5. The demand curve for a product is given by Qdx = 1,000 – 2Px +.02Pz where Pz

Question

5. The demand curve for a product is given by Qdx = 1,000 – 2Px +.02Pz where Pz = $400. (Hint: If you’re not comfortable with the calculus alternatives, compute Q at the given prices, then again with a 1% increase in price. Then figure percentage change in Q over the percentage change in P, %Q/%P).

a. What is the own price elasticity of demand when Px = $154? Is the demand elastic or inelastic? What would happen to the firm’s revenue if it decided to charge a price below $154?

b. What is the own price elasticity of demand when Px = $354? Is the demand elastic or inelastic? What would happen to the firm’s revenue if it decided to charge a price below $354?

c. What is the cross-price elasticity of demand between good X and good Z when Px = $154? Are good X and good Z substitutes are complements?

Please show and double check all work!

Explanation / Answer

With Pz = 400,

Qdx = 1000 - 2Px + (0.02 x 400) = 1000 - 2Px + 8

Qdx = 1008 - 2Px

(a) When Px = 154, Qdx = 1008 - (2 x 154) = 1008 - 308 = 700

Own price elasticity = (dQdx / dPx) x (Px / Qdx) = - 2 x (154 / 700) = - 0.44

Since absolute value of elasticity (0.44) is less than 1, demand is inelastic. With inelastic demand, a fall in price will lower the total revenue.

(b) When Px = 354, Qdx = 1008 - (2 x 354) = 1008 - 708 = 300

Own price elasticity = - 2 x (354 / 300) = - 2.36

Since absolute value of elasticity (2.36) is more than 1, demand is elastic. With elastic demand, total revenue rises as price falls.

(c) Cross price elasticity = (dQdx / dPz) x (Pz / Qdx) = 0.02 x (400 / 700) = 0.01

Since cross price elasticity is positive, X and Z are substitutes.

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