Assume the demand function for basketballs is given by qd = 150 −3p + 0.1i, where p = price of a basketball, and i = average income of consumers. also, assume the supply of basketballs is given by qs = 2p. if the market for basketballs is perfectly competitive, and the average income is equal to $1,500, what is the equilibrium price and quantity? what if a 20 percent income tax is introduced?

(1) Equilibrium price = 60 and Equilibrium quantity = 120, when I = $1500.

(2)  Equilibrium price = 54 and Equilibrium quantity = 108, when I = $1200.

Explanation:

(1) When Average income (I) = $1500

At equilibrium, QD = QS

150 - 3p + 0.1I = 2p

150 - 3p + 0.1 × 1500 = 2p

5p = 300

p =

p = 60

q = 2p ⇒ 2 × 60 = 120

Hence, p and q are equilibrium price and equilibrium quantity, respectively.

(2) If 20% income tax is introduced then Average income (I) = $1500 - 20% of  $1500 ⇒ $1500 - $300 = $1200

At equilibrium, QD = QS

150 - 3p + 0.1I = 2p

150 - 3p + 0.1 × 1200 = 2p

5p = 270

p =

p = 54

q = 2p ⇒ 2 × 54 = 108

Hence, p and q are equilibrium price and equilibrium quantity, respectively.