Econ452 Learning Unit 09 - Part 2 - 2020 fall

Learning Unit 9
Standard Trade Model
Part 2: Equilibrium Trade
ECON452
International Economics

Objectives
1. Determine an optimal combination production and consumption
under trade on the standard trade model.
2. Relate country’s PPF to relative supply and country’s preference to
relative demand
3. Determination of world equilibrium by world relative supply and
world relative demand
4. Apply the standard trade model to illustrate how trade patterns are
established by a combination of supply-side and demand-side
factors.
5. Explain an equilibrium pattern of trade in partial equilibrium model

Introduction
Four key relationships in the standard trade model
• Relationship between the production possibility frontier and the relative
supply curve.
• Relationship between the preference and the relative demand curve.
• Determination of world equilibrium by world relative supply and world relative
demand.
• Effect of terms of trade on a nation’s welfare.

PPF and Relative Supply
• Each country’s PPF is a smooth curve.
– Differences in labor services, labor skills, physical capital, land, and technology
between countries cause differences in production possibility frontiers.
– A country’s PPF determines its relative supply function.
– Given a relative price of cloth, a country chooses an optimal production.
• Relative supply of cloth increases with the relative price of cloth.
– Country’s relative supply curve is a smooth upward sloping curve.

Relative Prices and Relative Supply
• At (PC /PF)1 of relative price of cloth, a country
chooses Q1 as optimal production point, where
the isovalue line VV1 with slope of (PC /PF)1 is
tangent to PPF at Q1.
• When the relative price of cloth increases from
(PC /PF)1 to (PC /PF)2
• Isovalue line becomes steeper from VV1 to VV2.
• Production shifts from point Q1 to point Q2.
– Production of cloth increases from QC
1 to QC
2.
– Production of food decreases from QF
1 to QF
2.
• Relative supply of cloth increases from (QC
1/QF
1)
to (QC
2/QF
2) .

Indifference Curves and Relative Demand
• Country’s consumption preference is represented by indifference
curve.
– A country’s PPF and indifference curves determine its relative demand function.
– Given a relative price of cloth, a country chooses an optimal production, then
along the isovalue line with slope of the relative price of cloth passing the
optimal production point, a country chooses an optimal consumption point
which reaches highest indifference curve.
• Relative demand for cloth decreases with the relative price of cloth.
– Country’s relative demand curve is a smooth downward sloping curve.

Relative Prices and Relative Demand
• At (PC /PF)1 of relative price of cloth, a country
chooses Q1 as optimal production point. Given
the isovalue line VV1, passing Q1 and its slope
equal to (PC /PF)1, a country chooses D1 as optimal
consumption point.
• When the relative price of cloth increases from
(PC /PF)1 to (PC /PF)2
• Production shifts from point Q1 to point Q2.
• Isovalue line shifts from VV1 to VV2.
• Consumption choice shifts from point D1 to point
D2.
– Consumption of cloth increases from QC
1 to QC
2.
– Consumption of food increases from QF
1 to QF
2.
• Relative Demand for cloth falls from (QC
1/QF
1) to
(QC
2/QF
2) .

Relative Supply and Demand
• Country’s relative supply and relative demand jointly determine the
equilibrium under autarky.
– The equilibrium relative price of cloth and the equilibrium relative quantity of
cloth under autarky are determined.
• Under autarky (Without trade)
– A country’s production is equal to its consumption.
– It is a point on PPF where PPF is tangent to an indifference curve.
– Relative price of cloth = MRT (opportunity cost) = MRS (relative value)

Relative Supply and Demand - Diagram
• Given a country’s relative supply
curve (RS) and relative demand
curve (RD), the equilibrium is at
Point 3.
• At Point 3, a relative quantity of
cloth demanded is equal to a
relative quantity of cloth
supplied.
• Point 3 is the equilibrium under
autarky: What produced is
equal to what consumed.

Relative Supply and Demand - Example
• At Equilibrium under autarky
– Equilibrium relative price = ½
– Equilibrium relative quantity = ½
PC/PF
Supply Demand
QC QF QC/QF QC QF QC/QF
3 120 60 2 60 240 1/4
1.5 90 90 1 50 150 1/3
1/2 60 120 1/2 60 120 1/2

Production, Consumption, and Trade
• At relative prices of cloth other than the equilibrium, a relative quantity of cloth
demanded is different from a relative quantity of cloth supplied.
– At Point 2, a quantity of cloth produced is greater than a quantity of cloth
consumed. Where does this surplus of cloth go?
– At Point 2, a quantity of food produced is less than a quantity of food
consumed. Where does a country get this shortage of food?
• Difference between the consumption and the production is traded.
– When a country consumes less than its production, the surplus is exported.
– When a country consumes more than its production, the shortage is
imported.

