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Introduction to Modern Economic Growth 5.7 Sequential Trading A final issue that is useful to discuss at this point relates to sequential trading Standard general equilibrium models assume that all commodities are traded at a given point in time–and once and for all That is, once trading takes place at the initial date, there is no more trade or production in the economy This may be a good approximation to reality when different commodities correspond to different goods However, when different commodities correspond to the same good in different time periods or in different states of nature, trading once and for all at a single point is much less reasonable In models of economic growth, we typically assume that trading takes place at different points in time For example, in the Solow growth model of Chapter 2, we envisaged firms hiring capital and labor at each t Does the presence of sequential trading make any difference to the insights of general equilibrium analysis? If the answer to this question were yes, then the applicability of the lessons from general equilibrium theory to dynamic macroeconomic models would be limited Fortunately, in the presence of complete markets, which we assume in most of our models, sequential trading gives the same result as trading at a single point in time More explicitly, the Arrow-Debreu equilibrium of a dynamic general equilibrium model involves all the households trading at a single market at time t = and purchasing and selling irrevocable claims to commodities indexed by date and state of nature This means that at time t = 0, households agree on all future trades (including trades of goods that are not yet produced) Sequential trading, on the other hand, corresponds to separate markets opening at each t, and households trading labor, capital and consumption goods in each such market at each period Clearly, both for mathematical convenience and descriptive realism, we would like to think of macroeconomic models as involving sequential trading, with separate markets at each date The key result concerning the comparison of models with trading at a single point in time and those with sequential trading is due to Arrow (1964) Arrow showed that with complete markets (and time consistent preferences), trading at a single point in time and sequential trading are equivalent The easiest way of seeing this 241