A fractional optimal control problem for maximizing advertising efficiency

We propose an optimal control problem to model the dynamics of the communication activity of a firm with the aim of maximizing its efficiency. We assume that the advertising effort undertaken by the firm contributes to increase the firm's goodwill and that the goodwill affects the firm's sales. The aim is to find the advertising policies in order to maximize the firm's efficiency index which is computed as the ratio between "outputs" and "inputs" properly weighted; the outputs are represented by the final level of goodwill and by the sales achieved by the firm during the period considered, whereas the inputs are represented by the costs undertaken by the firm, fixed costs and advertising costs. The problem considered is formulated as a fractional optimal control problem. In order to find the optimal advertising policies we use the Dinkelbach's algorithm for fractional programming.

Painful Birth of Trade Under Classical Monopolistic Competition

In the standard Krugman (1979) non-CES trade model, several asymmetric countries typically lose from increasing trade costs. However, all countries transiently benefit from such increase at the moment of closing trade, under almost-prohibitive trade costs (i.e., near autarky, which is possible only under non-CES preferences). In other words, during trade liberalization the first step from autarky to trade is necessarily harmful. Our explanation rests on market distortion and business destruction effects

MATHEMATICAL METHODS IN ECONOMICS AND FINANCE

This is the special issue of Mathematical Methods in Economics and Finance devoted to the International Scientific Forum “Education and Entrepreneurship in Siberia: directions of Cooperation and Development of Regions” held in Novosibirsk (Russia) from October 12 to 13, 2018. The Forum was dedicated to the 50th anniversary of Novosibirsk State University of Economics and Managements. The purpose of the Forum was to contribute to the formation of a scientific environment that (1) stimulates research into the application of business-oriented educational technologies, taking into account regional development strategies; (2) creates favorable conditions for interdisciplinary studies of organizational, technological, institutional and behavioral factors in the functioning of the entrepreneurial university and training of business engineers. Mathematical Methods in Economics and Finance is a journal published by the Ca' Foscari Department of Economics since 2012, and formerly published by the Department of Applied Mathematics of the same University from 2006 to 2011. This journal replaces the former Rendiconti, a series in Italian issued annually from 1969 to 2005. The main features of the journal are: 1. Publication of original and unpublished papers that present theoretical results, methodological contributions, and applications in the areas of actuarial mathematics, financial mathematics, management science, mathematical economics, quantitative finance, and operational research. 2. Peer review process based on double-blind refereeing by at least two anonymous referees. 3. Inclusion in the MathSciNet list of journals and in the ANVUR (National Agency for the Evaluation of Universities and Research Institutes) list of journals. 4. Published papers online are free to access and download

The role of retailer's performance in optimal wholesale price discount policies

The main goal of this paper is to model the effects of wholesale price control on manufacturer’s profit, taking explicitly into account the retailer’s sales motivation and performance. We consider a stylized distribution channel where a manufacturer sells a single kind of good to a single retailer. Wholesale price discounts are assumed to increase the retailer’s motivation thus improving sales. We study the manufacturer’s profit maximization problem as an optimal control model where the manufacturer’s control is the discount on wholesale price and retailer’s motivation is one of the state variables. In particular in the paper we prove that an increasing discount policy is optimal for the manufacturer when the retailer is not efficient while efficient retailers may require to decrease the trade discounts at the end of the selling period. Computational experiments point out how the discount on wholesale price passed by the retailer to the market (passthrough) influences the optimal profit of the manufacturer

Increasing returns, monopolistic competition, and international trade: Revisiting gains from trade

CAT: EconomicsInternational audienceWe study the canonical Krugman (1979) trade model with non-CES preferences that yield autarky at finite trade costs. We prove a non-monotone impact of gradual trade liberalization. At first, near autarky, emerging trade reduces world welfare, while at free trade it becomes large enough to be beneficial (Krugman's result). This non-monotonicity persists under heterogenous firms. The harmful small-scale trade is explained by variable markups and underpriced imports, which become socially excessive. Unlike protectionists, we argue that “liberalization should go far”. On the other hand, we show that anti-dumping measures can be viewed as a remedy for the aforementioned imports distortion

Minimization of communication expenditure for seasonal products

We consider a firm that sells seasonal goods. The firm seeks to reach a fixed level of goodwill at the end of the selling period, with the minimum total expenditure in promotional activities. We consider the linear optimal control problem faced by the firm which can only control the communication expenditure rate; communication is performed by means of advertising and sales promotion. Goodwill and sales levels are considered as state variables and word-of-mouth effect and saturation aversion are taken into account. The optimal control problem is addressed by means of the classical Pontryagin Maximum Principle and the solution can be easily found solving, in some cases numerically, a system of two non linear equations. Moreover, a parametric analysis is performed to understand how the total expenditure in communication should be divided between advertising and sales promotion

The role of retailer's performance in optimal wholesale price discount policies

The main goal of this paper is to model the effects of wholesale price control on manufacturer's profit, taking explicitly into account the retailer's sales motivation and performance. We consider a stylized distribution channel where a manufacturer sells a single kind of good to a single retailer. Wholesale price discounts are assumed to increase the retailer's motivation thus improving sales. We study the manufacturer's profit maximization problem as an optimal control model where the manufacturer's control is the discount on wholesale price and retailer's motivation is one of the state variables. In particular in the paper we prove that an increasing discount policy is optimal for the manufacturer when the retailer is not efficient while efficient retailers may require to decrease the trade discounts at the end of the selling period. Computational experiments point out how the discount on wholesale price passed by the retailer to the market (pass-through) influences the optimal profit of the manufacturer.Wholesale price Sales motivation Optimal control