The paper argues that, in the absence of lump-sum payments, a Pareto optimum is achievable by marginal-cost pricing and/or competitive equilibrium only when the boundary of the social production set happens to be linearly homogeneous near that optimal solution. Thus, contrary to widespread belief, both diminishing and increasing returns can be incompatible with achievement of optimality via parametric prices. Generally, the best that any set of fixed prices can achieve is the Ramsey solution constrained by Walras's law. The resulting welfare loss is the price society must pay for using a price system to allocate resources.

The paper argues that, in the absence of lump-sum payments, a Pareto optimum is achievable by marginal-cost pricing and/or competitive equilibrium only when the boundary of the social production set happens to be linearly homogeneous near that optimal solution. Thus, contrary to widespread belief, both diminishing and increasing returns can be incompatible with achievement of optimality via parametric prices. Generally, the best that any set of fixed prices can achieve is the Ramsey solution constrained by Walras's law. The resulting welfare loss is the price society must pay for using a price system to allocate resources.

It has long been suggested that moves toward equality can have serious disincentive effects and, after a point, lead to unacceptable losses in real income.' We will now offer some theoretical grounds for believing that an approximation to equality achieved via the traditional instruments-transfer payments and progressive taxation-will cause an income loss far more serious than many of us have realized. We will prove that under a set of reasonable assumptions, any attempt to guarantee absolute equality of incomes using only progressive income taxes and transfers for the purpose must, at least in theory, reduce society's output to zero! However, we do not conclude from this that the search for very much increased equality is quixotic. Rather, we take this as a criticism of the means so far used for the purpose. What is called for is an exercise in imagination and ingenuity, to find some alternative ways to go about this quest. We will then show explicitly and examine an alternative procedure that, at least in theory, can achieve any desired degree of equality without necessarily exacting a serious loss in output, and will end by discussing briefly the possibility of practical approximations to such an arrangement.