Question

Part A. 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.

Part B. 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

Qd = 30 - 2P

Qs = P

Equilibrium condition

Demand = Supply

30 - 2P = P

30 = 3P

P = 30 /3

= 10

Q = 10

Excise Tax 2 per unit.

New Supply curve:

Qs =(P-2)

Equilibrium:

30 - 2P=P-2

32 = 3P

P = 32 /3

= 10.66

Q = 10.66 - 2

= 8.66

Deadweight loss = o.5(Base)Height

= 0.5 (10.66 -10)(10 -8.66)

= 0.44

Monopoly Equilibrium,:

MR = MC

MC = 0

Q = 30 -2P

P = 15 - 0.5Q

TR = 15Q - 0.5Q^2

MR = 15 - Q

15-Q = 0

Q = 15

P =15 - 0.5(15)

= 15 - 7.5

= 7.5

Dead weight loss:

Competitive output P = MC

15 -0.5Q = 0

Q =30

Deadweight loss = 0.5 (30 -15)(7.5 -0)

= 56.25