Question

If the demand for a product is given by (P) = 2250 + 18p - 11p2, find the point elasticity when the price is $5. What type of elasticity is involved and how will a price increase affect total revenue?

Answer 1

Point elasticity of demand = (dq/dp)*(p/q)

The demand equation is given as :

q = 2250 + 18p - 11p²

dq/dp = 0 + (18*1) - (11*2)p = 18 - 22p

When price = $5, (dq/dp) = 18 - (22*5) = -92

When price = $5, q = 2250 + (18*5) - 11(5)² = 2065

Therefore, point elasticity of demand = -92 * (5/2065) = -0.22

The absolute value of the elasticity is less than 1, therefore the demand is price inelastic.

Inelastic demand means even if price increases by a relatively larger amount, quantity demanded by a relatively small amount. In case of inelastic demand, percentage change in Quantity demanded is less than the percentage change in the price. Therefore, when demand is inelastic, change in the price and change in the total revenue moves in the same direction. Therefore, a price increase will increase the total revenue.