 The notions of Pareto improvements and Pareto efficiency might seem useless, because economic policies almost always have both winners and losers. Mainstream economists have nevertheless found these concepts useful in two ways. First, they have proved two theorems concerning properties of perfectly competitive equilibria (Arrow 1968). The first theorem says that equilibria in perfectly competitive markets are Pareto optimal, and the second says that any Pareto optimal allocation, with whatever distribution of income policy makers might prefer, can be achieved as a perfectly competitive market equilibrium, provided that one begins with just the right distribution of endowments among economic agents. The first theorem has been regarded as underwriting Adam Smith’s view of the invisible hand (Arrow and Hahn 1971, preface; Hahn 1973). This interpretation is problematic, because no economy has ever been or will ever be in perfectly competitive equilibrium. The second theorem provides some justification for the normative division of labor economists prefer, with economists concerned about efficiency and others concerned about justice. The thought is that the second theorem shows that theories of just distribution are compatible with reliance on competitive markets. The two fundamental theorems of welfare economics go some way toward explaining why mainstream economists, whether they support laissez-faire policies or government intervention to remedy market imperfections, think of perfectly competitive equilibria as ideals. But the significance of the theorems is debatable, since actual markets differ significantly from perfectly competitive markets and, when there are multiple market imperfections, the “theory of the second best” shows that fixing some of the imperfections may lead the society away from a perfectly competitive equilibrium (and diminish efficiency and welfare) rather than toward one (Lipsey and Lancaster 1956–7).