This paper considers value functions for maximization problems where the objective function is maximized subject to several constraints. I show that such value functions exhibit diminishing marginal rates of substitution (MRS) between the resource endowments which define the constraints. For the...

This paper provides expressions for solutions of a one-dimensional global optimization problem using an adjoint variable which represents the available one-sided improvements up to the interval “horizon.” Interpreting the problem in terms of optimal stopping or optimal starting, the solution...

Since Paul Samuelson introduced the theory of revealed preference, it has become one of the most important concepts in economics. This chapter surveys some recent contributions in the revealed preference literature. We depart from Afriat's theorem, which provides the conditions for a data set to...

The paper presents an extended version of the consumer choice problem. Different from the standard model, prices are not fixed but arise from Walrasian interactions of total demand and a stylized supply function for each of the goods. Three different types of evolutionary algorithms are set up...

The aim of this paper is to explore several features concerning the generalized marginal rate of substitution (GMRS)when the consumers utility maximization problem with several constraints is formulated as a quasi-concave programming problem. We show that a point satisfying the first order...

We provide a revealed preference analysis of the transferable utility hypothesis, which is widely used in economic models. First, we establish revealed preference conditions that must be satisfied for observed group behavior to be consistent with Pareto efficiency under transferable utility....

We develop a revealed preference approach to analyze non-unitary consumption models with intrahousehold allocations deviating from the cooperative (or Pareto efficient) solution. At a theoretical level, we establish revealed preference conditions of household consumption models with varying...

The transferable utility hypothesis underlies important theoretical results in household economics. We provide a revealed preference framework for bringing this (theoretically appealing) hypothesis to observational data. We establish revealed preference conditions that must be satisfied for...

We provide a revealed preference analysis of the transferable utility hypothesis, which is widely used in economic models. First, we establish revealed preference conditions that must be satisfied for observed group behavior to be consistent with Pareto efficiency under transferable utility....