Question

The NeverLost Company produces and sells popular and widely used portable GPS units for recreational use. Researchers at NeverLost have estimated that the point price elasticity of demand facing the company under current conditions is -1.2 while the point income elasticity is 2.2 and the point cross-price elasticity of demand with respect to the price of a competitor’s GPS unit is 1.4. NeverLost’s current sales are 2.2 million units per year.

1. What are expected sales next year once a new tax law takes effect that is expected to lower the disposable income of consumers by 1%?
2. After the tax law goes into effect, your competitor announces a 5% increase in the price of their GPS unit. What are NeverLost’s expected sales after the competitor’s new price takes effect?
3. In order to capture a significantly larger share of the market for these units, NeverLostwants to increase its sales next year by 6%. By how much must NeverLostchange its price to accomplish this goal?

Answer 1

Given

Point Income elasticity of demand=e_i=2.20

Point Price elasticity of demand=e_p=-1.2

Point cross price elasticity of demand=e_c=1.40

Current Sales=Q=2.2 million units

a)

Change in disposable income=-1%

Expected sales=Initial sales*(1+change in income*Point income elasticity of demand)

=Q*(1+change in disposable income*ep)

=2.2*(1+(-1%)*2.2)

=2.1516 million units

b)

Change in competitor's price=+5%

Expected sales=Q*(1+change in disposable income*ep)*(1+change in competitor's price*cross price elasticity of demand)

=2.2*(1+(-1%)*2.2)*(1+(+5%)*1.4)

=2.302212 million units

c)

Expected change in sales=+6%

Required Price change=Change in sales/ep=6%/(-1.2)=-5%

Company should decrease the price by 5%