Question

Suppose the demand curve for a product is given by Q = 11 - 2P + 3Ps Where P is the price of the product and Ps is the price of a substitue good. The price of the substitute good is $2.80. Suppose P = 1.20. what is the price elasticity of demand? What is the cross price elasticity of demand?

Answer 1

Answer: (a) -0.1412

(b) 0.4941

Explanation:

Q = 11 - 2P + 3Ps

Where,

P - price of the product

Ps - price of a substitute good

Ps = $2.80

P = $1.20

$\frac{dQ}{dP} = -2$

$\frac{dQ}{dPs} = 3$

$Price\ elasticity\ of\ demand= \frac{P}{Q}\times\frac{dQ}{dP}$

$Price\ elasticity\ of\ demand= \frac{1.20}{11-2P+3Ps}\times(-2)$

$Price\ elasticity\ of\ demand= \frac{1.20}{11-2\times1.2+3\times2.8}\times(-2)$

                                                     = $\frac{-2.4}{17}$

                                                     = -0.1412

$Cross\ Price\ elasticity\ of\ demand= \frac{Ps}{Q}\times\frac{dQ}{dPs}$

                                                                 = $\frac{2.8}{17}\times3$

                                                                 = 0.4941