Question

The demand curve for a product is given by QXd = 1,200 - 3PX - 0.1PZ where Pz = $300.

a. What is the own price elasticity of demand when Px = $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? Instruction: Enter your response rounded to two decimal places. Own price elasticity: Demand is: If the firm prices below $140, revenue will:

b. What is the own price elasticity of demand when Px = $240? Is demand elastic or inelastic at this price? What would happen to the firm’s revenue if it decided to charge a price above $240? Instruction: Enter your response rounded to one decimal place. Own price elasticity: Demand is: If the firm prices above $240, revenue will:

c. What is the cross-price elasticity of demand between good X and good Z when Px = $140? Are goods X and Z substitutes or complements? Instruction: Enter your response rounded to two decimal places. Cross-price elasticity: Goods X and Z are:

Answer 1

Demand function is QXd = 1,200 - 3PX - 0.1PZ

a. Own price elasticity of demand is given by PED = price coefficient of X * PX/QX.

Here, Pz = $300 and Px = $140.

Then PED = -3*140/(1200 - 3*140 - 0.1*300)

PED = -0.56

Since absolute value of PED is less than 1, the demand is considered inelastic at this price

There will be a decline in firm’s revenue if it decided to charge a price below $140 this is because when demand is inelastic, price and revenue move in same direction. Revenue will decline

b.Own price elasticity of demand is given by PED = price coefficient of X * PX/QX.

Here, Pz = $300 and Px = $240.

Then PED = -3*240/(1200 - 3*240 - 0.1*300)

PED = -1.6

Since absolute value of PED is more than 1, the demand is considered elastic at this price

There will be an increase in firm’s revenue if it decided to charge a price above $240 this is because when demand is elastic, price and revenue move in opposite direction. Revenue will decline

c. What is the cross-price elasticity of demand between good X and good Z when Px = $140?

CPE of demand between good X and good Z = price coefficient of Z * PZ/QX

CPE = -0.1*300/(1200 - 3*140 - 0.1*300)

= -0.04

Since elasticity is negative, goods X and Z are complements.