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Elasticity of Demand

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Wize University Calculus 1 Textbook > Applications of Differentiation for Business & Econ

Elasticity of Demand

3 Activities

Assume that the price pp and the demand qq of a certain good are related by the equation
q=2e1−p+4p+1q = 2e^{1- p} + \frac{4}{p + 1}
a) Find the price elasticity ε(p)\varepsilon(p) as a function of pp .

b) If p=1p = 1 , does increasing the price slightly increase the revenue?

c) Find the second order Taylor polynomial for the revenue function R(p)R(p) centered at p=1p = 1 .

d) If the demand is increasing at a rate of 24 units per week when the price is one dollar, find the rate of change of the price.
More Elasticity of Demand Questions:
Elasticity of Demand
Assume the relationship between the price (pp) and the number sold (qq) is p2+q2=98p^2+q^2=98
For what value of pp, is the revenue maximized?
Elasticity of Demand
The demand for Tit-Tat chocolate bars at price p is f(p)=20−1.5pf(p)=20-1.5p
a) Write a formula for the elasticity of demand at price p
b) compute the elasticity of demand at price p=1p=1 and p=8p=8 .
Elasticity of Demand
The price and quantity of certain commodity are related by the following expression:
2p2+3q2=3602p^2 + 3q^2 = 360
Elasticity of Demand
Assume the relationship between the price of pizza (pp) and the number of them sold (qq) is p2+q2=98p^2+q^2=98
For what value of pp, is the revenue maximized?