The modern conception of general equilibrium is provided by a model developed jointly b Kenneth Arrow, Gerard Debreu and Lionel W McKenzie in the 1950s. 

Gerard Debreu presents this model in Theory of Value (1959) as an axiomatic model. following the style of mathematics promoted by Bourbaki. Three important interpretations of the terms of the theory have been often cited. First, suppose commodities are distinguished by the location where they are delivered. Then the Arrow- Debreu model is a spatial model of, for example, international trade. Second, suppose commodities are distin- guished by when they are delivered. That is, suppose all markets equilibrate at some initial instant of time. 

Agents in the model purchase and sell contracts, where a contract specifies, for example, a good to be delivered and the date at which it is to be delivered. The Arrow-Debreu model of intertemporal equilibrium contains forward markets for all goods at all dates. No markets exist at any future dates. Third, suppose contracts specify states of nature which affect whether a commodity is to be delivered: "A contract for the transfer of a commodity now specifies, in addition to its physical properties, its location and its date, an event on the occurrence of which the transfer conditional. This new definition of a commodity allows one to obtain a theory of risk free from any probability concept...

" These interpretations can be combined. So the complete Arrow-Debreu model can be said to apply when goods are identified by when they are to be delivered, where they are to delivered and under what circumstances they are to be delivered, as well as their intrinsic nature.
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