The weekly demand for a small personal computer is $2,000 when the price of a computer is $100. A 10% price cut caused the demand to increase to 2,400 computers per week. Assume that the demand equation is linear.

a. Find the point elasticity of demand at the new price.

b. Approximate the change in demand if the price is increased by an additional 10% over the first 10% increase.

c. Will the second price increase cause the revenue to increase or decrease?

Question a

Let P denotes the price of a computer and Q denotes the weekly demand for a small personal computer. We know that Q = 2000 when P = 100. We also know that Q = 2400 when P declines from 100 to 90 (10% decline in price). The point elasticity of demand can be calculated as follows:

[Math Processing Error]E=(Q1−Q0P1−P0)(P0Q0)=(2400−200090−100)(1002000)=−2

Question b

Suppose the price has increased by 10%. An additional 10% increase in price implies that the overall increase in price is (1 + 0.1)(1 + 0.1) - 1 = 0.21 = 21%. Using the point elasticity of demand calculated in Question a, the demand will decrease by [Math Processing Error]2×21%=42%. That is, the approximate change in demand is 42%.

Question c

The second price increase will cause the revenue to decrease, since the demand is elastic. In particular, the elasticity of demand of -2 implies that 1% increase in price will lead to 2% decrease in quantity demanded. As the quantity demanded declines more than the increase in price, the revenue will decrease as a result of the increase in price.