Fundamental Theorems Of Welfare Economics Research Articles

Multihanded Adam Smith (Part two)

The paper analyzes the metaphor of “an invisible hand”, which was introduced two and a half centuries ago by Adam Smith (1723—1790) and which eventually became the central concept of the modern economics. The second part examines the origin and history of the reception of Smith’s metaphor at various stages of the evolution of economic thought. Paradoxically, it gained wide popularity only since the middle of the 20th century due to its mention in the famous textbook by P. Samuelson “Economics”. In the interpretation of this metaphor by modern economists, two traditions exist — neoclassical and Austrian. In mainstream, Smith’s “invisible hand” is identified with the First Fundamental Theorem of welfare economics, which looks like an anachronism. There are more grounds for the convergence of the concepts of “an invisible hand” and “spontaneous order”, from which the Austrian school proceeds. Smith almost accidentally stumbled upon a figurative expression which turned out to be heuristically extremely productive and has become firmly embedded in the lexicon of many modern disciplines — from economics to the philosophy of science

Capitalism and Distributive Justice: Musings of a Mormon Economist

Capitalism and Distributive Justice: Musings of a Mormon Economist

Competitive equilibria in a comonotone market

We investigate competitive equilibria in a special type of incomplete markets, referred to as a comonotone market, where agents can only trade such that their risk allocation is comonotonic. The comonotone market is motivated by the no-sabotage condition. For instance, in a standard insurance market, the allocation of risk among the insured, the insurer and the reinsurers is assumed to be comonotonic a priori to the risk-exchange. Two popular classes of preferences in risk management and behavioral economics, dual utilities (DU) and rank-dependent expected utilities (RDU), are used to formulate agents’ objectives. We present various results on properties and characterization of competitive equilibria in this framework, and in particular their relation to complete markets. For DU-comonotone markets, we find the equilibrium in closed form and for RDU-comonotone markets, we find the equilibrium in closed form in special cases. The fundamental theorems of welfare economics are established in both the DU and RDU markets. We further propose an algorithm to numerically obtain competitive equilibria based on discretization, which works for both the DU-comonotone market and the RDU-comonotone market. Although the comonotone and complete markets are closely related, many of our findings are intriguing and in sharp contrast to results in the literature on complete markets in terms of existence, uniqueness, and closed-form solutions of the equilibria, and comonotonicity of the pricing kernel.

The provision of collective goods through a social division of labour

We develop a general equilibrium framework in which a wide range of collective economic configurations are provided through specialised professionals as part of an endogenously emerging social division of labour. We extend the theory of value to this setting bringing together a model of an economy with collective goods with the model of a private-goods market economy with an endogenously emerging social division of labour. Natural applications are the presence of non-tradables in production, the effects of education on productive abilities, and the market system itself as an implementation of the price mechanism.For an appropriately generalised notion of valuation equilibrium, we prove the two fundamental theorems of welfare economics under very general conditions, notably allowing for incomplete, non-monotonic, and non-transitive preferences. We also incorporate Adam Smith’s principle of increasing returns to specialisation and establish that there emerge well-structured social divisions of labour in equilibrium.

The global economy: a framework for teachers of microeconomics

Economics instructors who take a pluralistic view may find useful a framework to show the relationship among the different schools of thought in economics. I construct a taxonomy based on Gassler's notion of political and social economics. It consists of non-market activities that either set up the market for success or correct for market failure. This framework illustrates how both neoclassical, and other approaches, can contribute to our understanding of the complexities of international political economy. First, I review the argument for free trade in the form of the first fundamental theorem of welfare economics, stressing the underlying assumptions. Second, using the same framework, I construct the neoclassical argument against free trade and show that it is much stronger than the argument in favour. I do this by simply describing the cases of market failure which are not difficult to find at the global level. Third, I argue that heterodox economics can help construct an alternative view of globalisation that is better both positively and normatively; and the neoclassical theory does not stand in its way.

The First Fundamental Theorem of Welfare in a General Equilibrium Evolutionary Setting

In the present note we prove the first fundamental theorem of welfare economics, according to which all equilibrium allocations are Pareto optimal, for the standard pure exchange model with shares. In this context the social interaction among agents enters the definition of equilibrium only through the market clearing conditions, but it does not affect the agents’ maximization problem. We show that the first fundamental theorem of welfare holds true also when introducing stationary equilibria in relation to a share updating mechanism.

Editorial

Editorial

Kenneth Joseph Arrow. 23 August 1921—21 February 2017

Kenneth Arrow was a mathematical economist and political scientist who made many ground-breaking contributions to the theory of economics and social values. His great mathematical ability led him to introduce new approaches to theoretical economics and in particular to a series of fundamental theorems in the discipline. These included the Arrow Impossibility Theorem, the two fundamental theorems of welfare economics and the existence of a competitive equilibrium. For these and many other contributions he was awarded the 1972 Nobel Prize in Economics shared with Sir John Hicks. He took a particular interest in computation and computability in economics. He was active and very productive as a researcher for over seven decades and was renowned as a generous and inspiring teacher and colleague.

