Question

Suppose the demand for good X has estimated to be:

lnQ_x^d = 10 - 4lnP_x – 2lnP_y – 4 lnM.

a. How can you tell that demand is downward sloping?

b. What is the cross-price elasticity of demand between good X and Y?

c. Are good X and Y substitutes or complements?

d. Is good X a normal or an inferior good?

e. If the price of good X increased by 2 percent, what would happen to the quantity demanded of good X?

Answer 1

a) This is because the own price elasticity of demand is -4 and this is negative which shows that quantity demanded is inversely related to price. Hence demand curve is downward sloping

b) It is -2 (as shown by the coefficient of lnPy)

c) Cross price elasticity is negative so X and Y are complements

d) Income elasticity is -4 and is negative so X is an inferior good

e) Quantity demanded will decrease by -4*2 = 8 % because own price elasticity of demand is -4.