Production, Consumption, and Trade -
Diagram
• Difference between production and consumption is
traded.
– A horizontal distance between Point Q and Point D
represents a quantity of cloth traded.
– A vertical distance between Point Q and Point D
represents a quantity of food traded.
– When a production quantity is greater than a
consumption quantity, the surplus is exported.
 Home exports cloth.
– When a production quantity is less than a
consumption quantity, the shortage is imported
 Home imports food.

Relative Prices and Trade
• For given relative price of cloth, a country wants to export its surplus of cloth
to other country and to import its shortage of food from other country.
– At PC/PF = 1.5, 90 unit of cloth are produced and 50 units of cloth are consumed. Surplus
of 40 units of cloth (90 – 50) are exported.
– At PC/PF = 1.5, 90 unit of food are produced and 150 units of food are consumed.
Shortage of 60 units of food (90 – 150) are imported.
PC/PF
Supply Demand Trade
QC QF QC QF QC QF QF/QC
3 120 60 60 240 60 -180 3
1.5 90 90 50 150 40 -60 1.5
1/2 60 120 60 120 0 0 

Relative Price and Rate of Exchange
• A rate of exchange of two goods in trade must be
equal to the relative price of cloth.
QF/QC = PC/PF
Where QF is a difference between production
and consumption quantities of food and QC is a
difference between production and consumption
quantities of cloth.
• A slope of isovalue line is PC/PF .
• A slope of isovalue line can be computed
geometrically as
Rise/Run = Food Imports/Cloth Exports QF/QC

Relative Price and Rate of Exchange -
Example
• At PC/PF = 1.5,
– 40 unit of cloth are exchanged for 60 units of food.
– A rate of exchange of cloth is 1.5 units of food (60/40).
PC/PF
Supply Demand Trade
QC QF QC QF QC QF QF/QC
3 120 60 60 240 60 -180 3
1.5 90 90 50 150 40 -60 1.5
1/2 60 120 60 120 0 0 

Relative Prices and Gains
• An economy that exports cloth is better off when the price of cloth
rises relative to the price of food (PC/PF) :
– the isovalue line becomes steeper and a higher indifference curve can be
reached.
– A higher relative price of cloth means that more units of food can be
imported for every unit of cloth exported.

Equilibrium Relative Price and Trade
• For trade to take place, a country must face a world relative price that
differs from the relative price under autarky.
• Assume that the relative price of Home under autarky is less than the
relative price of Foreign under autarky.
PC
A/PF
A < PC
A*/PF
A*
– Home will export Cloth and Foreign will import Cloth.

Partial Equilibrium Model – Set Up
• Looking at one good market at time
• Measure a relative price of the good along the vertical axis
• Measure a quantity of the good along the horizontal axis
• From demand and supply of the goods, an equilibrium relative price of
the good is determined in the world market.
– At equilibrium, one country’s import is equal to the other country’s export.
• For World Cloth market
– A relative price of cloth is measured along the vertical axis, and quantities of
cloth (produced, consumed, and traded) are measured along the horizontal axis.

Import Demand and Export Supply
• Import demand curve shows a relationship between the price of
goods and the quantity of goods imported, which is an excess
demand for the goods in domestic market.
• Export supply curve shows a relationship between the price of goods
and the quantity of goods exported, which is an excess supply of the
goods in domestic market.
• In World Cloth market, Home exports cloth and Foreign imports cloth.

Deriving Import Demand Curve
• Foreign imports Cloth.
• At PA, Cloth market is at
equilibrium in Foreign: PA is the
equilibrium relative price of cloth
under autarky.
• At PA, there is no excess demand,
so its import demand is zero.
• At P1, there is an excess of
demand by D1–S1, which is
Foreign’s import demand.
• Import demand curve looks like a
regular demand curve – as its
relative price decreases, Foreign
demands more to Home.
Import Demand by ForeignSupply and Demand in Foreign
Shortage Import

Deriving Export Supply Curve
• Home exports Cloth.
• At PA
*, Cloth market is at
equilibrium in Home: PA
* is the
equilibrium relative price of
cloth under autarky.
• At PA
*, there is no excess
supply, so its export supply is
zero.
• At P1
*, there is an excess of
supply by S1
*–D1
*, which is
Home’s export supply.
• Export supply curve looks like a
regular supply curve – As its
price increases, Home supplies
more to Foreign.
Export Supply by HomeSupply and Demand in Home
Surplus Export

Partial Equilibrium in World Market
• The equilibrium world price is where
Foreign’s import demand equals
Home’s export supply.
• At PW, both exports supply (XS) and
import demand (MD) are equal to Q.
• At equilibrium, one country’s export is
the other country’s import:
import demand = export supply
• The diagram looks like a regular supply
and demand diagram where an
intersection of supply and demand
curves determines an equilibrium.

