Demystifying Sraffa’s Theory of Value in the Light of Arrow and Debreu

This paper compares the models of Arrow and Debreu [1954] and Sraffa [1960], and concludes that (1) the models are informationally distinct conceptions of a capitalist economy, (2) they support radically distinct – though complete and entirely correct – theories of value, (3) the prices in the two theories are different both in terms of definitions and values, (4) in Sraffa‘s model it is impossible to define constant returns to scale, while in Arrow-Debreu this property is admissible, and (5) in Arrow-Debreu the interpersonal income distribution is determined whereas in Srafa‘s model the distribution of income between workers and capitalists is undetermined.constant returns to scale, theory of value, relations of production, counterfactual information, prices, exchange values, income distribution, general equilibrium, capital, marginal product

A theory of dynamic tariff and quota retaliation

This paper establishes relationships between static Nash equilibria and dynamic Markov perfect equilibria of tariff and quota retaliation games. In supermodular games where tariffs are strategic complements, the steady state of every, symmetric Markov perfect equilibrium must have lower tariffs than in the static equilibrium. If tariffs are strategic substitutes, tariffs in the dynamic game are higher than in the static equilibrium. The supermodular case is extended to quota competition. Instead of the well-known non-equivalence between tariff and quota retaliation outcomes under complete myopia, in some circumstances, free trade can be supported in the steady state of a Markov perfect equilibrium, regardless of whether policies employed are quotas or tariffs. We reach the conclusion that the effect of introducing dynamics crucially depends on whether the policy instruments employed by the countries are strategic substitutes or complements irrespective of whether they are tariffs or quotas.Foreign trade policy; Tariff; Quota; Retaliation; Dynamic Game; Markov perfect equilibrium; Supermodular games

International economic theory and politics: world structure before, during and after the early 21st Century Crisis

In his Inquiry into the Nature and Causes of the Wealth of Nations Adam Smith (1776) considered the phenomenon of division of labor so enormously significant for the creation of a nation’s wealth that he devoted the first three chapters of his book to an investigation of this process. This is an ongoing process of greater and greater specialization, and there have been episodes of faster pace, and some slower pace, but the process has never stopped so far in human history. However, this process, carried far enough, can eventually results in episodes, sometimes painfully prolonged, in which there emerges a divergence between the distribution of quantities supplied of horizontally-differentiated distinct types of human capital embodied in different persons and distribution of quantities demanded of persons with distinct skills by employers, private or public, or otherwise. This sustained divergence of supply and demand distributions of distinct skill categories may be called Embodied Human Capital Unemployment. This is a phenomenon not seen before in social history, simply because specialization of persons in very narrowly partitioned skill types that are, effectively, non-transferable across different persons, had never occurred before in our history. That is why it is a new phenomenon, and it is time we understood what it is. Moreover, it has an abiding character, a stationary state nature, and (1) thus should emerge as an equilibrium phenomenon in a fully specified general equilibrium model of a market economy, and (2) should be of concern to us, since it is going to be around for a while as we all live our lives. I illustrate the relevance of this new concept of unemployment to the U.S economy in the first decade of the 21st Century. This helps achieve a deeper understanding of the current global economic crisis, and inter alia to identification of potentially effective, and potentially ineffective, public policies. Additional implications are (b) the emergence of a new social formation that may be called World Market Capitalism, which has a vastly different economic foundation of relations of production and income distribution compared to the pre-21st Century economic system that then existed in the world, and (c) the transition from a uni-polar world, with the U.S.A. as the single center of power, after the fall of the Soviet Union in 1989, to a multi-polar world order at the end of the first decade of the 21st Century, with implications for strategic interaction and coalition formation. (403 words)Marxian; Keynesian; human capital; unemployment; economic; financial; political; crisis; globalization; capitalism; international capital mobility; division of labor; Adam Smith; USA; China; India; Japan

Constant returns to scale and economic theories of value

Jointly with Erkko Etula, Paul Samuelson [2006] claims that the “Leontief – Sraffa matrix equations for input/output must obey constant returns to scale”. However, in an unrelated work, Amartya Sen [2003] claims that Sraffa’s [1960] “analysis does not need any assumption of constant returns to scale.” In fact, Sraffa’s model cannot satisfy this property because it is impossible to define constant returns to scale in it. This claim is considerably stronger than Sen’s. The property of constant returns to scale is significant because it constitutes a line of demarcation between distinct, though interrelated, economic theories of value. (96 words)Constant returns to scale; Theory of Value; Relations of production; Counterfactual information; Exchange Values; Classical Political Economy; Neoclassical theory; Leontief technology

