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What is Differential Equation

Encyclopedia of Business Analytics and Optimization
A differential equation is an equation that involves the derivatives of a function as well as the function itself.
Published in Chapter:
Marketing Decisions with Reference Price Effect
Juzhi Zhang (University of Science and Technology of China, P.R. China), Erfeng Zhou (University of Science and Technology of China, P.R. China), Qinglong Gou (University of Science and Technology of China, P.R. China), and Susan Li (Adelphi University, USA)
Copyright: © 2014 |Pages: 10
DOI: 10.4018/978-1-4666-5202-6.ch133
Empirical research shows that there is a reference price existing in a consumer mind, which greatly affects the consumer's purchase decisions. However, what its impact is on a firm's advertising and pricing decisions has not been investigated. In this chapter we introduce a joint advertising and pricing model for a manufacturer-retailer supply chain, proposing an analytical framework to investigate the reference price's influence on these decisions. In detail, we assume that the reference price is affected by the brand advertising and retail price simultaneously and model its change in a differential equation. The manufacturer and retailer aim to maximize the present value of their profits. The way to solve this problem and future possible research on this issue are also suggested.
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