Home, Foreign, and World Market
• The equilibrium world relative price (Pw) is between the equilibrium relative price in
Foreign (PA) and the equilibrium relative price in Home (PA*) under autarky.
Shortage
Surplus
Export
=
Import

Partial Equilibrium vs. General Equilibrium
• Problems on Partial Equilibrium Model
– Equilibrium at one market does not guarantee an equilibrium in other markets.
– Equilibrium relative price in one market may not correspond to an equilibrium
relative price in other markets.
• General Equilibrium model takes into account of all markets together.
– Equilibrium in the general equilibrium model guarantees that all markets are at
equilibrium.
– Equilibrium relative prices are all equal across all markets.
– Every country has a balanced trade.

General Equilibrium Model – Set Up
• For two goods world:
• Measure a relative price of one good along the vertical axis
• Measure a relative quantity of the good along the horizontal axis
– World quantities are the sum of quantities from the two countries in the world:
(QC + QC
*)/(QF + QF
*) and (DC + DC
*)/(DF + DF
*).
• Country’s relative supply functions determine a world relative supply
function, and country’s relative demand functions determine a world
relative demand function
• World relative supply and world relative demand jointly determine the
equilibrium and the equilibrium relative price under international trade.

Relative Supply and Relative Demand under
Autarky
• Preference is assumed to be the same in two
countries.
– the relative demand curves are identical in
two countries.
– RD curve represents RD in Home, RD in
Foreign, as well as RD in world (Home +
Foreign).
• Relative supply of cloth is greater in Home than
Foreign.
– RS of Home lies right of RS of Foreign.
• Relative price of cloth is lower in Home.

Relative Supply and Relative Demand under
Trade
• The world relative supply curves lies
between two relative supply curves.
• The equilibrium relative price of cloth
under trade (PC/PF) is determined by an
interaction of world relative supply and
world relative demand.

Equilibrium Relative Quantity and Relative
Price
• As two countries trade, the world RS curve will be somehow between
RS and RS* curves.
Qc/Qf > (Qc+Qc*)/(Qf+Qf*) > Qc*/Qf*
• The equilibrium relative price of cloth under trade will be somehow
between relative prices in two countries under autarky.
– Because the world relative price is higher than the relative price (and
opportunity cost) in Home, Home has a comparative advantage in production
of cloth and export cloth.
– Because the world relative price is lower than the relative price (and
opportunity cost) in Foreign, Foreign has a comparative disadvantage in
production of cloth and will import cloth.

Trade at Equilibrium
At equilibrium world relative price,
• Home produces at Q and consume
at D.
• Foreign produces at Q* and
consumes at D*.
• Home exports QC-DC of cloth and
Foreign imports DC*-QC* of cloth.
QC-DC = DC*-QC*
• Foreign exports QF*-DF* of food and
Home imports DF-QF of food.
QF*-DF* = DF-QF
PPF
PPF
Indifference
curve Indifference curve

Specialization under Trade
• Each country will specialize in production
of one good with lower opportunity cost
(cloth for Home and food for Foreign) –
comparative advantage.
• When Home specializes in production of
cloth, its production point moves along its
PPF from A to Q.
– Home increases a production of cloth
and reduces a production of food.
• When Foreign specializes in production of
food, its production point moves along its
PPF from A* to Q*.
– Foreign reduces a production of cloth
and increases a production of food.

Specialization and Opportunity Cost
• When Home specializes in production of
cloth, moving along its PPF from A to Q.
– The slope of PPF increases and the
opportunity cost of producing cloth
increases.
• When Foreign specializes in production
of food, moving along its PPF from A* to
Q*.
– The slope of PPF decreases and the
opportunity cost of producing cloth
decreases.

