Question

6. Consider a linear demand curve Q=160-8P.

   a) (4 pts) What is the price elasticity of demand at p=5? Is it elastic, inelastic or unit elastic at this specific point?   b) (4 pts) At what price is demand unit-elastic (i.e. elasticity=-1)? Explain what does unit-elastic mean.

Answer 1

1. At p=5, elasticity = -0.33;   it is inelastic.
When p=5, q = 120 (160 - 8*5 = 120)
Elasticity at p=5:
Ed = (%change in quantity/ %Change in price) * (price/ quantity)
(%change in quantity/ %Change in price) is given in the deamdn function as -8. So, using point elasticity,
Ed = -8 * (5/ 120) = -0.33.
It is inelastic because the absolute value of elasticity is less than 1.

2. It is unit elastic at p =10, which is the midpoint of demand curve.
Y-intercept of demand curve is when q=0, which is 0 = 160 - 8*20)
Midpoint of demand curve would be where p = 20/2 = 10
We can check it out if elasticity is unit at this point.
Quantity is 80 @p=10 (160 - 8*10 = 80)
   -8 * 10/80 = -1

Unit elasicity indicattes that when there is a chanee in price, quantiy demanded changes in the opposite direction by proportionate amount.For example, if price increases fby 10%, quantity demanded decreases by 10%.