International Economics

The Ricardian Model

Harald FadingerUniversity of Mannheim

Outline Why do countries trade?Comparative advantage and the gains from trade: an exampleDigression: general equilibriumThe Ricardian model: comparative advantage and the gains from trade in a (general-equilibrium) model with international technological differences

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Why do countries trade? Countries engage in international trade for two basic reasons:

Because they are different from each other.To achieve economies of scale in production.In the real world, patterns of trade reflect the interaction of both these motives.It is useful to look at simplified models in which only one of these motives is present.We are going to focus first on how differences between countries give rise to trade between them and why this trade is mutually beneficial.

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Comparative advantage and the gains from trade Paul Samuelson: Comparative advantage is the best example of an economic principle that is undeniably true yet not obvious to intelligent people (including Adam Smith).

Example: Wine and cloth are the only two goods produced in the world (England and Portugal).One only production factor: labour. Freely mobile between industries within each country.Technologies are different (and fixed) across England and Portugal.International trade in commodities is costless. (No tariffs, no transport costs.)

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Comparative advantage and the gains from trade *Define ai(j) as country is unit labour requirement for producing good j.

Opportunity cost of wine: number of units of cloth the economy would have to forgo in order to produce an additional unit of wine.Portugal: aP(v)/aP(c)

England: aE(v)/aE(c)

WineClothAutarky Price RatiosPortugalaP(v)aP(c)aP(v)/aP(c)EnglandaE(v)aE(c)aE(v)/aE(c)

Comparative advantage and the gains from trade Assume:Portugal has an absolute advantage in the production of both commodities:

aP(v),aP(c) < aE(v),aE(c)Portugal has a comparative advantage in the production of wine (equivalent to England having a comparative advantage in the production of cloth):aP(v)/aP(c) < aE(v)/aE(c)

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Comparative advantage and the gains from trade Because of these relative cost differences, both countries have an incentive to trade.

Portugal would gain if it produced more wine (and less cloth) and imported cloth from England at a ratio aE(v)/aE(c):

Producing one unit less of cloth releases aP(c) units of labour.

These aP(c) units of labour yield aP(c)/aP(v) units of wine in Portugal.

Selling the additional wine at English prices for cloth yields [aP(c)/aP(v)]*[aE(v)/aE(c)] > 1 units of cloth.

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Comparative advantage and the gains from trade England would gain if it produced more cloth (and less wine) and imported wine from Portugal at a ratio aP(v)/aP(c):

Producing one unit less of wine releases aE(v) units of labour.These aE(v) units of labour yield aE(v)/aE(c) units of cloth in England.Selling the additional cloth at Portuguese prices for wine yields [aE(v)/aE(c)]*[aP(c)/aP(v)] > 1 units of wine.Very important: The argument above does not depend on a country having an absolute advantage.*

Comparative advantage and the gains from trade At what prices are England and Portugal going to trade with each other?

Wine is coming into England from Portugal (new supply) and Portugal is demanding English cloth (new demand) downward pressure on the relative price of wine in England.

Cloth is coming into Portugal from England (new supply) and England is demanding Portuguese wine (new demand) upward pressure on the relative price of wine in Portugal.

Under free trade, there will be a single relative price for wine p(v)/p(c): aP(v)/aP(c) p(v)/p(c) aE(v)/aE(c)

Problem: what is the exact value of p(v)/p(c)? We need a more complete model: when countries trade, the relative prices of commodities are not only determined by their labour contents, but also by their preferences.

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The Ricardian model Assumptions:There are two countries: England and Portugal.There are two homogeneous consumption goods: wine and cloth.Preferences over the two goods are identical (and homothetic) for all individuals and the two countries.

Preferences are subject to diminishing marginal utility in the consumption of each good.There is just one production factor: labour. Each country has a fixed number of workers: LE, LP.

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The Ricardian model England and Portugal have different technologies to produce the two goods. (Portugal has a comparative advantage in the production of wine.)

Technologies are subject to constant returns to scale (CRS):

qi(j) = Li(j)/ai(j).All markets are perfectly competitive.No means of storage: at each point in time consumer expenditure equals income.Labour is perfectly mobile between industries and perfectly immobile between countries.Free trade.

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Digression: general equilibrium Country is (i = E,P) autarkic general equilibrium consists of an allocation {xi(v), xi(c), qi(v), qi(c), Li(v), Li(c)} and a set of prices {pi(v), pi(c), wi}, such that:

Consumers maximise utility taking prices as given:maxU[xi(v),xi(c)]s.t. :pi(v)xi(v) + pi(c)xi(c) wiLixi(v), xi(c) 0

Firms maximise profits in each sector j (j = c,v) taking prices as given:max pi(j)qi(j) - wiLi(j)s.t.: qi(j) = Li(j)/ai(j) qi(j) 0

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Digression: general equilibriumEquilibrium profits are zero if commodity j is produced:

pi(j)qi(j) - wiLi(j) = 0ifqi(j) > 0

Markets clear:xi(j) = qi(j)

