Assume the demand function for basketballs is given by QD 1

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?

Solution

QD = 150 3P + 0.1I

QS = 2P

I=$1500

At equilibrium

Qs = Qd

150 3P + 0.1I = 2P

150 – 3P+.1*1500=2P

5P=300, Thus, P=60

Q=150-3*60+.1*1500=150-180+150 = 120

Thus, at equilibrium,

Q = 120, P = $60

If income tax @ 20% is applied

Now, new disposable income I = 1500*(1-20%) = $1200

Again, new equilibrium will be established.

150 3P + 0.1I = 2P

150-3P+.1*1200=2P

270=5P

P=$54

Q = 2P = 2*54 = 108

Thus, new equilibrium will have Price = $54 and Quantity = 108