Download ECONOMICS 8413 INTERNATIONAL TRADE THEORY FALL, 1999

ECONOMICS 8413
INTERNATIONAL TRADE THEORY
ASSIGNMENT 2
FALL, 1999
I. Internal Increasing Returns and Imperfect Competition
1. Use the linear duopoly model developed in class (linear demand (from quadratic utility
function), constant marginal cost (assume only labor as a factor of production), a fixed cost,
identical homogeneous goods, identical countries) to derive the reaction curves for the domestic
and foreign Cournot-Nash competitors. Solve for the equilibrium output and profit levels of the
firms in autarky and free trade. Use the utility function to show that both countries gain from trade.
Now assume that the two firms have different marginal costs (in units of labor). Is it possible for
one country to be worse off in free trade than in autarky?
2. Use the Helpman-Krugman trade model to show that if manufactures (monopolistically
competitive) are capital-intensive and food (perfectly competitive) is labor-intensive then the trade
equilibrium will involve both interindustry trade and intraindustry trade if relative factor
endowments differ. Derive an expression for the share of intra-industry trade in total trade and
indicate what happens to this share as: i. country sizes become more similar; ii. endowments
become more similar.
II. Demand and Trade
3. Show that the existence of a minimum consumption requirement in the labor-intensive good
implies the possibility of a "demand bias" or "demand reversal" that can overturn the HO model.
III. Tariffs
4. Let  (>0) be the domestic compensated demand elasticity in the importing country for good X2
and let  be the domestic supply elasticity for the same good. Define compensated imports as m2 =
c2 - x2, where the latter variables are domestic consumption (on the compensated demand curve)
and production. Show that the elasticity of compensated import demand (m > 0) is
m = ( + (x20/c20)*)/(1 - x20/c20), where the 0 superscripts refer to initial levels of
production and consumption. What do you conclude about the elasticity of import demand relative
to domestic demand and supply elasticities?
5. This problem will compute welfare losses or gains from a tariff imposed by a large country. The
figures get a little messy. Consider the following linear domestic supply and (compensated)
demand functions for good X1 in H and F (p is the relative price):
F: ps = 20 + 2x1s
H: ps = 10 + 2x1s
d
d
p = 90 - 3x1
pd = 80 - 2x1d
a. Draw demand and supply curves in F and H and derive and draw F's import demand curve and
H's export supply curve. Compute the free-trade price and quantity of trade.
b. Suppose F imposes a specific tariff of $1 per unit of imports (note this means $1 worth of X2 per
unit but treat it as $1). Discuss why H's export supply curve shifts up by $1 and draw the shift.
Compute the new prices in F and H, plus percentage changes in these prices. Which country
experiences the larger percentage change, and why?
c. Compute welfare effects in F, H, and the world (H plus F). Did F gain by imposing the tariff
and, if so, why?
6. Suppose that a small open economy wishes to increase production in the X1 industry. Discuss
and compare (in welfare terms) the following alternative methods for doing so:
a. an import tariff on X1;
b. an export tax on X2;
c. a production subsidy to X1;
d. a consumption subsidy to X1.
IV. Quotas
7. Compare the effects of an import tariff with an import-equivalent quota when the quota licenses
are auctioned off by the government, assuming the imported good is supplied by a foreign
monopolist and there is no domestic production of the good.
V. Strategic Trade Policy
8. Consider two identical countries, H and F, and suppose H initiates an export subsidy in good X1.
Compare the effects of this subsidy on trade and welfare in a model where the X1 industry is
perfectly competitive in both countries with the effects of this subsidy in a model in which X1 is
produced by a single firm in each country and the two (symmetric) firms engage in Cournot
competition. (Diagrams are fine for this purpose.)
VI. Preferential Trade Areas
9. Draw a partial-equilibrium diagram in which country A imports a homogenous product from
both country B and the rest of the world (ROW). Country A has market power relative to country B
(country B’s export supply curve is upward sloping) but is small relative to ROW (its supply curve
is horizontal at price p*). In the initial equilibrium A has a common (specific) tariff on both B and
ROW. Now let A form a FTA with B but not ROW. Analyze the price and welfare implications
for A in terms of this particular good.