General Equilibrium Theory, But Better

I construct a general, game theoretic model of markets. Agents in the model choose how much of each good to supply/demand, and at what prices. Trading can occur at non-market-clearing prices. There is an explicit rationing mechanism that kicks in if markets fail to clear. The game is very complicated, but a massive simplification occurs in the limit of a large number of players. This allows a proof of existence of a pure strategy equilibrium. I also prove an analogue of the first fundamental theorem of welfare economics. The game is Keynesian in that 1) markets needn't clear at equilibrium so there can be unemployment and 2) there is the possibility of multiple equilibria with different levels of aggregate supply/demand, and distinct Pareto rankings. The model is microfounded and Keynesian. Fiat money can be accommodated as a store of value and a medium of exchange. The model is well placed for investigating dynamics.

A Comparison of Electricity-Pricing Programs: Economic Efficiency, Cost Recovery, and Income Distribution

This article empirically compares four electricity-pricing programs—increasing-block pricing (IBP); floating increasing-block pricing (FIBP); free market pricing (FMP); and a price-cum-trade incentive system (PTS)—in terms of efficiency, cost recovery, and income distribution by using the residential electricity data of Taiwan. The research results show that IBP and FIBP suffer from the same problem: It is hard to be cost-neutral. Further, FMP is economically efficient while favoring the electric utility over the households. PTS—which is a pricing program that satisfies the second fundamental theorem of welfare economics—shows a better ability to consider economic efficiency and equity simultaneously.

A Legalistic Conception of the Market: Beyond Efficiency

This paper argues that the standard picture of the market is flawed not merely in practice but also, and especially, in principle. The basic difficulty with the standard picture is that trading (with contracts) gives rise to a form of recognition that is preference-independent and, therefore, that market participants cannot wish away its negative and positive effects on non-trading parties. The paper argues on the basis of this that such effects undermine the possibility of identifying the market with Pareto efficiency—to wit, the first fundamental theorem of welfare economics, showing that perfect competition yields Pareto efficient allocation of resources, cannot hold for market exchange that takes the contract form of interaction.

MARKET ECONOMIES WITH AN ENDOGENOUS SOCIAL DIVISION OF LABOR

AbstractI consider a general equilibrium model of a competitive market economy in which production is conducted through an endogenous social division of labor. I represent economic decision makers as “consumer–producers,” who consume as well as produce commodities. In this approach, the emergence of a nontrivial social division of labor is guided by Increasing Returns to Specialization (IRSpec) in production. Under IRSpec, I show existence of competitive equilibria, the two fundamental theorems of welfare economics, and characterize these equilibria. Markets equilibrate through the adjustment of the social division of labor; the production technologies completely determine the equilibrium prices.

Competitive Equilibria in a Comonotone Market

We investigate competitive equilibria in a special type of incomplete markets, referred to as a comonotone market, where agents can only trade such that their risk allocation is comonotonic. The comonotone market is motivated by the no-sabotage condition. For instance, in a standard insurance market, the allocation of risk among the insured, the insurer and the reinsurers is assumed to be comonotonic a priori to the risk-exchange. Two popular classes of preferences in risk management and behavioral economics, dual utilities (DU) and rank-dependent expected utilities (RDU), are used to formulate agents’ objectives. We present various results on properties and characterization of competitive equilibria in this framework, and in particular their relation to complete markets. For DU-comonotone markets, we find the equilibrium in closed form and for RDU-comonotone markets, we find the equilibrium in closed form in special cases. The fundamental theorems of welfare economics are established in both the DU and RDU markets. We further propose an algorithm to numerically obtain competitive equilibria based on discretization, which works for both the DU-comonotone market and the RDU-comonotone market. Although the comonotone and complete markets are closely related, many of our findings are intriguing and in sharp contrast to results in the literature on complete markets in terms of existence, uniqueness, and closed-form solutions of the equilibria, and comonotonicity of the pricing kernel.

Islamic economics and a third fundamental theorem of welfare economics

AbstractThe discipline of economics started as a moral science but became detached from moral concerns over time to emulate natural science and to adopt positivism. Consequently, mainstream economics assumes people to be sordidly selfish. The teachings of Islam, however, promote social preferences where individuals should be other‐regarding and have preferences over social outcomes. This paper replaces the selfish agent with a social agent and presents the results in a theorem referred to as the third fundamental theorem of welfare economics (TFTWE). The TFTWE states that “when the selfish agents are replaced with the social agents, market outcomes are Pareto optimal, equitable, and unique”. This is an important result which has widespread implications. We show that the TFTWE holds under conditions where the first two fundamental theorems of welfare economics fail and that a Walrasian equilibrium is more likely to exist when selfish preferences are non‐convex. Unlike the popular convention, there is no equity‐efficiency trade‐off. In fact we point to the possibility of reversal in equity‐efficiency trade‐off.

