Answer to Question #170202 in Microeconomics for janice joven

Question

The demand function for bicycles in Holland has been estimated to be Q = 2,000 + 15Y – 5.5P where Y in income in thousands of euros, Q is the quantity demanded in units, and P is the price per unit. When P = 150 euros and Y = 15(000) euros, determine the following:

a. Price elasticity of demand

b. Income elasticity of demand

 

Answer 1

Let's first find the quantity demanded at $P=150$ and $Y=15$:

$$Q=2000+15\cdot15-5.5\cdot150=1400.$$

(a) The price elasticity of demand can be found as follows:

$$\epsilon=\dfrac{P}{Q}\cdot\dfrac{dP}{dQ},$$ $$\epsilon=\dfrac{150}{1400}\cdot(-5.5)=-0.58.$$

(b) The income elasticity of demand can be found as follows:

$$\epsilon=\dfrac{I}{Q}\cdot\dfrac{dQ}{dI},$$ $$\epsilon=\dfrac{15}{1400}\cdot15=0.16.$$