We consider the class of linear programs that can be formulated with infinitely many variables and constraints but where each constraint has only finitely many variables. This class includes virtually all infinite horizon planning problems modeled as infinite stage linear programs. Examples include infinite horizon production planning under time-varying demands and equipment replacement under t...

For utility maximization problems under proportional transaction costs, it has been observed that the original market with transaction costs can sometimes be replaced by a frictionless shadow market that yields the same optimal strategy and utility. However, the question of whether or not this indeed holds in generality has remained elusive so far. In this paper we present a counterexample whic...

High speed networks are highly dynamical systems. Large deviation techniques have been employed to characterize their loss probability. Large deviation is also used to calculate shadow prices of quality of service of a scalable network queue with respect to buffer size B, capacity C and arrival rate N.In this paper we prove that these shadow prices are independent of (B,C,N) parameters. Gibbs D...

Manyeconomicmodels andoptimizationproblemsgenerate (endogenous) shadow prices—alias dual variables or Lagrange multipliers. Frequently the “slopes” of resulting price curves—that is, multiplier derivatives—are of great interest. These objects relate to the Jacobian of the optimality conditions. That particular matrix often has block structure. So, we derive explicit formulas for the inverse of ...

Empirical tests of the relationship between international competitiveness and the severity of environmental regulations are hampered by the lack of pollution abatement cost data for nonU.S. countries. The theory of the firm suggests that environmental stringency can be measured by the difference between a polluting input’s shadow price and its market price. We make a first attempt at quantifyin...

We present a generalization of the average shadow price in 0-1-Mixed Integer Linear Programming problems and its relation with bottlenecks including the analysis relative to the coefficients matrix of resource constraints. A mathematical programming approach to find the strategy for investment in resources is presented. KeywordsMixed Integer programming, Average shadow price, Bottlenecks, Resou...

a r t i c l e i n f o JEL classification: C14 D24 O13 O44 Q53 Q56 Keywords: Shadow price Emissions trading Directional distance function Marginal abatement cost Coal power plant Shadow prices, also termed marginal abatement costs, provide valuable guidelines to support environmental regulatory policies for CO 2 , SO 2 and NO x , the key contributors to climate change. This paper complements the...

Shanghai, one of the most developed cities in China, is implementing a pilot regional carbon emission trading scheme. Estimating the marginal abatement costs of CO2 emissions for the industrial sectors covered in Shanghai's emission trading scheme provides the government and participating firms useful information for devising compliance policies. This paper employs multiple distance function ap...