HO model - 2x2x2

Assumptions

2 countries + 2 sectors + 2 Factors

• H & F

• H: L-abundant L=L*, K* > K → L / K > L* / K*

Identical tech across countries with CRS

All markets perfectly competitive

Preferences identical across countries + homothetic

No trade costs

Factors move freely across sectors but not across countries

• no migration or capital flows

Not a small open economy - relative price endogenous

How to solve firm problem without factor prices

Using PPF

• max y2 for a given y1 & resource constraints

• How much you can produce of good 2 depends on how much you produce of 1

Any point on the PPF is efficient

PPF max equation

Solving the firm problem using PPF

Slope of PPF = MRT (Marginal rate of transformation)

Relative p = MRT → tangency is optimal production mix

Solving the consumer problem using PPF

Relative p = MRS (marginal rate of substitution)

Autarky equilibrium with PPF

Markets clear when c1 = y1 & c2 = y2

H is L-abundant & good 1 is L-intensive

• 1 cheaper in H than F

Equilibrium

• Quantities: y1 / y2 > y*1 / y*2

• Price: p = p1 / p2 < p* = P*1 / p*2

  • p < p*

Efficient point: MRS = MRT

Opening to trade effects on p

Since 1 is L-intensive p* > p

if world price is p then there will be excess D for 1 in F

• opening up to trade leads to equilibrium world price: p < p^w < p*

Relative world demand

same preferences implies same relative demand in World as in H and F

Relative world Supply

Marginal rate of Substitution (MRS)

Optimal consumer choice / equilibrium condition in trade

Same preferences in Home and Foreign ⇒ same relative-demand relationship

marginal rate of transformation (MRT)

Equilibrium in production / (profit maximisation) with trade:

MRS = MRT in equilibrium

Preferences identical - common world relative-D curve

Tech / Endowments may differ - World relative-S curve reflects global production possibilities

World relative price (p^w) equates D^w = D^S

Trade equilibrium (p & y graph)

Intuition: if H is abundant in L, when we open up to trade, the price of the L-intensive good goes up compared to its autarky level, opposite happens to the price of the other good

Gains from trade - H

A - autarky equilibrium

B - trade equilibrium for consumption

C - trade equilibrium for production

• under trade H consumes more of both 1&2 → better off

• Same for F

Increased p allows for greater consumption possibilities

Specialisation in trade equilibrium

no full specialisation in production (each nation produces some of 1 & 2)

• Different to Ricardian model

 BUT there is full specialisation in trade

• Only 1 nation exports each good

HO theorem & collaries

Theorem

• In a 2x2x2 economy, with same technologies, same homothetic preferences across countries, but different factor endowments, no FIR and both goods produced, the country relative abundant of labor exports the L-intensive good and the country relative rich of capital exports K-intensive goods.

  • Only difference between 2 nations is endowments

Corollaries

1. Trade increases welfare in both countries. Consumers reach a higher level of utility

2. Stolper-Samuelson: trade raises real reward of a country’s abundant factor and reduces that of the scarce factor

   1. leads to a conflict of interest between the scarce and abundant inputs.

3. Trade leads to factor price equalization

HO predictions - trade & inequality

Trade increase relative price of skilled good in skill-intensive country

Trade increases inequality in skill-intensive country (developed) and decreases it in the unskilled-intensive country (developing)

Trade increases inequality via across-sector reallocations of labor/production: from the scarce to the abundant sectors

HO predictions & real world data - inequality in developed nations

US skill premium has increased when nations more open to trade (globalisation increasing)

• increase in skill premium for production workers

• Lawrence & Slaughter (1993) & Acemoglu & Autor (2011)

BUT relative prices dont increase

• Negative relationship between skill intensity & Export price

• HO predicts opposite

HO model distributional effects assumptions

Assume goods produced with skilled & unskilled L

Assume trade between developed & developing nations

• North-South trade

HO predictions & real world data - inequality in developing nations

Inequality increases also in many developing countries

• Goldberg & Pavcnik (2007)

Evidence of a skill premium in South– skilled workers wages still rising

HO predictions & real world data - trade and inequality across sectors

High shares of within-industry contribution to skill premium / benefits to skilled workers

• Berman et al. (1998)

Why does HO model fail

No technology included in model

• Innovation / tech progress → Productivity gain → prices fall

• K cheaper or more complementary to skilled L → Productivity gain → prices fall

  • Increased D for skilled-L in developing → skill premium / inequality rise