Price Elasticity of Demand and its effect on Revenue

Seminar paper from the year 2014 in the subject Mathematics - Applied Mathematics, grade: 2, Leipzig International School, language: English, abstract: I have chosen to focus my mathematical exploration on applications of Calculus in Business situations. To begin with, I was looking for an interesting real life situation I could base my investigation on. Having lived in an economically well developed country like Germany for almost my whole life, the accessibility to a wide range of products and their varying appeal to the consumer are subconsciously part of my daily life. The fact that some products are enormously demanded by society whereas others aren¿t that successful on the market gave me the idea to investigate how demand is influenced by outside factors. Thereby I discovered the concept of Price Elasticity of Demand which is useful in indicating the responsiveness of the demand of a certain good to a change in its price. I thus decided to explore the different levels of Price Elasticity of demand, namely elastic, inelastic and unit elasticity, and their effect on revenue by means of both an exponential and a quadratic demand function. Finally I applied the acquired knowledge to a highly demanded and very popular product in Germany, which is coffee, and modeled its change in demand dependent on varying prices as well as outside factors such as brand loyalty and income.