Week 3 summary of our 'Important Economists' series

Our 'important economists' Twitter series brings you every day short summaries of the works of influential economists. This week, we summarized the contributions of David Ricardo, Thomas Malthus, John Nash, Kenneth Arrow, Paul Samuelson, Eugene Fama, and John Kenneth Galbraith. Clearly, Kenneth Arrow generated the most interest. Here is our summary of his contributions!

Kenneth J. Arrow (1921-2017) was an American economist and Nobel laureate known for his significant contributions to the fields of economic theory and social choice theory. Paul Samuelson would say in 1972 when Arrow won the Nobel Prize that “The economics of insurance, medical care, prescription drug testing — to say nothing of bingo and the stock market — will never be the same after Arrow.”

Arrow's most famous work is arguably his "impossibility theorem", which demonstrated that it is impossible to create a voting system that satisfies simultaneously 5 desirable properties: no dictatorship, individual sovereignty, unanimity, freedom from irrelevant alternatives, and uniqueness of group rank. This groundbreaking result has had a profound impact on the study of collective decision-making processes and the design of fair voting mechanisms.

Kenneth Arrow's most important work however may be his contributions to general equilibrium theory. He proved, with Gérard Debreu, the existence of general economic equilibrium, he analyzed the relationship between equilibria and optima, and he extended equilibrium theory to cover the case of uncertainty and volatility.

Classical economists (Adam Smith, Ricardo, J. S. Mill, and Marx) had a theory of value that is driven by the cost of production and a zero-profit condition. Their work had an aspect of general equilibrium because in their theory markets were related. However, they ignored the influence of demand on value. Leon Walras incorporated demand into the explanation of value and simultaneously considered the interrelationships of markets. Joseph Schumpeter (1954) put it most strongly: "the discovery [of economic theory] was not fully made until Walras, whose system of equations, defining (static) equilibria in a system of interdependent quantities, is the Magna Carta of economic theory". Price is not determined by technology alone, as a change in tastes also influences relative prices. Nothing that came before the Walrasian theory had this capacity (Duffie and Sonnenschein, 1989).

In 1954, Arrow and Gerard Debreu published their proof of the existence of equilibrium for a competitive economy at the same time as Lionel McKenzie (1954). The Arrow-Debreu proof of the existence of a Walrasian equilibrium for an economy proceeds by (1) associating a generalized game with the economy, (2) proving that there exists at least one equilibrium of the generalized game, and (3) demonstrating that in an equilibrium of the generalized game all markets in the economy clear.

In 1951, Arrow presented the first and second fundamental theorems of welfare economics and their proofs without requiring differentiability of utility, consumption, or technology, and including corner solutions. The first welfare theorem concerns the Pareto optimality of Walrasian equilibrium allocations. It offers the modern expression of Adam Smith's declaration that individuals acting in their own interest will promote the social good. The second welfare theorem concerns the possibility of obtaining the efficiency benefits of perfect competition while at the same time maintaining influence over the distribution of income. The theorem provides conditions under which, to each Pareto optimum, there is an assignment of units of account (income) and prices so that the given optimum is a Walrasian equilibrium (Duffie and Sonnenschein, 1989).

In 1952 Arrow presented the first general equilibrium theory of the allocation of uncertain consumption. He introduced the notion of contingent commodities, or Arrow-Debreu securities, which incorporate uncertainty into the general equilibrium theory of allocation. Arrow made the first explicit use of the so-called perfect foresight assumptions regarding equilibrium price expectations.

The extension by Arrow of general equilibrium theory to include the case of uncertainty represents one of the great moments in economic theory. He also greatly contributed to information economics, endogenous growth theory, operations research, and health economics, which would be too long to review here.

Watch this space or our Twitter profile for explanations of many more 'important' economists in coming weeks.