Question

Question 3: Suppose the inverse demand function for good X is given as P=100-2Q. Find

the price elasticity of demand when Q=40 units. What can you say about the type of the good

looking at the price elasticity of demand that you calculate in the first part?

Answer 1

$P=100-2Q\\ Solve for Q\\ Q=\frac{100-P}{2}\\ Q= 50-\frac{P}{2}\\ Q=40units\\ 40=50-\frac{P}{2}\\ P=20\\ E_p=\frac{dQ}{dP}×\frac{P}{Q}\\ Where \frac{dQ}{dP}= slope=50\\ E_p=50×\frac{20}{40}=25\\$

The demand is elastic; i.e the quantity changes faster than price. 1% increase in price= 25% increase in the quantities demanded.