On two theories of value and distribution

This paper compares the theory of value and distribution of Arrow and Debreu [1954] with that of Sraffa [1960]. I consider such versions of the two models that capture their salient features, without aiming at the greatest possible generality, so as to isolate the precise nature of the differences between the two conceptions of the same economic reality, and inter alia, to quarantine both the sources and the entailments of the differences in the two theories that respectively purport to determine the values of commodities and distribution of income in society. Both theories are complete and consistent. Sraffa’s model is based exclusively on factual information, so it achieves less in terms of determining endogenous variables. The Arrow-Debreu is based on counterfactual information regarding additional production scenarios that are unobserved, in addition to the factual information that Sraffa has, so it achieves more by way of determination of endogenous variables. In terms of entailments, in Sraffa's theory there is an insufficiency of determinants in the economic grounds of society, thereby requiring the political component of society to also play an influential role in the joint determination of values and distribution. In the Arrow-Debreu model this determination is made complete solely in the economic sphere of society, rendering this theory purely economic, rather than political-economic, as in Sraffa. Both the information content difference at source, and the purely-economic versus political-economic difference in the entailments of what it takes to determine values and distribution, render the two theories radically different. In addition, (1) the prices in the two theories are different both in terms of definitions and values, and (2) since Sraffa’s model has only one set of numbers on the observed production of commodities by means of commodities and labor for a single year, it is impossible to define constant returns to scale, while in the Arrow-Debreu model, this property is admissible, and possible to define, because their model’s information base is sufficiently larger than Sraffa’s. Further, Sraffa’s theory is invariant to (a) the interpretation of prices – market-clearing, long-period, or whatever, (b) multiplicity of profit rates across industries, instead of a uniform rate of profit, and (c) presence or absence of general aggregate demand functions for commodities, and is (d) more general than the Arrow-Debreu theory because it is based on weaker assumptions, in the sense of a strictly smaller information set, so that it is only to be expected that the Arrow-Debreu theory would be capable of determining more endogenous variables in the model of an economy. (416 words)theory of value; income distribution; general equilibrium; capital; constant returns to scale; rate of profit

Real economy causes of the Great Deprivation of early 21st Century

The American economy has undergone a dramatic structural change in the first decade of the 21st Century. The real-economy causes of this transformation, and their expression via the real estate market and its financial derivatives’ market, and their final manifestation in world financial markets, is explained using traditional economic theory. A three-sector Walrasian general equilibrium model, and a non-Walrasian temporary equilibrium model with fixed prices and quantity constraints, are both utilized to explain the real-economy causes of the observed stylized facts. Some remedies that will likely work, and ones that will not, are also identified. (95 words)financial crisis, credit crunch, mortgage backed securities, fiscal policy, monetary policy, the U.S. economy, outsourcing, international capital mobility

Market-dependent production set

A country’s production possibility frontier or PPF is defined as the boundary of its economy’s production set in the net output space for a given technology and fixed quantities of primary factors of production. In general equilibrium theory, exogenous changes in technology or primary-factor supplies alter equilibrium prices; however, government-policy induced domestic relative commodity price changes do not alter the shape of an economy’s production set. We show that, under international capital mobility, which is empirically significant, the shape of a country’s production set does, in fact, depend on market forces and this shape can be manipulated by government policy.general equilibrium; production possibility frontier; production set; international capital mobility; economic policy

Existence of a Pareto optimal social interaction outcome with non-binary preferences

We prove the existence of a Pareto optimal state of a society with non-binary personal preferences. To our knowledge, this is the weakest set of conditions under which the existence of a Pareto optimal state has been proven. In our theory everybody in society engages in maximization as a personal act of volitional choice based on non-binary preferences, as in Sen (1997). The resultant equilibrium belongs to a unanimity-based nonempty social maximal set. Our generalization exposes the fact that such equilibria support discrimination, which is a surprising, though serious, indictment of relying exclusively on the Pareto principle in social evaluation.Non-binary choice; Non-binary preferences; Maximization; Pareto optimality

Demystifying Sraffa’s Theory of Value in the Light of Arrow and Debreu

concludes that (1) the models are informationally distinct conceptions of a capitalist economy, (2) they support radically distinct – though complete and entirely correct – theories of value, (3) the prices in the two theories are different both in terms of definitions and values, (4) in Sraffa‘s model it is impossible to define constant returns to scale, while in Arrow-Debreu this property is admissible, and (5) in Arrow-Debreu the interpersonal income distribution is determined whereas in Srafa‘s model the distribution of income between workers and capitalists is undetermined

On Non-binary Personal Preferences in Society, Economic Theory and Racial Discrimination

This paper examines some of the consequences for economic theory of the replacement of binary personal preferences by non-binary personal preferences in an Arrow-Debreu society as in Debreu (1959), and reaches the conclusion that there is both much damage to existing theory and greater opportunity for providing formal explanations of such phenomena as discrimination, personal freedoms and power, among others, which are impossible to explain at a formal level on the basis of an economic theory that is founded on a choice theory that is based exclusively on binary relational personal preferences