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The Nobel Series : Kenneth & Hicks

Exploring the varied contributions made to policymaking — ranging from international trade and environmental policy to even electoral reform — by Kenneth Arrow and John Hicks

The Nobel Series : Kenneth & Hicks
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The 1972 Nobel Prize in Economics was awarded to the American economist Kenneth Arrow, jointly with Sir John Hicks of Oxford University. The Prize was awarded for their work in general equilibrium theory and welfare theory. However, this is not the only contribution of these two economists. While Arrow's contributions are well known in social choice theory and growth theory, Hicks is also known for his contributions in monetary theory and business cycles.

Works of Kenneth Arrow

Arrow is perhaps best known for the famous 'Arrow's Impossibility Theorem', which he outlined and proved in his PhD dissertation. This dissertation was later published as a book 'Social Choice and Individual Values'. However, Arrow was awarded the Nobel for his work on general equilibrium. Let us review some of the works of Arrow.

Impossibility theorem

This theorem, variously known as the impossibility theorem, possibility theorem or Arrow's paradox, was first proposed by Arrow in his PhD dissertation and reproduced in his book of 1951, 'Social Choice and Individual Values'. He showed that under certain assumptions about people's preferences between options, it is always impossible to find a voting rule under which one option emerges as the most preferred one, provided certain mandatory principles of fair voting procedures are met. These principles include:

Non-dictatorship.

Pareto efficiency (meaning that if every voter prefers candidate A over candidate B, candidate A should win).

Independence of irrelevant alternatives (if the candidate A is preferred over B, then A would still be ahead of B even if a third candidate C is removed from the competition).

Unrestricted domain (meaning that all individual preference must be accounted for).

Social ordering (each individual should be able to rank order his preference in any way and even indicate ties).

In short, it states that if the above five conditions are met, it is impossible to formulate a social ordering where individuals have to rank preferences over three or more options. In other words, clear individual preferences cannot be aggregated to form a clear social preference. This can be best illustrated by the instability of majority rule, which was first demonstrated by Condorcet in 1785 and came to be known as the voting paradox. This paradox is as follows:

We can see from the above table, where three voters have to choose between three candidates A, B and C. If A is chosen as the winner, one can argue that C should win instead since 'Voter 2' and 'Voter 3' prefer C to A by a margin of 2 to 1 votes. Similarly, A is preferred over B and B over C. We thus have a situation where voters' preferences have not given a clear winner even though each individual voter has a clear rank ordering of preference over a pair of candidates. In other words, rational individual preferences have led to a cyclical irrational collective preference.

This paradox was rediscovered by Duncan Black who modified the Condorcet method, whereby each voter assigns points to alternatives, which are arranged in a single dimension, in order of his preference. Further, each voter's preference has a single peak (or a single maximum point). In such a situation Black found that majority cycles would not occur. Instead, majority rule would yield an equilibrium at the ideal point of the median voter. This also came to be referred to as the 'median voter theorem'. However, Black realised that if the number of policy dimensions was increased from one (say education policy) to many (say education, health and infrastructure policy), we would be back in the world of cyclicity and unstable majority rule.

General equilibrium

Arrow's work on general equilibrium is also well known. His paper of 1954, co-authored with Gerard Debreu (who got the Nobel Prize later in 1983), is established as the standard model to demonstrate and prove Walrasian equilibrium. It is also the standard reference for other microeconomic models. The model basically specifies the following:

A competitive economy in which there are finite numbers of consumers, commodities (some being used as production inputs), and production units.

Consumers have a set of well-defined preferences (with certain mathematical properties such as continuous, non-satiation, and convex)

Each consumer holds an initial endowment of the commodities, with a positive quantity of at least one commodity.

The technology that converts inputs into outputs is either non-increasing returns to scale or constant returns to scale (returns to scale tell us how much output one gets from a unit of inputs. Hence, constant returns mean one unit of input gets you one unit of output; increasing returns means one unit of input gets you more than one unit of output; decreasing returns means that one unit of input gets you less than one unit of output).

Every producer maximises profit and every consumer maximises utility over their budget sets.

Under the above conditions, the equilibrium of the whole economy is characterised by a set of prices at which the excess demand is zero for every commodity, and producers make zero profit. These market-clearing prices are reached through a tâtonnement process (like an auction), in which "a fictitious price-setter" facilitates the price adjustment following a set of rules that resembles the way in which prices are reached in the real competitive economy.

Arrow also showed that a competitive economy in equilibrium is efficient and that any efficient allocation can be reached by having the government use lump-sum taxes to redistribute and then letting the market work. This basically means that the government should not control prices to redistribute income, but should do so directly.

Arrow & welfare economics

Both the works of Arrow discussed above, namely the impossibility theorem and general equilibrium fits nicely with his work on welfare economics. The impossibility theorem tells us that it is impossible to construct an aggregate social welfare function from individual preferences in the manner of the Bergson-Samuelson welfare function. The general equilibrium work led Arrow to the theorem about Pareto-optimality of a competitive equilibrium. We can then state the two fundamental theorems of welfare economics as follows:

Theorem one: A perfectly competitive equilibrium (where there are no externalities, everyone is a price taker and there is perfect information) will be Pareto-optimal (in the sense that no further exchange would make one person better off without making another worse off).