Equality Conditions at Equilibrium under
Trade (1)
• At equilibrium, slopes of PPFs are equal to the relative price, so the slope of PPF
of Home is equal to the slope of PPF of Foreign.
MRTCF = PC/PF = MRTCF
*
– This equality means that every country is producing at the same opportunity
cost at the relative price.
– Similar to Price = MC (marginal cost) condition for all profit-maximizing firms
under perfect competition.

Equality Conditions at Equilibrium under
Trade (2)
• At equilibrium, Isovalue line is tangent to PPF and an indifference curve.
MRTCF = PC/PF = MRSCF
– This equality means that an opportunity cost of production of good (MRT) is
equal to the relative price of the good (PC/PF), and the relative value of the
goods for consumers (MRS).
– This is similar to MC = MU condition under competitive market.

Budget Constraint under Trade
• Budget constrain: Country cannot spend more than it earns
PC x QC
C + PF x QF
C = PC x QC
P + PF x QF
P
– total value of two goods consumed = total value of two goods produced
– Isovalue line represents the budget constraint: Both production and
consumption points must be on the same isovalue line.
• Budget constrain implies
 PF x (QF
C – QF
P) = PC x (QC
P – QF
C)  PC/PF = (QF
C – QF
P)/(QC
P – QF
C)
– The equilibrium relative price of cloth (PC/PF) is equal to the ratio of import of
food to export of cloth.

Balance Trade
• Balance trade between two countries
– Budget constraints must be met in both countries.
– Relative prices must be equal in two countries.
– Export by one country must be equal to import by the other country.

Terms of Trade
• Terms of trade: the price of exports relative to the price of imports.
Price of Export / Price of Import
– Home exports cloth and imports food: Home’s terms of trade = PC/PF.
– Foreign exports food and imports cloth: Foreign’s terms of trade = PF/PC.
– When a relative price of country’s export increases, its terms of trade rise.

Welfare Effects of Changes in Terms of Trade
• An increase in country’s terms of trade raises its welfare.
– A higher relative price for exports means that the country can afford to buy
more imports.
– With higher relative price of shoe, the isovalue line becomes steeper and
Home can reach a higher indifference curve.

Gains from Trade
• Under the Ricardian model, gains from trade are measured by additional goods
that a country can consume under trade over the autarky.
– As long as a consumption combination under trade falls in the definitely
better combination area, we can conclude that a country gains from trade.
• However, if a country can consume more food but less cloth under trade than the
autarky, how we can determine if a country gains from trade and how to measure
gains?
– We know that a country can always choose the autarky combination even
under trade, so if a country decides to trade, it must be the case that the
country gains from trade.
– Instead of additional quantities of goods, gains are measured by additional
utility (satisfaction) a country gains from trade.

Gains from Trade
• Under autarky, Home’s consumption
point is A.
– Home consumes QC
A of cloth and QF
A of food.
– Home reaches ICA of indifference curve.
• Under trade, Home’s consumption point
is D.
– Home consumes QC
D of cloth and QF
A of food.
– Home reaches ICD of indifference curve.
• Home’s gains from trade is measured by
an increase in utility (satisfaction) from
ICA to ICD (higher indifference curve).
ICA
*
ICA
ICD
*ICD

Decomposition of Gains from Trade and
Specialization
• Gains from international trade comes from
– Gains from specialization
– Gains from exchange (trade)
• Gains from trade: Without changing production under autarky (no
specialization), Home can gain by selling cloth at higher world price to Foreign
and purchasing cloth at lower world price from Foreign.
• Gains from specialization: By specializing to produce cloth, Home can sell even
more cloth and purchase more food from Foreign at the world prices (No change
in prices).
• Similar to decomposition of income and substitution effects.

Decomposition of Gains from Trade and
Specialization - Diagram
• Gains from trade: movement from
Point A to Point T
– Increase in utility (satisfaction)
from indifference curve I to II
– Point T is on the isovalue line with
slope of world relative price and
passing Point A.
• Gains from specialization:
movement from Point T to Point D
– Increase in utility (satisfaction)
from indifference curve II to III
D
QF
PC/PF
A
QC
QC
T
PC/PF
WPC/PF
W
QF
A
QC
A
QF
T
DC
DC

Disclaimer
Please do not copy, modify, or distribute
this presentation
without author’s consent.
This presentation was created and owned
by
Dr. Ryoichi Sakano
North Carolina A&T State University
Disclaimer
Please do not copy, modify, or distribute
this presentation
without author’s consent.
This presentation was created and owned
by
Dr. Ryoichi Sakano
North Carolina A&T State University

Econ452 Learning Unit 09 - Part 2 - 2020 fall

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