1. Find out consumer surplus and producer surplus of the Home country in autarky. (3pts)
2. Derive the import demand function of the Home country and the export supply function of the Foreign country. Solve for the equilibrium price of computers in the world market. (3pts)
?3. What are the total gains from trade in terms of total social welfare, when t = 0? (3pts) now the home country imposes an import tariff t =?
4: for every computer imported into the Home market, the foreign firm needs to pay $4 to the Home government. 4. Find the new equilibrium price in the Home market after the tariff is imposed. (3pts)
?5. How large is the deadweight loss associated with the tariff? How large is the terms of trade gain? Will the total social welfare in the Home country be higher after the tariff? (4pts)
?6. Find out the optimal tariff that maximizes the total social welfare of the Home country. (3pts)
?7. Suppose that the Home government has imposed an optimal tariff t ?. How will the total social welfare of the foreign country be affected? If you have computed the optimal tariff in the previous part, use the value that you have computed. If not, you can express the change in social welfare as functions of t ?. (3pts)
8. How will the total social welfare of the entire world (Home + Foreign) be affected by t ?? (3pts)
Answer:
1. Outlawing the purchase of computers is the same as saying there is no demand for imports, or MDc = 0.
D= (100-P)/3
? ? S= P/2
Equate D= 0 to find the price p
(100-P)/3= 0
Thus P= 100
Equate S= 0 for the supply side
P/2= 0
Thus P=0
Then equate demand to supply as below;
(100-P)/3=?P/2
Thus P= 40
Substitute P= 40 in the demand curve (100-P)/3, and get;
Q=?(100-P)/3
? ?= (100-40)/3
Q= 20
Thus consumer surplus
= 1/2(Quantity)(Price-Equilibrium price)
= 1/2(20)(100-40)
= 600
Thus, consumer surplus= 600
2. Import demand for home country
= Demand function (Home) - Supply function (Home)
= (100-P)/3-P/2
= (200-5P)/6
Thus, Import demand for home country=(200-5P)/6
Export supply for foreign country
=?Supply function (Foreign) - Demand function (Foreign)
= 2P-(100-P)/2
= (5P-100)/2
Thus,?Export supply for foreign country= (5P-100)/2
Equilibrium
Import demand= Export supply
(200-5P)/6= (5P-100)/2
Solving the above equation, P= 25
Thus, the equilibrium price= 25.
3. Total welfare gain= Consumer surplus (Home) + Consumer surplus ( Foreign)
Consumer surplus (Home)= 600
Consumer surplus (Foreign)
Equate foreign demand to zero
(100-P)/2= 0
P= 100
Equate foreign supply to zero
2P= 0
P= 0
Then equate foreign demand to foreign supply
(100-P)/2= 2P
Solving, P= 20
Substitute P= 20 into (100-P)/2
Q= (100-20)/2= 40
Q= 40
Consumer surplus (Foreign) = 1/2(Quantity) (Price- Equilibrium price)
= 1/2(40) (100-20)
= 1600
Total welfare= Consumer surplus (Home) + Consumer surplus (Foreign)?
= 600+1600
= 2200 at t=0
4. Assuming the tariff cost is equally borne by both the producer and consumer, each incurs $2.
Thus, the price will rise by 2.
Price after tariff= $40+$2
Price after tariff= $42.
5. Substitute P= 42 in the home market demand function as below:
(100-42)/3= Q
Q= 19.33
Dead weight loss
= 1/2(Initial quantity- Final quantity)(Tariff)
= 1/2(20-19.33) (4)
= 1.34
Thus, the dead weight loss= 1.34
Terms of trade= Price of export/Price of import×100
Initial Terms of trade
= 40/20×100
= 200%
Final terms of trade
= 42/20×100
= 210%
Gain in terms of trade= 210%-200%= 10%
Thus, the gain in terms of trade= 10%
With an increase in tariff, the social welfare will fall as consumers will have to pay more for a good.
6.A tariff of zero will maximize the total social welfare in the home country. This is because consumers will not have to pay more to get the computer in the form of tariffs and thus social welfare is increased. (Fernando, 2020)
7. With an imposition of an optimal tariff of t*, the total social welfare of a country will be increased and maximized.
The change in social welfare
= 1/2(20) (100-40t*)
= 400-400t*
8. The total social welfare of the world will increase by:
= Final social welfare- Initial social welfare
= (2200+400-400t*)- 2200
= 2600-400t*-2200
= 400-400t*
Thus, the total social welfare will increase by?400-400t*
