Public Good Menus and Feature Complementarity

The distance metric on the location space for multidimensional public good varieties represents complementarity between the goods features. "Euclidean" feature complementarity has atypical strong properties that lead to a failure of intuition about the optimal-menu design problem. If the population is heterogeneous, increasing the distance between two varieties is welfare-improving in Euclidean space, but not generally. A basic optimal-direction principle always applies: "anticonvex" menu changes increase participation and surplus. A menu replacement is anticonvex if it moves the varieties apart in the common line space. The result extends to some impure public goods with break-even pricing and variety-specic costs. A sufficient condition for menus to be Pareto-optimal is that "personal price" (nominal price plus perceived distance from a variety) is linear in the norm that induces the distance metric.Public Good Menus; complementarity

\u27Dred Scott v. Sandford\u27 Analysis

The Scott v. Sandford decision will forever be known as a dark moment in America\u27s history. The Supreme Court chose to rule on a controversial issue, and they made the wrong decision. Scott v. Sandford is an example of what can happen when the Court chooses to side with personal opinion instead of what is right

Can Rivalry Increase Prices?

Spatially differentiated duopolists set higher-than-monopoly prices at some distances. This phenomenon is shown to occur in any finite- dimensional space for a class of reservation prices that covers concavity and convexity in perceived distance from a design. But an upper bound on the equilibrium duopoly price converges monotonically and quickly to the monopoly price in dimensionality. If consumers care about sufficiently many features of the product (a very small number of criteria is enough), monopoly nearly leads to an extreme price.price effect of competition, multidimensional product spaces, duopoly pricing, spatial competition

Rapid healing of a patient with dramatic subacute combined degeneration of spinal cord: a case report

Background: Prevalence of cobalamin deficiency is high especially in older patients and an immediate therapy start is necessary to prevent irreversible neurological damages. Unfortunately, the diagnosis of cobalamin deficiency is difficult and at present, there is no consensus for diagnosis of this deficiency. Therefore, we aim to elucidate a meaningful diagnostic pathway by a case report with an initially misleading medical history. Case presentation: A 57 year-old Caucasian man suffering from dramatic myelosis of the cervical posterior columns. Apart from associated neurological symptoms (tactile hypaesthesia, reduced vibration sensation, loss of stereognosis and of two-point-discrimination) there were no further complaints; especially no gastrointestinal, haematological or psychiatric disorders were provable. Cobalamin (vitamin B12) serum level was normal. The diagnosis of subacute combined degeneration of spinal cord was confirmed by an elevated methylmalonic acid, and hyperhomocysteinemia. Cobalamin deficiency was caused by asymptomatic chronic atrophic inflammation of the stomach with a lack of intrinsic factor producing gland cells. This was revealed by increased gastrin and parietal cell antibodies and finally confirmed by gastroscopy. Parenteral substitution of cobalamin rapidly initiated regeneration. Conclusions: This case demonstrates that normal cobalamin serum levels do not rule out a cobalamin deficiency. In contrast, path-breaking results can be achieved by determining homocysteine, holotranscobalamin, and methylmalonic acid