Question

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?

Answer 1

Answer: (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 = $\frac{300}{5}$

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 = $\frac{270}{5}$

p = 54

q = 2p ⇒ 2 × 54 = 108

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