Problem II: A competitive market is defined by the following demand and supply f
ID: 1205935 • Letter: P
Question
Problem II: A competitive market is defined by the following demand and supply functions: P = 210 2Q and P = 30 + Q. a) Calculate total welfare on this market (5400) b) Calculate total welfare and the deadweight loss if a price floor of $80 is introduced by the government (5400, 0) c) Calculate consumer surplus, producer surplus, and the deadweight loss if a price floor of $110 is introduced by the government (2500, 2750, 150) d) Calculate total welfare and the deadweight loss if a price ceiling of $70 is introduced by the government (4800, 600) e) Calculate total welfare and the deadweight loss if a price ceiling of $100 is introduced by the government (5400, 0) f) Calculate total welfare and the deadweight loss if a per unit tax of $30 is introduced by the government (5250, 150) g) At this tax level, calculate the marginal effect of a tax increase on deadweight loss? (10)
Explanation / Answer
a. Total Welfare = producer + consumer Surplus
Equilibrium Market price , Where Demand = Supply
P = 210 2Q = 30 + Q
Q = 60
and P = 90
Consumer Surplus = 1/2(y-intercept of demand - price)*Q
= 1/2(210 - 90)*60
= 3,600
Producer surplus = 1/2(price - y-intercept of Supply curv)*Q
= 1/2(90 - 30)*60
= 18,000
Total welfare = 36,000 + 18,000
= 54,000
b. Since price is 90 and price floor is 80 , it will not effect the equilibrium price , hence Total Welfare will remain at
54,000 and there will be no dead weightt loss.
c. price floor of $110
So, New price = 110
new Quantity supplied = 110 - 30 = 80
Quantity demanded = 210/2 - 110/2 = 50
Consumer surplus =
= 1/2(y-intercept of demand - price)*Q
= 1/2(210 - 110)*50
= 2,500
Producer surplus = 1/2(price - y-intercept of Supply curve)*Q supplied - 1/2(quantity supplied - Eq. Q)(price cieling - Marker Price)
= 1/2(110 - 30)*80 - 1/2(80 - 50)(110-90)
= 2,750
Dead weight loss = 1/2(equilibriumQ - Quantity supplied )(price cieling - Marker Price)
= 1/2(60 - 50)(110-90) + 1/2(60 - 50)(90- 80)
= 300/2
= 150
e Since the price cieling $100 is above the market price of $90 , there will be no change in ewuilibrium
and hence total welfare = 54,000
and Dead weight loss = 0
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