Question

Consider two countries and a single good produced competitively. At Home, the supply and demand curves for this good are given by the following expressions where q' is quantity supplied and is quantity demanded: q"(p) = 100 + 2002 (P) = 1900 - 400p. In the foreign country, these curves are given by the following expressions where asterisks denote that they are foreign q** (P) = 100p q4*(p) = 600 -200p. 1. Solve for the closed economy (autarky) equilibrium price and quantity in each country. 2. With free trade which country imports the good and which country exports the good? 3. Assume that trade is free for this good between these two countries. What is the free trade world price and what is the quantity traded? 4. For this good, graph and calculate consumer surplus, producer surplus, and total surplus in each country.

Answer 1

1. Equilibrium under Autarky

For home:

qs = qd

100 + 200p = 1900 – 400p

p = $3

q = 700

For foreign:

qs* = qd*

100p = 600 – 200p

p = $2

q = 200

2. To find which country will export and which will import the good we need to find the world price of good.

World demand (Qd) = qd + qd*

                                 = 2500 – 600p

World supply (Qs) = qs + qs*

                                 = 100 + 300p

Qd = Qs

2500 – 600p = 100 + 300p

900p = 2400

P = 2.66

At this price domestic demand and supply are:

qd = 1900 – 400(2.66) = 836

qs = 100 + 200(2.66) = 632

Foreign demand and supply

qd* = 600 – 200(2.66) = 68

qs = 100(2.66) = 266

Thus, there is excess demand in home and excess supply in foreign.

Therefore, home will import and foreign will export.

3. Free trade world price is $2.66 and quantity (Q) is

Q = 2500 – 600(2.66) = 904

4.

In the home country consumer surplus (CS), producer surplus (PS), and total surplus (TS)

Home Price F Demand +-Supply +World price -500 0 500 1000 1500 2000 2500 Quantity

Before trade is:

CS = area (ABE) = 0.5 * 700 * 2 = 700

PS = area (OCEB) = 0.5 * (100 + 700) * 3 = 1200

TS = CS + PS = 1900

After trade is:

CS = area (AFD) = 0.5 * 836 * 2.34 = 978.12

PS = area (OCGD) = 0.5 (100+ 632) * 2.66 = 973.56

TS = CS + PS = 1951.68

In the foreign country:

Foreign 3.5 34 2.66 2.5 7G Price Demand Supply + World Price 0 100 200 300 400 500 600 700 Quantity

Before trade:

CS = area (AEC) = 0.5 * 200 * 1 = 100

PS = area (OEC) = 0.5 * 200 * 2 = 200

TS = CS + PS = 300

After Trade:

CS = area (ADG) = 0.5 * 68 * 0.34 = 11.56

PS = area (OFG) = 0.5 * 266 * 2.66 = 353.78

TS = CS + PS = 365.34