Excerpt

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.

### Introduction

Price fluctuation is a phenomenon we frequently encounter in our daily life. Therefore, Price Elasticity of demand is a useful indicator of the relation between a change in price and the willingness to purchase a certain product. In general it is proposed that an increase in price of a certain product results in a decrease in demand, however this concept is also dependent on several factors such as the availability of substitute products, the indispensability of products or brand loyalty.

Moreover, Price Elasticity of demand provides information about the revenue of the product sold at a certain price, as revenue and Price Elasticity are calculated with the same variables, namely the price p and the quantity demanded q. In regard of the elasticity of the product, an increase in price can entail both an increase and decrease in revenue, differing always in relation to its demand. Consequently, it is of immense importance to companies to model demand functions in order to foretell the implications of a change in price on demand and revenue.

The aim of this exploration is to look at the concept of Price Elasticity of demand and its effect on revenue in order to determine whether a product‘s price is elastic, inelastic or of unit elasticity. Thereby I will explore different types of demand functions and model their optimum price as well as maximum revenue. This concept is eventually applied to a real life situation.

To begin with, the responsiveness of demand to price change can be measured as a ratio of the percentage rate of change in the quantity that is demanded to the percentage rate of change in the price of the good. [1]

Defining the quantity demanded as q and the price for the good demanded as p, and relying on the equation that the rate of change of a quantity:

[Formulas are omitted from this preview]

Hence, Price Elasticity of Demand

[Formulas are omitted from this preview]

As it can be assumed that an increase in price will lead to a decrease in demand and that q > 0 and p > 0, E(p) has to be negative, thus .

[Formulas are omitted from this preview]

As mentioned before, the Price Elasticity is largely dependent on the good, therefore there are 3 different levels of demand. [2]

- In case that E(p) > 1, the demand is said to be elastic, indicating that the percentage increase in price is less than the resulting percentage decrease in demand, hence demand is sensitive to price change

- In case that E(p) < 1, the demand is said to be inelastic, indicating that the percentage increase in price is greater than the resulting percentage decrease in demand, hence demand is rather insensitive to price change

- In case that E(p) = 1, the demand is said to be of unit elasticity, indicating that percentage change in price and demand are relatively equal [3]

In order to connect E(p) and R(p) in one equation, the rate of change of revenue with respect to price has to be found by differentiating R(p)=pxq implicitly with respect to p while q is a constant, using the product rule.

[…]

[1] http://www.ncssm.edu/courses/math/apcalcprojects/econ/Elasticity_of_Demand_Student_Handout.pdf

[2] http://www.ncssm.edu/courses/math/apcalcprojects/econ/Elasticity_of_Demand_Student_Handout.pdf

[3] http://www.economicshelp.org/blog/7019/economics/examples-of-elasticity/

- Quote paper
- Stefanie Mücka (Author), 2014, Price Elasticity of Demand and its effect on Revenue, Munich, GRIN Verlag, https://www.grin.com/document/276575

Publish now - it's free

Comments