Consider a market defined as follows: Demand: Q = 400 – P Supply: Q = 2P...
Consider a market defined as follows: Demand: Q = 400 – P Supply: Q = 2P – 200 Additionally, a negative externality of $75 per unit is associated with the traded good.
How many units should be traded in this market to maximize benefit to society?
If the government does not implement the policy you proposed in part (b), what is the size of the deadweight loss?
Homework Answers
Answer
The negative externality is internalized to produce at the socially optimum level by taxing the market.
Adding the tax to the supply curve by converting the supply curve to inverse supply
Q=2P-200
2P=Q+200
P=0.5Q+100+75=0.5Q+175
converting back
0.5Q=P-175
Q=2P-350
equating to demand curve to find the equilibrium
400-P=2P-350
3P=750
P=250
Q=400-250=150 units
150 units should be traded in this market to maximize the benefit to society
===
Without tax, the market is in market equilibrium at Qd=Qs
400-P=2P-200
3P=600
P=200
Q=400-200=200
===
DWL=0.5*externality per unit * change in output
=0.5*75*(200-150)
=1875
The DWL is $1875
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