Phenotype phase plane analysis is a linear optimization procedure which can be used to study the value of the objective function (a desired phenotype) as two variables (external substrates) vary simultaneously. Existing methods for phenotype phase plane analysis are based on computing shadow prices as defined in classical linear programming duality theory. Since different bases may produce diff...

In a financial market with a continuous price process and proportional transaction costs we investigate the problem of utility maximization of terminal wealth. We give sufficient conditions for the existence of a shadow price process, i.e. a least favorable frictionless market leading to the same optimal strategy and utility as in the original market under transaction costs. The crucial ingredi...

This paper tests the proposition that Russian nominal prices were distorted to support bankrupt sectors, which is the foundation of the virtual economy. The input-output table for 1997 is converted from rubles into dollars using American prices as shadow values. Three sectors belonging to the intermediate stage of processing are found to have negative value-added. An alternative measure of the ...

We consider a geographic optimization problem in which we are given a region R, a probability density function f(·) defined on R, and a collection of n utility density functions ui(·) defined on R. Our objective is to divide R into n sub-regions Ri so as to “balance” the overall utilities on the regions, which are given by the integrals ̃ Ri f(x)ui(x) dA. Using a simple complementary slackness a...

This study examines the effect of banning antimicrobial growth promoters on efficiency in the production of weaned and slaughter (finishing) pigs. We focus on the reaction of producers and production efficiency. We evaluate the estimated output and input shadow prices relative to market prices to analyse producer reactions and capture the impact on production efficiency by evaluating the effect...

Stoichiometric models of metabolism, such as flux balance analysis (FBA), are classically applied to predicting steady state rates - or fluxes - of metabolic reactions in genome-scale metabolic networks. Here we revisit the central assumption of FBA, i.e. that intracellular metabolites are at steady state, and show that deviations from flux balance (i.e. flux imbalances) are informative of some...

The estimation of the value of carbon emissions has become a major research and policy topic since the establishment of the Kyoto Protocol. The shadow price of CO2 provides information about the marginal abatement cost of this pollutant. It is an essential element in guiding environmental policy issues, since the CO2 shadow price can be used when fixing carbon tax rates, in environmental cost-b...

In the preceding chapter on sensitivity analysis, we saw that the shadow-price interpretation of the optimal simplex multipliers is a very useful concept. First, these shadow prices give us directly the marginal worth of an additional unit of any of the resources. Second, when an activity is ‘‘priced out’’ using these shadow prices, the opportunity cost of allocating resources to that activity ...