What is the cross-price elasticity of demand

Question

Question 1: The demand curve for a product is given by Q^d_x =1,000 – 2pPx +.02P_z where P_z = $400.

a. What is the own price elasticity of demand P_x = $154? Is demanded elastic or inelastic at this price? 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 P_x = $354? Is demanded elastic or inelastic at this price? 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 P_x = $154? Are goods X and Z substitutes or compliments?

Question 2: Suppose the demand function for a firm’s product is given by

In Q^d_x = 3 – 0.5 In P_x  - 2.5 In P_y + In M  + 2 In  A

Where

P_x = $10
P_y = $4
M = $20,000, and
A = $250

a. Determine the own price elasticity of demand, and state whether demand is elastic, inelastic, or unitary elastic.

b. Determine the cross-price elasticity of demand between good X and good Y, and state whether these two are substitutes or complements.

c. Determine the income elasticity of demand, and state whether good X is a normal or inferior good.

d. Determine the own advertising elasticity of demand.