Seven Kinds of Computable and Constructive Infelicities in Economics

At least seven kinds of misconceptions about constructive and computable mathematics prevail in economics. In this paper, the infelicitous claims of computable or constructive frameworks for the excess demand functions of microeconomics, constructive general equilibrium theory and computable general equilibrium modeling, agent-based economics, search theory, game theory, index number theory and Neo Ricardian economics and the fundamental theorems of welfare economics are considered. The claims are shown to be misleading from the point of view of formal computability theory or constructive mathematics (especially but not only when based on Brouwerian Intuitionistic Logic).

Concave Preferences Over Bundles

In this paper we are concerned with numerical representation of preferences over bundles. Specifically, we provide an axiomatic characterization of preferences that have a numerical representation that look similar to a concave function defined on a convex set. We call such preferences concave. We also show that the concept of a super-gradient is inherent to rational choice. We discuss additively separable preferences and their axiomatization due to Fishburn (1970) since they are an important example of concave preferences. Using the same methods that we use to prove earlier results we show that the first fundamental theorem of welfare economics holds for combinatorial assignment problems.

Efficiency of Innovations: What are the Practical Implications of the Second Fundamental Theorem of Welfare Economics?

The second fundamental theorem of welfare economics suggests that our market economy can be inefficient in non-convex environments. Then, what kind of inefficiencies are we facing? Where can we find them? How can we eliminate them? In this paper, a total surplus analysis is used to show that one of the most serious such inefficiencies is “inactive innovation” and it can be eliminated if buyers of an innovative commodity have a sense of “gratitude” and are willing to pay the prices which are the same as their benefit from the commodity.

Constructive and computable Hahn–Banach theorems for the (second) fundamental theorem of welfare economics

The Hahn–Banach Theorem plays a crucial role in the second fundamental theorem of welfare economics. To date, all mathematical economics and advanced general equilibrium textbooks concentrate on using non-constructive or incomputable versions of this celebrated theorem. In this paper we argue for the introduction of constructive or computable Hahn–Banach theorems in mathematical economics and advanced general equilibrium theory. The suggested modification would make applied and policy-oriented economics intrinsically computational.

Towards a political economy of the theory of economic policy

The theory of economic policy, in its mathematical modes, may be said to have had two incarnations, identified in terms of pre-Lucasian and ultra-Lucasian on a timescale whose origin can be traced to the Scandinavian works of the 1920s and early 1930s, beginning with Lindahl, Frisch, Myrdal and Hammarskjold. The end of the ultra-Lucasian period, in Frances Fukuyama senses, might well have been the date (2004) of Prescott’s Nobel Prize Lecture. The codification of what may be called the ‘classical’ theory of economic policy was initiated in the pioneering formalisations by Frisch and Tinbergen, and elegantly summarised in Bent Hansen’s early (1955), advanced text book. The launching pads for the ultra-Lucasian period were the Lucas critique, the elementary saddlepoint dynamics-based policy ineffectiveness ‘theorem’ of Sargent and Wallace and the dynamic programming-based time-invariance proposition of Kydland and Prescott. Further, the important contribution by Ramsey is another kind of ‘origin’. In this article I first try to trace a path of the mathematisation of the theory of economic policy, from this specific origin to the stated culminating point. Second, an attempt is made to expose the nature of the Emperor’s New (Mathematical) Clothes in which the mathematisation of the theory of economic policy was attired. Finally, it is shown that the obfuscation by the mathematics of efficiency, equilibrium and the fundamental theorems of welfare economics can be dispelled by an enlightened, alternative mathematisation that makes it possible to resurrect the poetic tradition in economics and ‘connect the prose in us with the passion’ (E. M. Forster) for policy in the manner in which Geoff Harcourt has ‘connected’ them.

Could Homo Oeconomicus Become a Revolutionary?: On the Need to Teach and Practice a Different Economics

This paper investigates the standard economic paradigm as to the possibility for the agents to become revolutionaries, i.e., to develop the desire and effective action to overturn the prevailing social order. We take our cue from Amartya Sen's remark that the Second Fundamental Theorem of Welfare Economics might be part of 'a revolutionary's handbook'. In analyzing the meaning of Sen's assertion, we uncover the deep-lying difficulties which the standard paradigm, characterized by a vision of individuals as self-enclosed 'monads' and of social order as monadological coordination, has in even making sense of the notion of revolution. We are thus led to the intermediary conclusion that the neoclassical paradigm is structurally unable to see the agents as (even only potential) revolutionaries. In the course of our demonstration, we show that economics needs to be conceived not primarily as a 'teaching about' the economic system and the agents' actions, but as a 'resource for' the agents within the model itself to reflect on the directions they want to give to social change. We endow the economic agents themselves (and not just the theorist who looks at them 'from above') with a significant capacity to educate themselves in order to form a judgment about what kind of economy they want to act in. In other words, asking whether the economic agents might in some cases become revolutionaries leads us to militate for the need to fully endogenize economics as a component of the economic model itself.