Necessary and sufficient conditions for Pareto optimality are derived for problems involving convex criteria and convex constraints. For a wide class of convex functions, the characterization of Pareto optimality is given in terms of systems of linear programs, which, under suitable regularization conditions, reduce to a single linear program. The consideration of a system of linear programs and their duals leads naturally to a system of partial prices associated with a Pareto optimum. (Author)

WE PROPOSE to study here the relationship between externalities, public goods, and returns to scale. The ideas behind this connection are certainly not new. Indeed, Marshall frequently spoke of external economies and diseconomies of scale. He had in mind situations in which expansion of one firm conferred external benefits on the industry and led to increased efficiency of the agggregate operations. The quantitative relationship has been explored from time to time in a number of specific contexts. For example, Arrow [1] showed that the presence of learning by doing (a public good) introduced an element of increasing returns into the aggregate relationships. We are after a general quantitative relationship. Our first task is to construct a general measure of returns to scale for multiproduct technologies. A starting point is the theory of homogeneous functions (see Henderson and Quandt [8] for a general discussion of this subject). The degree of returns to scale of a homogeneous function is naturally measured by its degree of homogeneity. This measure is used as a matter of course by economists (see for example, Intriligator [9]) and can be extended to multiproduct technologies. We certainly want our measure to agree with this one for homogeneous functions. However, it is very unlikely that the aggregate technology can be represented by a function which is homogeneous of any particular degree. Thus, we must find a measure which will apply to more general functions. In the next section we develop a measure which has some intuitive appeal and can be shown to be the ideal measure under some circumstances. It can be thought of as a generalization of the well known elasticity of production used by many authors (see, e.g., Carlson [2], Frisch [4] or Johansen [10]). We will show that our measure is a natural one from several different points of view. Having developed a measure, we will use it to quantify the returns to scale effect of public goods (or bads). This is done in Sections 5 and 6.

This paper develops an econometric model of production technology in terms of the ante-ex description of production possibilities. Ex ante and ex post substitution characteristics are allowed to differ from one another and parametric representations are derived which provide arbitrary second-order approximations to the true underlying characteristics. Nested in the maintained model are the specialized putty-putty, puttyclay, and structures of technology; and hypothesis tests are developed to test for the applicability of these specialized structures. An example is provided in which the hypotheses that fossil fuel electricity generation can be characterized by putty-clay or clay-clay technologies are tested using data drawn from individual United States electricity generating plants.

The low estimates of the income elasticity of housing demand obtained when individual households are the unit of observation are theoretically reconciled with the high estimates obtained when metropolitan-wide averages are used. The omission of the housing price term biases the ungrouped (whether stratified by metropolitan areas or not) estimate(s) downward and the grouped estimate upward. The inclusion of a metropolitan-wide average housing price term worsens the downward bias of the unstratified ungrouped estimate. The corresponding price elasticity estimate is biased upward (toward zero). These results are interpreted in terms of the theory of residential location and used to explain the empirical evidence. For the evidence considered, the true income and price elasticities are approximately .75 and -.75, respectively.

[The Rawlsian maximin is defined for situations involving risk and applied to growth with an uncertain technology. Existence and uniqueness are discussed and it is shown to unambiguously lead to at least the same savings as under certainty.]

is misleading if o-2 $ o-2 and n, and n2 are both small, where Y, and Xi are ni x 1 and ni x k observation matrices, ,li is a k x 1 coefficient matrix, and ei is an n, x 1 error matrix for i=1,2. A valid asymptotic test may easily be obtained by regarding (1) and (2) as seemingly unrelated regression equations. In this paper we establish a small sample test which may readily be extended to a test of some of the coefficients in the two regressions.