Li(c) + Li(v) = Li

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Digression: general equilibriumA free-trade general equilibrium consists of an allocation {xi(v), xi(c), qi(v), qi(c), Li(v), Li(c)} for i = E, P, and a set of prices {pi(v), pi(c), wi}, such thatThe law of one price holds:pE(j) = pP(j) = p(j)Consumers maximise utility taking prices as given:max U[xi(v),xi(c)]s.t.:pi(v)xi(v) + pi(c)xi(c) wiLixi(v), xi(c) 0

Firms maximise profits in each sector j (j = c,v) taking prices as given:

max pi(j)qi(j) - wiLi(j)s.t.: qi(j) = Li(j)/ai(j) qi(j) 0

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Digression: general equilibriumEquilibrium profits are zero if commodity j is produced:pi(j)qi(j) - wiLi(j) = 0ifqi(j) > 0

Markets clear:xE(j) + xP(j) = qE(j) + qP(j)

Li(c) + Li(v) = Li *

The Ricardian model: production possibilities Each countrys limits on production are defined by the following inequality:ai(v)qi(v) + ai(c)qi(c) Li

The production possibility frontier (PPF) is defined as the combinations of wine and cloth that an economy can produce efficiently, given its resources and technology.

In our model, the PPF is given by the following equation (from the labour market clearing condition):

ai(v)qi(v) + ai(c)qi(c) = Li

Slope of the PPF: - [ai(v)/ai(c)]. When the PPF is a straight line, the opportunity cost of wine in terms of cloth is constant.

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The Ricardian model: consumer behaviour Consumer preferences are described by indifference curves.In equilibrium, the slope of the indifference curve equals the slope of the budget constraint:MRS = [U/xi(v)]/[U/xi(c)] = p(v)/p(c)

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The Ricardian model: producer behaviour Producers of good j maximise profits taking prices as given:max pi(j)[Li(j)/ai(j)] - wiLi(j)s.t.: Li(j) 0First-order condition:pi(j)/ai(j) wiandLi(j) 0[pi(j)/ai(j) - wi]Li(j) = 0 *

The Ricardian model: producer behaviour Both goods will be produced in positive amounts if and only if

pi(v)/ai(v) = pi(c)/ai(c) pi(v)/pi(c) = ai(v)/ai(c)

If pi(v)/ai(v) = wi > pi(c)/ai(c), the relative price of wine is greater than its opportunity cost, and the economy specializes completely in the production of wine:Li(v) = Liandqi(v) = Li/ai(v)

If pi(c)/ai(c) = wi > pi(v)/ai(v), the relative price of cloth is greater than its opportunity cost, and the economy specializes completely in the production of cloth:

Li(c) = Liandqi(c) = Li/ai(c)

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The Ricardian model: autarky equilibrium *q(c), x(c)q(v), x(v)Portugalq(c), x(c)q(v), x(v)England

The Ricardian model: autarky equilibrium With no trade, consumption of each good j must equal production.The autarkic equilibrium occurs at the point of tangency between an indifference curve and the PPF.Diminishing MU implies consumers demand positive amounts of both goods in equilibrium.Positive production of both goods implies pi(v)/ai(v) = pi(c)/ai(c).

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The Ricardian model: free-trade equilibrium *q(v)/q(c), x(v)/x(c)p(v)/p(c)aE(v)/aE(c)

aP(v)/aP(c)RSW

RDW

The Ricardian model: free-trade equilibrium *q(v)/q(c), x(v)/x(c)p(v)/p(c)aE(v)/aE(c)

aP(v)/aP(c)RSW

RDW

The Ricardian model: free-trade equilibrium *q(v)/q(c), x(v)/x(c)p(v)/p(c)aE(v)/aE(c)

aP(v)/aP(c)RSW

RDW

The Ricardian model: free-trade equilibrium From F.O.C. of firms profit maximization problem, firms specialise in the production of wine if the relative price of wine exceeds its opportunity cost, and viceversa.At least one country specializes in the production of a single good:pE(j) = pP(j) = p(j).For one country to produce both goods, p(v)/p(c) = ai(v)/ai(c).But aP(v)/aP(c) < aE(v)/aE(c).

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The Ricardian model: free-trade equilibrium The free-trade equilibrium has three possible cases:

aP(v)/aP(c) = p(v)/p(c) < aE(v)/aE(c)aP(v)/aP(c) < p(v)/p(c) < aE(v)/aE(c)aP(v)/aP(c) < p(v)/p(c) = aE(v)/aE(c)World relative prices are determined by supply and demand at the level of the world economy.

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The Ricardian model: free-trade equilibrium The world PPF:*q(v), x(v)

q(c), x(c)

The Ricardian model: free-trade equilibrium The world PPF:*q(v), x(v)

q(c), x(c)

The Ricardian model: free-trade equilibrium The world PPF:*q(v), x(v)

q(c), x(c)

The Ricardian model: gains from trade *q(c), x(c)

q(v), x(v)

Portugalq(v), x(v)

q(c), x(c)

England

The Ricardian model: gains from trade Gains from trade:Trade expands each countrys consumption possibilities.Consumers can attain a higher indifference curve than prior to trade.Consumption possibilities frontier lies outside the PPF.More formally: country i gains from trade if and only if p(v)/p(c) ai(v)/ai(c). (Why?)

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