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Basic ModelSummary
International EconomicsLecture 2 # The Ricardian Model I
Weigang Liu
Beijing University of Technology
21st, January, 2019
Weigang Liu International Economics
Basic ModelSummary
Outline
1 Basic ModelAssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
David Ricardo (1772-1823)
A British political economist, one of the most influential ofthe classical economists along with Thomas Malthus, AdamSmith and James Mill.Ricardo was the third of 17 children.Died from an ear infection at 51.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
The Ricardian Model of Trade
Ricardo wrote his rst economics article at the age of 37.Ricardo’s theory of international trade was reformulated byJohn Stuart Mill. The term "comparative advantage" wasstarted by J. S. Mill and his contemporaries.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Outline
1 Basic ModelAssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Model assumptions
Two countries
Two goods
One factor of production
Country-specific production technology
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Model assumptions
Two countries
Two goods
One factor of production
Country-specific production technology
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Model assumptions
Two countries
Two goods
One factor of production
Country-specific production technology
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Model assumptions
Two countries
Two goods
One factor of production
Country-specific production technology
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Example
Two countries:China, USA
Two goods:ChipsT-shirts
One factor of production: LaborChina: 100 people.USA: 20 people
Country-specific production technology:China: Each worker can produce 1 chip or 1 T-shirtUSA: Each worker can produce 2 chips or 1 T-shirt.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Example
Two countries:China, USA
Two goods:ChipsT-shirts
One factor of production: LaborChina: 100 people.USA: 20 people
Country-specific production technology:China: Each worker can produce 1 chip or 1 T-shirtUSA: Each worker can produce 2 chips or 1 T-shirt.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Example
Two countries:China, USA
Two goods:ChipsT-shirts
One factor of production: LaborChina: 100 people.USA: 20 people
Country-specific production technology:China: Each worker can produce 1 chip or 1 T-shirtUSA: Each worker can produce 2 chips or 1 T-shirt.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Example
Two countries:China, USA
Two goods:ChipsT-shirts
One factor of production: LaborChina: 100 people.USA: 20 people
Country-specific production technology:China: Each worker can produce 1 chip or 1 T-shirtUSA: Each worker can produce 2 chips or 1 T-shirt.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Outline
1 Basic ModelAssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
The production possibility frontier
Consider the China in autarky. (“Autarky” means in theabsence of trade).We first characterize the production possibilities of the China:
The set of production possibilities of the China is all thedifferent combinations of chips and T-shirts that the China canproduce.The production possibility frontier (PPF) is the most chips theChina can produce for each number of T-shirts produced.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
The production possibility frontier
Consider the China in autarky. (“Autarky” means in theabsence of trade).We first characterize the production possibilities of the China:
The set of production possibilities of the China is all thedifferent combinations of chips and T-shirts that the China canproduce.The production possibility frontier (PPF) is the most chips theChina can produce for each number of T-shirts produced.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
PPF for the example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
PPF for the example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
PPF for the example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
PPF for the example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Warning: Math ahead
I am now going to define things formally using mathematics:This is a general plan for the course: first provide the intuition,then formalize it.
Why use math at all?Allows us to derive general insights (does not depend onparticular examples).Sometimes, models get too complicated to give full insight in apicture.
What do you need to know?Denitely understand the intuition.Work through the math on the problem sets (they are meantto be hard).Math is fair game for exams.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Warning: Math ahead
I am now going to define things formally using mathematics:This is a general plan for the course: first provide the intuition,then formalize it.
Why use math at all?Allows us to derive general insights (does not depend onparticular examples).Sometimes, models get too complicated to give full insight in apicture.
What do you need to know?Denitely understand the intuition.Work through the math on the problem sets (they are meantto be hard).Math is fair game for exams.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Warning: Math ahead
I am now going to define things formally using mathematics:This is a general plan for the course: first provide the intuition,then formalize it.
Why use math at all?Allows us to derive general insights (does not depend onparticular examples).Sometimes, models get too complicated to give full insight in apicture.
What do you need to know?Denitely understand the intuition.Work through the math on the problem sets (they are meantto be hard).Math is fair game for exams.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
The production possibility frontier generalized
Let QChipCHN denote the number of chips produced and QT−shirt
CHNdenote the number of T-shirts produced by the China.
Let LChipCHN and LT−shirt
CHN denote how much labor is required toproduce a chip or T-shirt by a China worker, respectively. Wecall this the unit labor cost;
Note that the unit labor cost is the inverse of workerproductivity.