Theorem two: Any Pareto optimum can be supported as a competitive equilibrium for some initial set of endowments. The implication is that any desired Pareto optimal outcome can be supported; Pareto efficiency can be achieved with any redistribution of initial wealth. However, attempts to correct the distribution may introduce distortions, and so full optimality may not be attainable with redistribution.

Works of John Hicks

Hicks was educated at Oxford where he studied philosophy, politics and economics. From 1926 to 1935, Hicks was a lecturer at the London School of Economics. While he started as a labour economist, he moved on to mathematical applications in consumer demand and other areas in microeconomics. Hicks was greatly influenced by the great economist Lionel Robbins and his contemporaries included Hayek and Kaldor. From 1935 to 1938, he lectured at Cambridge University and after that at the University of Manchester. In 1946, he returned to Oxford, where he continued after his retirement.

Hick's most well-known work 'Value and Capital' was published in 1939, where he presented a general equilibrium model with aggregated markets for commodities, factors of production, credit and money. Hicks built his model on his earlier work on consumption and production and formulated conditions for multimarket stability and multiperiod analysis.

Hicks also introduced the concept of elasticity of substitution. This elasticity is the change in the ratio of the use of two goods with respect to the ratio of their marginal values or prices. The most common application is to the ratio of capital (K) and labour (L) used with respect to the ratio of their marginal products and/or their prices. Another application is to the ratio of two consumption goods with respect to the ratio of their marginal utilities or their prices. When applied to inputs, say labour and capital, the elasticity of substitution measures the degree and extent to which the two inputs can be substituted in response to a change in their prices (price here means wage rate for labour and rental value for capital).

Hicks also introduced the IS-LM model, which is a graphical depiction of Keynes general theory (General Theory of Employment, Interest and Money,1936). The IS-LM (IS stands for investment-saving and LM for liquidity preference-money supply) model basically depicts the equilibrium in the goods and services markets and the money market. The intersection of the IS and LM curves tells us the general equilibrium point in the goods and services markets and the money market. The Keynesian aggregate demand and aggregate supply (these are economy-wide macroeconomic variables) curves can be further derived from the IS-LM model.

Lastly, Hicks major contribution was in welfare economics, where he suggested a criterion to compare two economic conditions in terms of welfare gains (also called Hicks-Kaldor criterion). Hicks's fourth contribution is the idea of the compensation test. Simply, this criteria asked if gainers could compensate the losers fully and everyone was still better off. If the answer was 'yes', then the policy passed the 'Hicks compensation test,' even if the compensation was never paid, and was judged to be good.

Arrow, Hicks & public policy

The pioneering works of Sir John Hicks and professor Kenneth Arrow in general equilibrium and welfare economics are landmarks in economic theory. While Hicks began this work in the 1930s, Arrow pushed it forward in the 1950s and 60s. Hicks and Arrow, while similar in their choice of problems, had different methods of analysis.

The works of Arrow find resonance in many public policy areas. In particular, his contributions in welfare economics and his impossibility theorem have implications for a variety of public policy questions. We saw above, the application of the theorem in Condorcet's voting paradox. But equally, instead of candidates in an election, it can be applied to environmental questions such as choosing between alternative policy options to cut greenhouse emissions. Similarly, it can be applied to choosing between development projects or development models.

The more profound applications of Arrow's theorem have been seen in works of political economists. For example, William Riker has argued that Arrow's impossibility theorem undermined the logical foundations of 'populism,' the view that in a democracy, laws and policies ought to express "the will of the people" (Riker, 1982). This was because Arrow's theorem refutes the notion that the will of the people can be discovered through any voting mechanism without the outcome being either irrational or dictatorial. In other words, since there is no voting system that will generate a well-behaved social preference ordering without making one person a dictator, replacing first-past-the-post system in a parliamentary democracy with any other electoral system would not make any difference.

In response to Riker's work, his critics have questioned his use of Arrow's theorem on the grounds that not all configurations of preferences are likely to occur in practice. Others like Mckelvey (who proposed his chaos theorem) have attempted to rescue majority rule from cyclicity and instability. He found that under perfect information and rational foresight, there is no policy combination that cannot be beaten by another similar combination. This has an implication for decision making in political institutions. Anyone who controls the agenda can guide the voting trajectory to an outcome desired by the agenda setter. In other words, the majority vote can lead to a stable outcome under certain conditions.

The Arrow-Debreu model has also seen applications in financial and monetary markets (asset pricing model), international trade, etc. With a general equilibrium structure, the model is also applicable in evaluating the overall impact on resource allocation of policy changes in areas such as taxation, tariff, and price control.

Similarly, Hicks work has given us insights into many policy areas. The fields concerned are the theory of wages, value theory, welfare economics, the Keynesian revolution, monetary theory, growth and capital theory, and other topics. As we have seen above, he contributed to the field of economics with his IS/LM model, which summarised the Keynesian view of macroeconomics in graphical form. He also introduced the idea of elasticity of substitution, which showed that labour-saving technical progress does not reduce labour's share of income. In his book, 'Value and Capital', one of the first works on general equilibrium theory, Hicks showed that value could be understood without having to quantify utility. He also contributed to welfare economics, developing a way to compare the impact of different policies, regarding the one that produced sufficient gain to compensate for any losses and still provide benefit to be worthy of implementation.

Conclusion

Both Arrow and Hicks have made lasting and wide-ranging contributions to economic theory from general equilibrium to macroeconomics and welfare economics. Their works have found policy applications in international trade, project evaluation, taxation, environmental policy and even in areas of electoral reform.

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