Question

Demand function for a cola-type soft drink in general is q= 20 – 2P, where Q stand
for quantity and P stands for price.

a. Calculate point elasticities at prices of 5 and 9. Is the demand curve elastic or inelastic at these points?

b. Calculate arc elasticity at the interval between P = 5 and P = 6.

Answer 1

Point elasticity (Ed).
E_d=δQ/δP * P/Q , where δQ/δP= -2
P₁=5, Q₁=20-2*5=10;
P₂=9, Q₂=2;
Point elasticity at the price P₁: E_d1 = -2 * 5/10= -1. Unitarily elastic demand.
Point elasticity at the price P₂: E_d2 = -2 * 9/2= -9. The demand curve is elastic.
Arc elasticity (Ed).
E_d=δQ/δP * (P₁+P₂)/(Q₁+Q₂ )

P₁=5, Q₁=10;
P₂=6, Q₂=8;
E_d1= -2/1 * 11/18= -11/9=-1.22
The demand curve is elastic.