General equilibrium theory attempts to explain the behavior of supply, demand, and prices in a whole economy with several or many interacting markets, by seeking to prove that a set of prices exists that will result in an overall (or "general") equilibrium. General equilibrium theory contrasts to the theory of partial equilibrium, which only analyzes single markets. As with all models, general equilibrium theory is an abstraction from a real economy; it is proposed as being a useful model, both by considering equilibrium prices as long-term prices and by considering actual prices as deviations from equilibrium.
It is considered a state of efficiency, because in general equilibrium demand equals supply and there is no deadweight loss.
The efficiency, in the sense of a Pareto Optimum, means, that the existed situation can't be improved without the loss in any other factor.
The scientist proved the existence of a general competitive equilibrium, because it is a simplified model, which clearly explains the behavior of supply, demand, and prices in a whole economy with several or many interacting markets.
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