On the trace of an endofunctor of a small category

The trace of a square matrix can be defined by a universal property which, appropriately generalized yields the concept of "trace of an endofunctor of a small category". We review the basic definitions of this general concept and give a new construction, the "pretrace category", which allows us to obtain the trace of an endofunctor of a small category as the set of connected components of its pretrace. We show that this pretrace construction determines a finite-product preserving endofunctor of the category of small categories, and we deduce from this that the trace inherits any finite-product algebraic structure that the original category may have. We apply our results to several examples from Representation Theory obtaining a new (indirect) proof of the fact that two finite dimensional linear representations of a finite group are isomorphic if and only if they have the same character.

Still More On Why We Should Bury The Marginal Productivity Theory Of The Price Of Capital: A Supplementary Note

The purpose of this note is to supplement the author’s earlier remarks on the unsatisfactory nature of the neoclassical account of how the return on capital is determined. (See Strathclyde Discussion Paper 12-03: “The Marginal Productivity Theory of the Price of Capital: An Historical Perspective on the Origins of the Codswallop”). The point is made via a simple illustration that certain matters which are problematical in neoclassical terms are perfectly straightforward when viewed from a classical perspective. Basically, the marginalist model of the nature of an economic system is not fit for purpose in that it fails to comprehend the essential features of a surplus-producing economic system as distinct from one merely of exchange.

Caught Between Theory and Practice: Government, Market, and Regulatory Failure in Electricity Sector Reforms

The world-wide electricity sector reforms of the early 1990s have revealed the considerable complexities of making market driven reforms in network and infrastructure industries. This paper reflects on the experiences to date with the process and outcomes of marketbased electricity reforms across less-developed, transition and developed economies. The reforms outcomes suggest similar problems facing the electricity sector of these countries though their contexts vary significantly. Many developing and developed economies continue to have investment inadequacy concerns and the need to balance economy efficiency, sustainability and social equity after more than two decades of experience with reforms. We also use a case study of selected countries that in many respects represent the current state of the reform though they are rarely examined. Nepal, Belarus and Ireland are chosen as country-specific case studies for this purpose. We conclude that the changing dynamics of the electricity supply industry (ESI) and policy objectives imply that analysing the success and failure of reforms will indeed remain a complex process.

Suppliers of Priors: A Theory of Retailing Inspired by the Market for Chinese Antiquities

Adverse selection may thwart trade between an informed seller, who knows the probability p that an item of antiquity is genuine, and an uninformed buyer, who does not know p. The buyer might not be wholly uninformed, however. Suppose he can perform a simple inspection, a test of his own: the probability that an item passes the test is g if the item is genuine, but only f < g if it is fake. Given that the buyer is no expert, his test may have little power: f may be close to g. Unfortunately, without much power, the buyer's test will not resolve the difficulty of adverse selection; gains from trade may remain unexploited. But now consider a "store", where the seller groups a number of items, perhaps all with the same quality, the same probability p of being genuine. (We show that in equilibrium the seller will choose to group items in this manner.) Now the buyer can conduct his test across a large sample, perhaps all, of a group of items in the seller's store. He can thereby assess the overall quality of these items; he can invert the aggregate of his test results to uncover the underlying p; he can form a "prior". There is thus no longer asymmetric information between seller and buyer: gains from trade can be exploited. This is our theory of retailing: by grouping items together - setting up a store - a seller is able to supply buyers with priors, as well as the items themselves. We show that the weaker the power of the buyer�s test (the closer f is to g), the greater the seller�s profit. So the seller has no incentive to assist the buyer � e.g., by performing her own tests on the items, or by cleaning them to reveal more about their true age. The paper ends with an analysis of which sellers should specialise in which qualities. We show that quality will be low in busy locations and high in expensive locations.

Did Keynes in the General Theory significantly misrepresent J S Mill?

It has been alleged that J M Keynes, quoting in the General Theory a passage from J S Mill's Principles, misunderstood the passage in question and was therefore wrong to cite Mill as an upholder of the 'classical' proposition that 'supply creates its own demand'. We believe that, although Keynes was admittedly in error with respect to, so-to-say, the 'letter' of Mill's exposition, he did not mislead readers as to the 'substance' of Mill's conception. The purpose of this paper is to demonstrate that J S Mill did indeed stand for a 'classical' position, vulnerable to Keynes's critique as developed in the General Theory. [This is a revised version of an earlier working paper: 'Keynes, Mill and Say's Law', Strathclyde Papers in Economics, 2000/11]

Imperfect Attention and Menu Evaluation

We model the choice behaviour of an agent who suffers from imperfect attention. We define inattention axiomatically through preference over menus and endowed alternatives: an agent is inattentive if it is better to be endowed with an alternative a than to be allowed to pick a from a menu in which a is is the best alternative. This property and vNM rationality on the domain of menus and alternatives imply that the agent notices each alternative with a given menu-dependent probability (attention parameter) and maximises a menu independent utility function over the alternatives he notices. Preference for flexibility restricts the model to menu independent attention parameters as in Manzini and Mariotti [19]. Our theory explains anomalies (e.g. the attraction and compromise effect) that the Random Utility Model cannot accommodate.