Let LCHN be the number of workers in the China.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
The production possibility frontier generalized
Let QChipCHN denote the number of chips produced and QT−shirt
CHNdenote the number of T-shirts produced by the China.
Let LChipCHN and LT−shirt
CHN denote how much labor is required toproduce a chip or T-shirt by a China worker, respectively. Wecall this the unit labor cost;
Note that the unit labor cost is the inverse of workerproductivity.
Let LCHN be the number of workers in the China.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
The production possibility frontier generalized
Let QChipCHN denote the number of chips produced and QT−shirt
CHNdenote the number of T-shirts produced by the China.
Let LChipCHN and LT−shirt
CHN denote how much labor is required toproduce a chip or T-shirt by a China worker, respectively. Wecall this the unit labor cost;
Note that the unit labor cost is the inverse of workerproductivity.
Let LCHN be the number of workers in the China.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Warning: Math ahead
Then the set of production possibilities is:{QChip
CHN ,QT−shirtCHN |LChip
CHNQChipCHN + LT−shirt
CHN QT−shirtCHN ≤ LCHN
}And the production possibility frontier is:
QChipCHN(QT−shirt
CHN ) ≡ maxQ>0Q
s.t.LChipCHNQ + LT−shirt
CHN QT−shirtCHN ≤ LCHN
[Class question]: what is the solution to above equation?Answer:Q = LCHN
LChipCHN− LT−shirt
CHNLChip
CHNQT−shirt
CHN
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Warning: Math ahead
Then the set of production possibilities is:{QChip
CHN ,QT−shirtCHN |LChip
CHNQChipCHN + LT−shirt
CHN QT−shirtCHN ≤ LCHN
}And the production possibility frontier is:
QChipCHN(QT−shirt
CHN ) ≡ maxQ>0Q
s.t.LChipCHNQ + LT−shirt
CHN QT−shirtCHN ≤ LCHN
[Class question]: what is the solution to above equation?Answer:Q = LCHN
LChipCHN− LT−shirt
CHNLChip
CHNQT−shirt
CHN
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Warning: Math ahead
Then the set of production possibilities is:{QChip
CHN ,QT−shirtCHN |LChip
CHNQChipCHN + LT−shirt
CHN QT−shirtCHN ≤ LCHN
}And the production possibility frontier is:
QChipCHN(QT−shirt
CHN ) ≡ maxQ>0Q
s.t.LChipCHNQ + LT−shirt
CHN QT−shirtCHN ≤ LCHN
[Class question]: what is the solution to above equation?Answer:Q = LCHN
LChipCHN− LT−shirt
CHNLChip
CHNQT−shirt
CHN
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
More general PPF
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Outline
1 Basic ModelAssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Opportunity cost
The slope of the production possibility frontier is LT−shirtCHNLChip
CHN.
[Class question]: What is the economic interpretation of thisslope?To see this:
A worker can make 1LChip
CHNchip or 1
LT−shirtCHN
T-shirt.
Equivalently, it takes LChipCHN workers to make a chip and
LT−shirtCHN workers to make a T-shirt.
Hence, for each chip made, we could have made LT−shirtCHNLChip
CHNT-shirt..
We call this the opportunity cost of producing a football.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Opportunity cost
The slope of the production possibility frontier is LT−shirtCHNLChip
CHN.
[Class question]: What is the economic interpretation of thisslope?To see this:
A worker can make 1LChip
CHNchip or 1
LT−shirtCHN
T-shirt.
Equivalently, it takes LChipCHN workers to make a chip and
LT−shirtCHN workers to make a T-shirt.
Hence, for each chip made, we could have made LT−shirtCHNLChip
CHNT-shirt..
We call this the opportunity cost of producing a football.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Opportunity cost
The slope of the production possibility frontier is LT−shirtCHNLChip
CHN.
[Class question]: What is the economic interpretation of thisslope?To see this:
A worker can make 1LChip
CHNchip or 1
LT−shirtCHN
T-shirt.
Equivalently, it takes LChipCHN workers to make a chip and
LT−shirtCHN workers to make a T-shirt.
Hence, for each chip made, we could have made LT−shirtCHNLChip
CHNT-shirt..
We call this the opportunity cost of producing a football.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Opportunity cost
The slope of the production possibility frontier is LT−shirtCHNLChip
CHN.
