Question

1. Consider the market for apples where the market demand is given by QD = 30 − 2p and market supply is given by QS = P Find the market equilibrium. What will be the quantity traded if an excise tax of $2/unit is imposed? Calculate the deadweight loss of the excise tax.

2. Consider the same market from question #1. Consider that you are the only seller in that market and you produce apple for a marginal cost of $0/unit. How much price would you charge? What will be the deadweight loss?

Answer 1

(1)

(a) In pre-tax equilibrium, QD = QS.

30 - 2P = P

3P = 30

P = 10

Q = 10

(b) The $2 tax will shift supply curve leftward by $2 at every output, and new supply function becomes

QS = P - 2

Equating with QD,

30 - 2P = P - 2

3P = 32

P = 10.67 (Price paid by buyers = market price)

Price received by sellers = 10.67 - 2 = 8.67

Q = 10.67 - 2 = 8.67

(c) Deadweight loss = (1/2) x Unit tax x Change in quantity = (1/2) x $2 x (10 - 8.67) = $1 x 1.33 = $1.33

(2)

As a monopolist I would equate Marginal revenue (MR) with MC.

QD = 30 - 2P

2P = 30 - QD

P = 15 - 0.5QD

Total revenue (TR) = P x QD = 15QD - 0.5QD²

MR = dTR/dQD = 15 - QD

15 - QD = 0

QD = 15

P = 15 - (0.5 x 15) = 15 - 7.5 = 7.5

In competitive equilibrium, setting P = MC,

15 - 0.5QD = 0

0.5QD = 15

QD = 30

P = MC = 0

Deadweight loss = (1/2) x Change in Price x Change in Quantity = (1/2) x (7.5 - 0) x (30 - 15) = (1/2) x 7.5 x 15 = 56.25