The Effects of Experience on Preference Uncertainty: Theory and Empirics for Public and Quasi-Public Environmental Goods

This paper develop and estimates a model of demand estimation for environmental public goods which allows for consumers to learn about their preferences through consumption experiences. We develop a theoretical model of Bayesian updating, perform comparative statics over the model, and show how the theoretical model can be consistently incorporated into a reduced form econometric model. We then estimate the model using data collected for two environmental goods. We find that the predictions of the theoretical exercise that additional experience makes consumers more certain over their preferences in both mean and variance are supported in each case.

On a size-structured two-phase population model with infinite states-at-birth

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’ size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.

A Theory of Wage Setting Behavior

Concerns for fairness, workers' morale and reciprocity infuence firms' wage setting policy. In this paper we formalize a theory of wage setting behavior in a simple and tractable model that explicitly considers these behavioral aspects. A worker is assumed to have reference-dependent preferences and displays loss aversion when evaluating the fairness of a wage contract. The theory establishes a wage-effort relationship that captures the worker's reference-dependent reciprocity, which in turn in uences the firm's optimal wage policy. The paper makes two key contributions: it identifies loss aversion as an explanation for a worker's asymmetric reciprocity; and it provides realistic and generalized microfoundation for downward wage rigidity. We further illustrate the implications of our theory for both wage setting and hiring behavior. Downward wage rigidity generates several implications for the outcome of the initial employment contract. The worker's reference wage, his extent of negative reciprocity and the firms expectations are key drivers of the propositions derived.

Migration and trade: Theory with an Application to the Eastern- Western European Integration

The remarkable increase in trade flows and in migratory flows of highly educated people are two important features of globalization of the last decades. This paper extends a two-country model of inter- and intraindustry trade to a rich environment featuring technological differences, skill differences and the possibility of international labor mobility. The model is used to explain the patterns of trade and migration as countries remove barriers to trade and to labor mobility. We parameterize the model to match the features of the Western and Eastern European members of the EU and analyze first the effects of the trade liberalization which occured between 1989 and 2004, and then the gains and losses from migration which are expected to occur if legal barriers to labor mobility are substantially reduced. The lower barriers to migration would result in significant migration of skilled workers from Eastern European countries. Interestingly, this would not only benefit the migrants and most Western European workers but, via trade, it would also benefit the workers remaining in Eastern Europe. Key Words: Skilled Migration, Gains from Variety, Real Wages, Eastern-Western Europe. JEL Codes: F12, F22, J61.

Evaluation of the molluscicidal property of Euphorbia splendens var. Hispolii (N.E.B.) (Euphorbiaceae): 2. Investigation in lotic habitat

The latex of Euphorbia splendens var. hispolii in 12 ppm concentration (12 mg/l) caused 100% mortality for a Biomphalaria tenagophila population in a lotic habitat after 9 hr of dripfeed application. For sentinel snails, in cages placed at the water surface and buried under 0.10 m, the mortality rates varied with the distance from the application point and were: 100% (0 m); 92.6% (50 m) and 94.7% (100). No lethal effects were observed for the other living species in this habitat (Pomacea haustrum and Poecilia reticulata).

On the current existence of a coccidial line of development in the malaria parasites: a theory

Most opinion favors the origin of the malaria parasites from a coccidial ancestor. It is assumed that whatever the process through which the coccidia differentiated into a Plasmodium this phenomenon very probably occured millions of year ago, and during that differentiation process the original coccidia vanished. Therefore it has never repeated. At the light of some experiments the existence, at the present time, of a coccidial cycle of development in the malaria parasites, is proposed. The conection routes and mechanisms through which the malaria parasite changes to a coccidial life, and the routes in reverse are exposed. Transmission of the malaria-coccidial forms is suggested.

A well-posedness theory in measures for some kinetic models of collective motion

We present existence, uniqueness and continuous dependence results for some kinetic equations motivated by models for the collective behavior of large groups of individuals. Models of this kind have been recently proposed to study the behavior of large groups of animals, such as flocks of birds, swarms, or schools of fish. Our aim is to give a well-posedness theory for general models which possibly include a variety of effects: an interaction through a potential, such as a short-range repulsion and long-range attraction; a velocity-averaging effect where individuals try to adapt their own velocity to that of other individuals in their surroundings; and self-propulsion effects, which take into account effects on one individual that are independent of the others. We develop our theory in a space of measures, using mass transportation distances. As consequences of our theory we show also the convergence of particle systems to their corresponding kinetic equations, and the local-in-time convergence to the hydrodynamic limit for one of the models.

Lp theory for the multidimensional aggregation equation

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