Question

In this question, we are calculating the Welfare Effects of Free Trade vs a Ban on Imports

QD(USA) = D(P) = 50 - 2P

QS(USA) = S(P) =     8 + 4P

a.In this example, what is the equilibrium quantity and price?

b.What is consumer surplus created by the price and quantity determined in #1a?

c.However, if the world price for this good were $5.70, how much would be imported and how much would be produced domestically?

d.What is the decrease in consumer surplus created by eliminating free trade?

e. What is the increase in producer surplus created by eliminating free trade?

f. What is the decrease in welfare caused by the elimination of free trade?

Answer 1

a) Set QD=QS to find the equilibrium price and quantity

50-2P=8+4P

50-8=4P+2P

42=6P

P=42/6 = 7

Q=50-2(7) = 36

b) Y axis intercepts would be:

When QD=0, P=50/2 =25

When QS=0, P=8/4=2

Consumer surplus = 0.5*36*(25-7) = 324

c) When the world price is 5.7

QD=50-2P = 50-2(5.7) = 38.6 is the quantity demanded domestically

QS=8+4P = 8+4(5.7) = 30.8 is the quantity produced domestically

Imports = 38.6-30.8 = 7.8

d) New CS with trade= 0.5*38.6*(25-5.7) = 372.49

When the free trade is eliminated, decrease in consumer surplus = 372.49-324 = 48.49

e) Initial PS = 0.5*36*(7-2) = 90

New PS witn trade = 0.5*30.8*(5.7-2) = 56.98

When the free trade is eliminated,increase in producer surlplus = 90-56.98 = 33.02

f) Total welfare with free trade = CS+PS = 372.49+56.98 = 429.47

Total welfare when there is no trade = CS+PS = 324+90 = 414

Decrease in welfare = 429.47-414 = 15.47