## Production and the First Welfare Theorem

Recall that in the case of a pure exchange economy, a competitive equilibrium is Pareto efficient. This fact is known as the First Theorem of Welfare Economics. Does the same result hold in an economy with production? The diagrammatic approach used above is not adequate to answer this question, but a generalization of the algebraic argument we provided in Chapter 31 does nicely. It turns out that the answer is yes: if all firms act as competitive profit maximizers, then a competitive equilibrium will be Pareto efficient.

This result has the usual caveats. First, it has nothing to do with distribution. Profit maximization only ensures efficiency, not justice! Second, this result only makes sense when a competitive equilibrium actually exists. In particular, this will rule out large areas of increasing returns to scale. Third, the theorem implicitly assumes that the choices of any one firm do not affect the production possibilities of other firms. That is, it rules out the possibility of production externalities. Similarly, the theorem requires that firms' production decisions do not directly affect the consumption possibilities of consumers; that is, that there are no consumption externalities. More precise definitions of externalities will be given in Chapter 33, where we will examine their effect on efficient allocations in more detail.

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