Some conceptual difficulties regarding "net" multipliers

Multipliers are routinely used for impact evaluation of private projects and public policies at the national and subnational levels. Oosterhaven and Stelder (2002) correctly pointed out the misuse of standard 'gross' multipliers and proposed the concept of 'net' multiplier as a solution to this bad practice. We prove their proposal is not well founded. We do so by showing that supporting theorems are faulty in enunciation and demonstration. The proofs are flawed due to an analytical error but the theorems themselves cannot be salvaged as generic, non-curiosum counterexamples demonstrate. We also provide a general analytical framework for multipliers and, using it, we show that standard 'gross' multipliers are all that is needed within the interindustry model since they follow the causal logic of the economic model, are well defined and independent of exogenous shocks, and are interpretable as predictors for change.

On a series of Goldbach and Euler

Theorem 1 of Euler s paper of 1737 'Variae Observationes Circa Series Infinitas', states the astonishing result that the series of all unit fractions whose denominators are perfect powers of integers minus unity has sum one. Euler attributes the Theorem to Goldbach. The proof is one of those examples of misuse of divergent series to obtain correct results so frequent during the seventeenth and eighteenth centuries. We examine this proof closelyand, with the help of some insight provided by a modern (and completely dierent) proof of the Goldbach-Euler Theorem, we present a rational reconstruction in terms which could be considered rigorous by modern Weierstrassian standards. At the same time, with a few ideas borrowed from nonstandard analysis we see how the same reconstruction can be also be considered rigorous by modern Robinsonian standards. This last approach, though, is completely in tune with Goldbach and Euler s proof. We hope to convince the reader then how, a few simple ideas from nonstandard analysis, vindicate Euler's work.

Smoked cocaine in socially-depressed areas

Background: The main objectives of this study are to describe the smoked cocaine user's profile in socially-depressed areas and their needs from a harm-reduction perspective, to investigate their use of smoking crack and compare the acute effects between injecting and smoking consumption. Methods: The study took place in SAPS, Barcelona, Spain. Two focus group sessions were undertaken with a total of 8 drug users. Secondly, the 8 participants answered a structured questionnaire and in the course of the sessions, as a snowball activity, were trained to survey 6 other crack smokers. Results: We obtained 56 questionnaires. The majority of participants were from non-European Community countries (62.69%), 70.2% of participants referred to sharing the smoking equipment. The most frequent symptoms reported during smoked cocaine were mydriasis (83.33%)), perspiration (72.92%) and compulsive object search (70.83%) During the group sessions, participants said that smoked cocaine is much more addictive than injected cocaine and causes more anxiety. Participants also reported the difficulty of changing from injected use to smoked use, due to the larger amount of cocaine needed to reach the same effects as when having injected. Conclusions We can conclude that the research, focused on achieving greater knowledge of the smoked cocaine user's profile, their usage of smoking crack, consumption patterns and acute effects, should be incorporated into substance misuse interventions.