Question

Consider a country that is small in the market of a particular good, facing an international price of 30. In this country, the demand is given by D = 400 - 5P and the supply is given by S = -200 + 10P.

1) What is the total welfare when there is free trade?

2) What is the welfare change caused by a 5 dollar import tariff?

3) Should this country impose the 5 dollar tariff? (Yes/No)

4) Now assume that the production of this good generates a positive externality. The more of this good is produced, the more the society in this country gains from the externality, albeit at a decreasing rate. This is described by a social marginal benefit function of MSB = 9 - (1/25)Q, where Q is the quantity produced of the good. Then, what is the welfare change cause by the 5 dollar tariff?

5) Then, should this country impose this 5 dollar tariff? (Yes/No)

Answer 1

1. When there is free trade then P=$30.

Demand D=400-5*30 =250 units

Supply S= -200+30*10= 100 units

Consumer surplus = 1/2*250*50=$6250

Producer surplus= 1/2*100*10 = $500

Total welfare = $6250+$500=$6750.

2. When a import tariff of $5 is levied then P=$35

Then demand D= 400-5*35= 225 units

Supply S=-200+10*35 = 150 units

Consumer surplus= 1/2*225*45 =$5062.5

Producer surplus= 1/2*150*15= $1125

Total welfare= $5062.5 +$1125 =$6187.5

3. Since there is a decrese in the total welfare from $6750 to @6187.5 after imposing a tarrif of $5 on imports therefore, the tariff of $5 should not be imposed.

4.When tariff is not imposed quantity produced in the country is 100 units.

Then MSB= 9-(1/25)*100=9-4=5 units

When tariff is imposed then quantity produced in the country = 150 units

Then MSB = 9-(1/25)*150=3 units

When tariff of $5 is imposed there is a decrease in the marginal social benefit decreases from 5 units to 3 units.

5. Since there is a decrease in the marginal social benefit after imposing a tariff of $5, therefore the country should not impose this $5 tariff.