of UVM Extension and the Vermont Agricultural Experiment Station

2013 Annual report of outreach and research from UVM Extension and Vermont Agricultural Experiment Station

Agri-Environmental Policies When the Spatial Pattern of Biodiversity Reserves Matters

The aim of this paper is to compare different policy instruments for cost-effective habitat conservation on agricultural lands, when the desired spatial pattern of reserves is a random mosaic. We use a spatially explicit mathematical programming model which studies the farmers' behavior as profit maximizers under technical and administrative constraints. Facing different policy measures, each farmer chooses its land-use at the field level, which determines the landscape at the regional level. A spatial pattern index (Ripley L function) is then associated to the obtained landscape, indicating on the degree of dispersion of the reserve. We compare a subsidy per hectare of reserve with an auction scheme and an agglomeration malus. We find that the auction is superior to the uniform subsidy both for cost-efficiency and for the spatial pattern of the reserve. The agglomeration malus does better than the auction for the spatial pattern but is more costly.agri-environmental policies, biodiversity, mathematical programming, spatial optimization, reserve design, cost-efficiency, Environmental Economics and Policy, Resource /Energy Economics and Policy, H23, Q57, Q12, Q28,

The Angel is in the Big Picture: A Response to Lemley

An invention within close reach of multiple inventors differs from an invention within distant reach of a lone inventor. The differences between these two archetypes of invention - reinventables and singletons - remain unexploited under current U.S. law. Should we reform the law to exploit the differences? Mark Lemley and I agree that we should. To date, those economists who have closely examined the issue concur. What are the differences between reinventables and singletons? First, reinventables can be brought into existence with incentives of lower magnitude. This suggests that we can obtain reinventables at a lower price than we currently pay-i.e., with less monopoly loss than we incur today. Second, reinventables generate disproportionately more haste and redundancy, as the rival inventors race and duplicate each other\u27s efforts. This suggests that we already pay more, in rent dissipation and lost opportunity, for reinventables than for singletons (holding all other things equal). Third, reinventables generate disproportionately more litigation as the race winners, or the trolls to whom the winners transfer patents, eat up time and resources suing the inventors who finished a close second or third. This suggests that we already pay more in administrative costs for reinventables than for singletons. The angel is in the big picture in that there is consensus among those who have closely examined the issue that we should reform the law to exploit these differences. The devil is in the details of just how to reform it. Naturally, professional economists have elided the law-related details, focusing instead on their models-models that show an increase in social welfare if the law is reformed so that reinventables hold out the prospect of shared duopoly. Lemley and I, in contrast, take a stab at some of the details of how legal reform could take shape. My proposal is that we regard an independent inventor ( reinventor ) as exempt from the first inventor\u27s patent, provided that the reinventor completed the invention before receiving notice that the first inventor had already completed it. Lemley expresses three reservations about my proposed reinvention defense, and then offers four alternative proposals