Question

Consider a closed market with the following domestic demand and supply functions:

P=540- (3/4)Q

P=120+3Q

(a) (4 points) What is the domestic equilibrium price and quantity?

(b) (4 points) Calculate the consumer surplus and the producer surplus.

(c) (6 points) Suppose that the domestic market opens up and it joins the world market. If the world price is $126 less than the old domestic equilibrium price, how much quantity is produced domestically? How much quantity is imported?

(d) (6 points) What is the change in consumer surplus and producer surplus due to trade?

(e) (3 points) By how much did the total domestic economy gain/lose (Hint: change in total surplus) due to trade?

(f) (5 points) Suppose that a few years after the markets opened, leaders of the domestic country decide to impose a tariff of $50 on the imported goods. How much is produced by the domestic producers now? How much is still imported?

(g) (2 points) How much revenue does the government receive due to the tariff?

Answer 1

Sol :

P = 540 - (3/4)Q

P = 120 + 3Q

a) Equilibrium is the point where demand and supply are equal to each other.

540 - (3/4)Q = 120 + 3Q

540 -120 = 3Q + (3/4)Q

420 = [(12 + 3)/4]Q

420 = 15Q/4

420 × 4 = 15 Q

1680/15 = Q

112 = Q (Equilibrium Quantity)

P = 120 + 3(112)

= 120 + 336

= 456 (Equilibrium Price)

b)

Consumer Surplus is the Area between the above of price line and below the demand curve.

producer surplus is the area between the below of price line and above the supply curve .

Price (at Qd =0) = 540

So,

CONSUMER SURPLUS =

Area of triangle of consumer surplus.

= 1/2 × 84(price) x 112(quantity)

= 4704

PRODCUER SURPLUS =

Area of triangle of producer surplus

= 1/2 × 456 (price) x 112 (quantity)

= 25536

c) if world price = 456 - 126 = 330

Qs = P = 120 + 3Q

330 - 120 = 3Q

210/3 = Q

70 = Q

Qd = 540 - (3/4)Q

330 = 540 - (3/4)Q

210 = (3/4)Q

( 210 x 4)/3 = Q

280 = Q

Imports = Demand - Supply

= 280 - 70

= 210

D) consumer surplus = 1/2 × 210 x (540 - 330)

= 1/2 × 280 × 210

= 29400

Producer surplus = 1/2 × 70 × 330

= 11550

Note : As per the policy , we have to solve only four subparts of the questions. Kindly for the remaining question , please create a separate post.