Question

Suppose the demand curve for a product is given by Q=10-2P+Ps1, where P is the price of the product and Ps is the price of a substitute good. the price of the substitute good is $2.00.
a. Suppose P=$1.00, what is the price elasticity of demand? what is the cross-price elasticity of demand?

b. Suppose the price of the good, P, increases to $2.00. Now, what is the price elasticity of demand, and what is the cross-prices elasticity of demand?

Answer 1

Solution:

a. Find quantity demanded when P = $1.00 and $P_{s}$= $2.00

Q = 10 - 2(1) + 2 = 10

Price elasticity of demand = $\frac{p}{q}$  ΔQ / ΔP = $\frac{1}{10}$ (-2) = $-\frac{2}{10}$ = -0.2

Cross-price elasticity of demand = $\frac{P_{s} }{q}$ ΔQ / Δ$P_{s}$ = $\frac{2}{10}$ (1) = 0.2

b. When P = $2.00

             Q = 10 - 2(2) + 2 = 8

Price elasticity of demand = $\frac{p}{q}$ ΔQ / ΔP = $\frac{2}{8}$ (-2) = $-\frac{4}{8}$ = -0.5

Cross-price elasticity of demand = $\frac{P_{s} }{q}$ ΔQ / Δ$P_{s}$ = $\frac{2}{8}$ = 0.25