Question

Suppose that the world price for a good is 50, and the domestic demand and supply curves are given by the following equations:

D^X: P^D=100-4Q^D S^X: P^S=10+6Q^S

1. How much is consumed? How much is produced domestically? What are the values of producer and consumer surplus?
2. If a 5% import tariff is imposed, by how much do consumption and domestic production change? What is the change in consumer and producer surplus? How much revenue does the government earn from the tariff?
3. What is the net national cost of the tariff? Show your results through a graphical representation.

Answer 1

world price for a good is 50
demand and supply curves are given by the following equations:

DX: PD=100-4QD
SX: PS=10+6QS

A) solving the above equation
QD = QS =  10
PS = PD = 60
we get normal production level of the country according to which PD = 60 and QD = 10 ,
but world price is 50 so price in country will fall to 50 due to import and reduce domestic supply (can see in fig. below )
DX: PD=100-4QD
SX: PS=10+6QS
putting in place of P = 50 we get domestic consumption level and domestic production level
i.e. (25/2 ) and 20/3 respectively  
the values of producer and consumer surplus are triangle shown below figure

Producer surplus = 1/2 * 20/3* (40) = 400/3
consumer surplus = 1/2 * 25/2* (50) = 625/2

B )If a 5% import tariff is imposed,
price in doomestic ciuntry will incrase by 2.5 rs
now new price is 52.5
DX: PD=100-4QD
SX: PS=10+6QS
putting in place of P = 52.5 we get domestic consumption level and domestic production level
i.e. (95/8 ) and 85/12 respectively  

change in domestic consumption = 25/2 - 95/8 = 5/8
change in domestic production  = 85/12- 20/3 = 5/12

the values of producer and consumer surplus are triangle shown below figure

Producer surplus = 1/2 * 85/12* (42.5) = 150.52
consumer surplus = 1/2 * 95/8* (47.5) = 282.03

change in producer surplus = 150.52 - 400/3 = 17.18
change in consumer surplus  = 282.03 - 625/2 = -30.46 (-) sign show reduction in  consumer surplus
import = 95/8 - 85/12 = 115/24
revenue the government earn from the tariff = (3) column area = (52.5 - 50 ) * 115/24 = 11.97

C) What is the net national cost of the tariff? Show your results through a graphical representation.

answer: due to this tarrif consumer surplus decreases and deadweight loss arises but due to this tariff production in domestic market increases and government revenue also generated.
so net national cost of the tariff = increases in producer surplus (1) + government revenue(3) - deadweight loss(2)and (4) =
17.18 + 11.97 - 0.5 - 0.78 = 27.87
areas of deadweight loss triangle (2) = 1/2 * (85/12 - 20/3) * 2.5 = 0.5 ( compare both figure )
areas of deadweight loss triangle (4) = 1/2 * (25/2 - 95/8) * 2.5 = 0.78