Discrete Choice Prox-Functions on the Simplex

We derive new prox-functions on the simplex from additive random utility models of discrete choice. They are convex conjugates of the corresponding surplus functions. In particular, we explicitly derive the convexity parameter of discrete choice prox-functions associated with generalized extreme value models, and specifically with generalized nested logit models. Incorporated into subgradient schemes, discrete choice prox-functions lead to a probabilistic interpretations of the iteration steps. As illustration, we discuss an economic application of discrete choice prox-functions in consumer theory. The dual averaging scheme from convex programming adjusts demand within a consumption cycle.

A New Wavelet Tool to Quantify Non-Periodicity of Non-Stationary Economic Time Series

We introduce a new wavelet tool, the windowed scale index, to study the degree of non-periodicity of time series. The windowed scale index is based on some recently defined tools, such as the windowed scalogram and the scale index. This novel measure is appropriate for non-stationary time series whose characteristics change over time and, therefore, it can be applied to a wide variety of disciplines. Furthermore, we revise the concept of the scale index and pose a theoretical problem: it is known that if the scale index of a function is not zero then it is non-periodic, but if the scale index of a function is zero, then it is not proved that it has to be periodic. This problem is solved for the particular case of the Haar wavelet, reinforcing the interpretation of the windowed scale index as a useful tool to quantify non-periodicity. In addition, the applicability of this wavelet-based measure is illustrated through several examples, including an economic application which compares the non-periodicity of two major commodities in the world economy, such as crude oil and gold. Finally, we discuss the relationship between non-periodicity and unpredictability, comparing the windowed scale index with the sample entropy.

Finding Vector Critical Points on Hadamard Manifolds: Nonsmooth Case

The aims of this paper are twofold. First, it is shown, for the first time, which types of nonsmooth functions are characterized by all vector critical points as being efficient or weakly efficient solutions of vector optimization problems in constrained and unconstrained scenarios on Hadamard manifolds. This implies the need to extend different concepts, such as the Karush--Kuhn--Tucker vector critical points and generalized invexity functions, to Hadamard manifolds. The relationships between these quantities are clarified through a great number of explanatory examples. Second, we present an economic application proving that Nash's critical and equilibrium points coincide in the case of invex payoff functions.

Use of Healthy Life Expectancy to Estimate Future Provision of Household and Personal Use Services

Healthy life expectancy (HLE) combines a measure of morbidity with life expectancy to measure the average years of healthy life (YHL) projected for a cohort based on age, sex, and perhaps race or other characteristics, developed by public health officials to set goals and measure accomplishments in improving public health. Some forensic economists have adopted this data source to project how far into the future lost household or personal services should appropriately be claimed in case of death or injury. The measure of YHL adopted for the U.S. by the Department of Health and Human Services is not well suited to this forensic economic application; in the author's opinion, it is likely to overstate years of lost provision of household or personal services for an average member of the cohort; whether or not this opinion is correct, use of HLE invites vigorous cross-examination. The note concludes with suggested modification that would remove two objections to use of the measure for forensic economic application.

Application of optimal control theory on optimal advertising expenditure in monopoly

Presented paper is being focused on Optimal control theory, Variation Calculus and its economic application. Aim of this research paper is to shortly describe Optimal control and Variation Calculus and to present how can we deal with these type of issues. The last part of this paper is presenting possible economic application of Optimal control, based on the maximization of profit in monopoly while introducing new product on the market. Our control variable is the advertising rate, which affects the profit of monopoly through advertising expenditures and as a state variable was the market share defined.