C. Henry, A. Zylberberg; Planning Algorithms to deal with Increasing Returns, The Review of Economic Studies, Volume 45, Issue 1, 1 February 1978, Pages 67

AS Professor Samuelson has recently redemonstrated, the following two problems cannot be logically separated: (1) how much of a public good it is efficient to produce, (2) how in justice the costs of the good are to be borne by the public.' Even under the stringent assumptions of constant marginal cost for the public good, and constant marginal utility of income for all consumers, allocative efficiency in no way logically determines how cost burdens should be shared even when the income distribution, before taxes and before public good production, is considered just. As a result, public authorities are generally denied the luxury of sequential, independent, or separable decision rules for allocative efficiency and distributional equity. An omniscient decision maker, interested in maximizing social welfare as defined by some social welfare function, must simultaneously determine the quantity of the public good to produce, the share of the cost burden so generated to be charged each person, and income transfers among individuals or groups. There is, however, one tax-allocation-and-public-good-supply decision rule, namely, the Lindahl voluntary exchange decision rule which leaves the initial (i.e., pre-tax, pre-benefit) income distribution unchanged, and hence can argue for separation between allocation and distribution decisions. These conclusions derive from the following propositions: 1) Where the costs of public good production must be shared by individuals in predetermined proportions (by customs or fixed tax laws, etc.) and no direct income transfers are allowed among individuals, the decision of how much public good to supply is ethical. At the supply feasible under these conditions, the MC of production need not equal the sum of individual MRS's. In this case the restrictions on transfers and on variable tax rates generally insure that the best feasible outcome is not Pareto-efficient. 2) If either direct lump-sum income transfers or variable cost sharing tax burdens are allowed, such that the authority deciding how much public good to produce can also vary one of these two factors, then the choice of a final utility distribution dictates a unique Pareto optimal public goods supply decision. This public goods supply will be efficient in the sense that MC = X MRS; it need not be true, however, that each individual's MRS equals that individual's marginal cost share. Relaxing either of the restrictions in 1, insures that Pareto efficiency in resource allocation can be achieved. There exists an infinite number of Pareto optimal public goods supplies each related to a particular utility distribution. 3) If both tax shares are variable and lumpsum income transfers are allowed, then the optimal utility distribution is Pareto-efficient (i.e., MC = I MRS) and can be achieved as a Lindahl solution to the public good supply problem (i.e., MRS of each individual equals that individual's marginal cost share). In this case also, as in 2, the utility distribution choice determines a particular level of public goods supply. One purpose of this paper is to demonstrate the foregoing propositions. This is done in part I with the aid of ordinary box diagrams. In part II the demonstration is repeated with simple mathematics. Part III summarizes the implications of the foregoing for the theory of taxation and expenditure and particularly for the viability of the theory of the public household as containing separable allocation and distribution branches.

We analyze competition among informed traders in the continuous‐time Kyle(1985) model, as Foster and Viswanathan (1996) do in discrete time. We explicitly describe the unique linear equilibrium when signals are imperfectly correlated and confirm the conjecture of Holden and Subrahmanyam (1992) that there is no linear equilibrium when signals are perfectly correlated. One result is that at some date, and at all dates thereafter, the market would have been more informationally efficient had there been a monopolist informed trader instead of competing traders. The relatively large amount of private information remaining near the end of trading causes the market to approach complete illiquidity.