Question

2. Consider a domestic closed market (no international trade) with the following demand and supply functions:

P = 150 − 1/2Q

P=Q
(a) Calculate the domestic equilibrium price and quantity

(b) Calculate the consumer surplus and the producer surplus

(c) Suppose the domestic country decides to open up its markets and begins international trade. The world price (Pw) is $30 lower than the former domestic equilibrium price. How much quantity is now supplied by the domes- tic producers in the market? (QDomestic) How much quantity is imported from international producers in the market? (QImport). You must show work.

(d) (What is the new consumer surplus and producer surplus?

(e) Who benefited from opening up the market (Domestic consumers? Domestic producers?)

(f) (2 points) Did the domestic market efficiency improve?

Answer 1

2.

P = 150 − (1/2)Q

P=Q

a)

Equilibrium: Demand = Supply

150-(1/2)Q= Q

300-Q= 2Q

3Q= 300

Q*= 100 Equilibrium quantity

P*= Q= 100 Equilibrium price

b)

For consumer surplus:

P= 150-(1/2)Q

At Q= 0, Price=Pm= 150

Consumer surplus = (1/2)(Pm-P*)Q*= (1/2)(150-100)(100)= 2500

For producer surplus:

P=Q

If Q=0, then Price=Ps=0

Producer surplus= (1/2)(P*-Ps)Q*= (1/2)(100-0)(100)= 5000

c)

If world price= Pw= 30

Supply by domestic producer:

P=Qs= 30 units

Demand by domestic consumer:

P= 150-(1/2)Q

30 x 2= 300-Q

Qd= 300-60= 240

Quantity import= Quantity demand - Quantity supplied= 240-30= 210 units

d)

Consumer surplus= (1/2) (Pm-Pw)(Qd)= (1/2)(150-30)(240)= 60 x 240= 14400

Producer surplus= (1/2)(Pw-Ps)(Qs)= (1/2)(30-0)(30)= 15 x 30= 450

e)

Domestic consumer's surplus increases from 2500 to 14400 so it means domestic consumer benefitted from opening up of the market.

f)

Market efficiency improves as total market surplus increases from the initial situation.