Price Elasticity of Demand

Question

Using the price-demand function;𝑥=𝑓(𝑝)=4800−60𝑝 determine the price elasticity of demand when 𝑝=$48

Answer 1

x = 4800- 60p is the demand function, a downward sloping linear function

price elasticity of demand is the percentage change in quantity demanded divided by the percentage change in price, . or change in quantity times perc

point price elasticity of demand is the derivative of x with respect to p divided by x/p

for p=48, elasticity = -60(48)/(4800-60(48)) = 288/192 = 1.5

for p=45 elasticity = 9/7 or about 1.29

for p=40 elasticity = 1. It's the midpoint of the demand function line segment

above p=40, elasticity > 1

below p=40, elasticity <1

actually, the actual elasticity is negative, but since they're all (almost) always negative, the negative sign is conventionally dropped.

If you did use the negative sign

then above p=40, elasticity <-1

below p=40 elasticity >-1

p=80, elasticity = -60(80/(4800-60(80)) = (-)infinity

p=0 elasticity = 0

that's the range of price, from 0 to 80. At 80 no one buys anything. at 0 they stop buying at 4800

Answer 2

Elasticity of demand E(p) = -px'/x = -p(-60)/(4800 - 60p) = p/(80 - p);

If p = $48 then E(48) = 48/(80 - 48) = 48/32 = 1.5