Question

The supply curve for T-shirts is given by the equation P = 8Q+2. The demand curve is given by the equation P =40-5Q. At a price to buyers of $20/shirt,

1)how much of a surplus or a shortage will there be?

2)At a price to buyers of $12/shirt, how much of a surplus or a shortage will there be?

3) Suppose that the government imposes a sales tax of $15 per T-shirt. What is the market price for the buyer?

4) Suppose that the government imposes a sales tax of $15 per T-shirt. What is the final price for the seller?

Answer 1

From demand function, Quantity demanded (Qd) = (40 - P)/5 = 8 - 0.2P

From supply function, Quantity supplied (Qs) = (P - 2)/8 = 0.125P - 0.25

(1)

When P = 20,

Qd = 8 - 0.2 x 20 = 8 - 4 = 4

Qs = 0.125 x 20 - 0.25 = 2.5 - 0.25 = 2.25

Since Qd > Qs, there will be a shortage.

Shortage = Qd - Qs = 4 - 2.25 = 1.75

(2)

When P = 12,

Qd = 8 - 0.2 x 12 = 8 - 2.4 = 5.6

Qs = 0.125 x 12 - 0.25 = 1.5 - 0.25 = 1.25

Since Qd > Qs, there will be a shortage.

Shortage = Qd - Qs = 5.6 - 1.25 = 4.35

(3)

The tax will shift supply curve leftward by $15 at every output and new supply function is

P = 8Q + 2 + 15 = 8Q + 17

Equating with demand function,

40 - 5Q = 8Q + 17

13Q = 23

Q = 1.77

P = 40 - (5 x 1.77) = 40 - 8.85 = 31.15 (Price paid by buyers)

(4)

Price received by sellers = Price paid by buyers - Unit tax = 31.15 - 15 = 16.15