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

The Calibration of CES Production Functions

This note addresses some issues that arise when using 'normalized' CES production functions, an approach that has become popular in the literature. The results of Klump and de La Grandville (2000) provide a simple way to calibrate the parameters of the CES production function when the necessary data are available. But some of the other applications of normalized CES production functions appear problematic, especially when used to argue that productivity is increasing in the elasticity of substitution.CES production functions, elasticity of substitution, normalization

Heavy flavours: theory summary

I summarize the theory talks given in the Heavy Flavours Working Group. In particular, I discuss heavy-flavour parton distribution functions, threshold resummation for heavy-quark production, progress in fragmentation functions, quarkonium production, heavy-meson hadroproduction.Comment: 6 pages. Talk given at DIS 2005, XIII Workshop on Deep Inelastic Scattering, April 27-May 1, 2005, Madison, WI, U.S.

Fitting of Cobb-Douglas Production Functions: Revisited

The set of Cobb-Douglas production functions is usually fitted by first linearizing the models through logarithmic transformation and then applying method of least squares. However, this procedure is valid only when the underlying assumption of multiplicative error-terms is justified. Unfortunately, this assumption is rarely satisfied in practice and accordingly, the results obtained are of doubtful nature. Further, nonlinear estimation procedures generally yield parameter estimates exhibiting extremely high correlations, implying thereby that the parameters are not estimated independently. In this paper, use of expected-value parameters has been highlighted and the advantages of their use have also been discussed. Finally, the developed methodology has been illustrated by applying it to the wheat yield time-series data of Punjab.Production Economics,

Recent Progress on Perturbative QCD Fragmentation Functions

The recent development of perturbative QCD (PQCD) fragmentation functions has strong impact on quarkonium production. I shall summarize $B_c$ meson production based on these PQCD fragmentation functions, as well as, the highlights of some recent activities on applying these PQCD fragmentation functions to explain anomalous $J/\psi$ and $\psi'$ production at the Tevatron. Finally, I discuss a fragmentation model based on the PQCD fragmentation functions for heavy quarks fragmenting into heavy-light mesons.Comment: 13 pages and 6 Postscript figures, Standard LaTeX. Complete Postscript version can be found at http://www.ph.utexas.edu/~cheung/paper/hopkin/hopkin-hep.ps.gz Invited talk at PASCOS/HOPKINS 1995 Symposium, Johns Hopkins University, Baltimore, Maryland, March 22--25, 199

Allocating Time: Individuals' Technologies, Household Technology, Perfect Substitutes, and Specialization

In an efficient household if the spouses' time inputs are perfect substitutes, then spouses will “specialize" regardless of their preferences and the governance structure. That is, both spouses will not allocate time to both household production and the market sector. The perfect substitutes assumption implies that spouses' "unilateral" production functions (i.e., the household production function when only one spouse allocates time to home production) are closely related, satisfying a highly restrictive condition that I call "compatibility." I introduce the “correspondence assumption,” which postulates that the unilateral production functions in a newly formed household coincide with individuals’ production functions before they enter marriage. The correspondence assumption provides a plausible account of the genesis of household technology and simplifies its estimation. I introduce the "additivity assumption” which postulates that the household production function is the sum of the spouses' unilateral production functions and argue that additivity is implicit in much of the new home economics. Together, the correspondence and additivity assumptions imply that individuals’ technologies reveal the entire household technology. I show that perfect substitutes, additivity and concavity imply that the household production function is of the same form as the unilateral production functions, exhibits constant returns to scale, and depends on the spouses' total time inputs, measured in efficiency units.