One of his earliest and most famous contributions was to social choice theory “Arrow’s impossibility theorem”. He also contributed to neoclassical General Equilibrium Analysis but also contributed to other areas such as endogenous growth theory. He also contributed to health economics arguing against a purely market approach to health care provision, Arrow was active as a trustee of Economists for Peace and Security and a member of the Advisory Board of Incentives for Gobal Health until his death.
The Impossibility Theorem is regarded as an important breakthrough proof and is studied in many disciplines including economics, philosophy, political science, and computer science. Arrow was always attempting to bring the rigor of mathematics into economics and allied disciplines. The theorem is rather complicated but there is a simplified discussion in Wikipedia.
To put matters simply the theorem proves that assuming a voting process must meet certain conditions, no voting system can be satisfactory. As a an article in Forbes puts it: Arrow sets forth three desirable properties for voting procedures: (1) efficiency, (2) consistency, and (3) no-dictatorship. He then proves that no voting procedure will allow all three to coexist. If you maintain two of them, you will have to give up the third. This brilliant but very frustrating result initiated a new research field in economics, called “Social Choice,” aimed at discovering flaws in various voting procedures and proposing remedies
Many analysts have questioned some of the assumptions underlying the theory some of which are discussed in the Wikipedia article.
The Arrow theorem was applied more widely than to voting. Michael Roberts claims: As developers of this ‘impossibility’ theorem, like Amartya Sen, went on to show, this also meant that there was no way that markets, perfectly competitive or not, could deliver equality of outcomes for each individual – no Pareto optimality. Another way of putting this is to say that it is impossible to get ‘society’ to make a choice that leads to satisfaction for everyone. As Sen said, “It is important to recognize that Arrow was not only establishing a theorem, he was opening up a whole subject to social choice.”
A situation is Pareto optimal when no one can be made better off without making someone else worse off. While this result may seem quite unsurprising and even trivial it provides a rigorous proof that what was long thought possible was not.
Arrow’s next important contribution was to General Equilibrium Theory (GE). Arrow’s contribution is often referred to as the Arrow-Debreu model. The principle of the GE theory is that supply and demand in markets can be equalised and stabilised at a certain price providing an equilibrium. The theory showed that capitalist markets tend towards stability an equilibrium rather than being inherently unstable as was argued by Marx and Marxist economists. As Roberts suggests: So the invisible hand of the market (Smith) can lead to harmonious equilibrium in markets where supply and demand are ‘cleared’. Working with Gerard Debreu, the Arrow-Debreu theorem in 1954 supposedly provided a rigorous mathematical proof of a ‘market-clearing’ equilibrium — or the price at which the supply of an item is equal to its demand. It became just what mainstream economics needed to ‘prove’, namely that a theory of value and price formation could be based on individual consumer choices and not on the labour theory of value as put forward by the classical economists and Marx. “Their (neoclassical) theory of value and price formation was really a fundamental element of economics…It’s the ABCs of economics and economic theory.”, said one follower of Arrow.
While the Arrow-Debreu model appears to provide a rigorous demonstration of a basic truth of neoclassical economists it at the same time involves assumptions that demonstrate clearly that the model cannot fit reality. For example, one assumption is that each participant must have the same power and knowledge. The theory was even applied to financial markets where it was assumed quite incorrectly that everyone had the same power and knowledge. As the dysfunctional derivatives market showed this assumption is completely unwarranted. Purchasers of the derivatives did not have the knowledge of risk that the sellers of them had resulting in disastrous losses for many investors and huge profits for those peddling the risky goods.
Arrow himself noted that health care provision should not be modelled in terms of markets because participants did not have equal information or power. The doctor has superior knowledge about the quality and provision and distribution of health-care services compared to the patient, creating what Arrow calls “information asymmetry”. He talks of health care provision of being a non-market relationship. One could very well argue as many have that the solution to this problem is to provide health care as a public good paid for by the state as universal insurer based upon health needs of the people.
The classical economists Adam Smith, David Ricardo as well as Karl Marx unlike the neo-classicals considered capitalist economies as dynamic rather than static systems. It is theories about this dynamic system that are more relevant to understanding how the economy works rather than the models of neo-classicists with their often unrealistic assumptions. Debreu himself in his endogenous growth theory took the economy as a dynamic system.
This theory explains the source of technical change as part of the process of accumulation and not external to supply and consumer demand. The neo-classical view set these sources as external or exogenous. Arrow pointed out that factors such as innovation came from the desire of companies to expand. To Marxists it was a desire to increase profits or profitability. Roberts summarises some of the main contributions of Arrow to economics as follows: So Kenneth Arrow leaves us with three arrows to enrich our understanding of the economic world: 1) markets collectively can never properly deliver every individual’s needs; 2) markets cannot equate supply and demand except under the most unrealistic assumptions and 3) economic growth is not achieved by just meeting the demand of consumers but requires decisions of investors to innovate.
