Question

The market demand for brand X has been estimated as

Qx = 1,500 - 3Px - 0.05I - 2.5Py + 7.5Pz

where Px is the price of brand X, I is per-capita income, Py is the price of

brand Y, and Pz is the price of brand Z. Assume that Px = $2, I = $20,000,Py = $4, and Pz = $4. a. With respect to changes in per-capita income, what kind of good is

brand X?

b. How are brands X and Y related?

c. How are brands X and Z related?

d. How are brands Z and Y related?

e. What is the market demand for brand X?

Answer 1

Equation of demand function is Q = a - bP

a) A rise in per capita income will reduce Qx due to negative sign in front of I which means that good is a inefrior good.

b) As both of them have negative sign. rise in price of Y will reduce quantity consumed of good X which means they are complement to each other ad consumed together.

c) As Pz have positive sign in front of it, rise in price of z will raise demand of Qx which means they are substitute to each other. Consumer buy whichever is cheaper.

d) Rise in price of z means that there must be rise in price of y by three times of z to keep demand of X constant. These goods are substitute to each other.

e) Qx = 1,500 - 3 * 2 - 0.05 * 20,000 - 2.5 * 4 + 7.5 * 4 = 514