A CHARACTERIZATION OF HOMOGENEOUS PRODUCTION FUNCTIONS

This paper states a theorem that characterizes homogeneous production functions in terms of the ratio of average to marginal costs. The theorem claims that a production function is homogeneous of degree k if and only if the ratio of average costs to marginal costs is constant and equal to k. In order to prove the theorem two lemmas -with theoretical value of their own- are demonstrated before hand: the first one establishes that a production function is homogeneous of degree k if and only if its elasticity of scale is k; the second one determines the conditions on the production function under which any input vector can be an optimum, for some choice of the price vector and the level of production.Elasticity of scale, homogeneous production functions, returns to scale, average costs, and marginal costs

On the Curvature of the Reporting Function from Objective Reality to Subjective Feelings

I suggest the idea of a reporting function, r(.), from reality to feelings. The ‘happiness’ literature claims we have demonstrated diminishing marginal utility of income. I show not, and that knowing r(.)’s curvature is crucial. A quasi-experiment on heights is studied.height, diminishing marginal utility, money, concavity

Hybrid Copula Estimators

An extension of the empirical copula is considered by combining an estimator of a multivariate cumulative distribution function with estimators of the marginal cumulative distribution functions for marginal estimators that are not necessarily equal to the margins of the joint estimator. Such a hybrid estimator may be reasonable when there is additional information available for some margins in the form of additional data or stronger modelling assumptions. A functional central limit theorem is established and some examples are developed.Comment: 17 page

A class of random fields on complete graphs with tractable partition function

The aim of this short note is to draw attention to a method by which the partition function and marginal probabilities for a certain class of random fields on complete graphs can be computed in polynomial time. This class includes Ising models with homogeneous pairwise potentials but arbitrary (inhomogeneous) unary potentials. Similarly, the partition function and marginal probabilities can be computed in polynomial time for random fields on complete bipartite graphs, provided they have homogeneous pairwise potentials. We expect that these tractable classes of large scale random fields can be very useful for the evaluation of approximation algorithms by providing exact error estimates.Comment: accepted for publication in IEEE TPAMI (short paper