The demand curve for a product is given by 12003P0 P where

The demand curve for a product is given by = 1,200-3P-0, P. where P -$300 a. What is the own price elasticity of demand when P $140? Is demand elastic or inelastic at this price? What would happen to the firm\'s revenue if it decided to charge a price below $140? What is the own price elasticity of demand when elastic or inelastic at this price? What would happen to the firm\'s revenue if it decided to charge a price above $240? b. $240? Is demand c. What is the cross-price elasticity of demand between good X and good z when = $140? Are goods X and Z substitutes or complements?

Solution

When Pz = $300,

Qdx = 1,200 - 3Px - (0.1 x 300) = 1,200 - 3Px - 30

Qdx = 1,170 - 3Px

(a) When Px = 140,

Qdx = 1,170 - (3 x 140) = 1,170 - 420 = 750

Own-Price elasticity = (dQdx / dPx) x (Px / Qdx) = - 3 x (140 / 750) = - 0.56

Since absolute value of elasticity is less than 1, demand is inelastic. With inelastic demand, a decrease in price (below $140) will decrease total revenue.

(b) When Px = 240,

Qdx = 1,170 - (3 x 240) = 1,170 - 720 = 450

Own-Price elasticity = (dQdx / dPx) x (Px / Qdx) = - 3 x (240 / 450) = - 1.6

Since absolute value of elasticity is higher than 1, demand is elastic. With elastic demand, an increase in price (above $140) will decrease total revenue.

(c) When Px = 140, Qdx = 750

Cross-price elasticity = (dQdx / dPz) x (Pz / Qdx) = - 0.1 x (300 / 750) = - 0.04

Since cross price elasticity is negative, X and Z are complements.