[Class question]: What is the economic interpretation of thisslope?To see this:
A worker can make 1LChip
CHNchip or 1
LT−shirtCHN
T-shirt.
Equivalently, it takes LChipCHN workers to make a chip and
LT−shirtCHN workers to make a T-shirt.
Hence, for each chip made, we could have made LT−shirtCHNLChip
CHNT-shirt..
We call this the opportunity cost of producing a football.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Prices and specialization
Now suppose the price of chip and T-shirt in the China arepChip
CHN and pT−shirtCHN .
Take the perspective of a worker.
[Class question]: Suppose (as in the example) thatLChip
CHN = LT−shirtCHN = 1. Suppose that pChip
CHN = 1 andpT−shirt
CHN = 1. Then what would happen?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Prices and specialization
Now suppose the price of chip and T-shirt in the China arepChip
CHN and pT−shirtCHN .
Take the perspective of a worker.
[Class question]: Suppose (as in the example) thatLChip
CHN = LT−shirtCHN = 1. Suppose that pChip
CHN = 1 andpT−shirt
CHN = 1. Then what would happen?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Prices and specialization
Now suppose the price of chip and T-shirt in the China arepChip
CHN and pT−shirtCHN .
Take the perspective of a worker.
[Class question]: Suppose (as in the example) thatLChip
CHN = LT−shirtCHN = 1. Suppose that pChip
CHN = 1 andpT−shirt
CHN = 1. Then what would happen?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Prices and specialization
[Class question]: Suppose (as in the example) thatLChip
CHN = LT−shirtCHN = 1. Suppose that pChip
CHN = 4 andpT−shirt
CHN = 2. Then what would happen?Note: The units of the prices don’t actually matter. Whatmatters is the relative price pChip
CHNpT−shirt
CHN.
This is true throughout the course (and in economics moregenerally; it doesn’t matter if something is measured in centsor yuans).
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Prices and specialization
[Class question]: Suppose (as in the example) thatLChip
CHN = LT−shirtCHN = 1. Suppose that pChip
CHN = 4 andpT−shirt
CHN = 2. Then what would happen?Note: The units of the prices don’t actually matter. Whatmatters is the relative price pChip
CHNpT−shirt
CHN.
This is true throughout the course (and in economics moregenerally; it doesn’t matter if something is measured in centsor yuans).
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Prices and specialization
[Class question]: Suppose (as in the example) thatLChip
CHN = LT−shirtCHN = 1. Suppose that pChip
CHN = 4 andpT−shirt
CHN = 2. Then what would happen?Note: The units of the prices don’t actually matter. Whatmatters is the relative price pChip
CHNpT−shirt
CHN.
This is true throughout the course (and in economics moregenerally; it doesn’t matter if something is measured in centsor yuans).
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Prices and specialization
[Class question]: What is the relative price pChipCHN
pT−shirtCHN
at whichworkers are indifferent between producing chips and T-shirts?
Answer: when pChipCHN
pT−shirtCHN
= 1 workers earn the same amountregardless if they produce chips and T-shirts.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Prices and specialization
[Class question]: What is the relative price pChipCHN
pT−shirtCHN
at whichworkers are indifferent between producing chips and T-shirts?
Answer: when pChipCHN
pT−shirtCHN
= 1 workers earn the same amountregardless if they produce chips and T-shirts.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Prices and specialization
[Class question]: For a general technology LChipCHN and LT−shirt
CHN ,at what relative price are workers indifferent betweenproducing chips and T-shirts?
Answer: Worker revenue from producing chips is pChipCHN
LChipCHN
and
T-shirt is pT−shirtCHN
LT−shirtCHN
, so they are indifferent when:
pChipCHN
LChipCHN
= pT−shirtCHN
LT−shirtCHN
=⇒ pChipCHN
pT−shirtCHN
= LChipCHN
LT−shirtCHN
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Prices and specialization
[Class question]: For a general technology LChipCHN and LT−shirt
CHN ,at what relative price are workers indifferent betweenproducing chips and T-shirts?
Answer: Worker revenue from producing chips is pChipCHN
LChipCHN
and
T-shirt is pT−shirtCHN
LT−shirtCHN
, so they are indifferent when:
pChipCHN
LChipCHN
= pT−shirtCHN
LT−shirtCHN
=⇒ pChipCHN
pT−shirtCHN
= LChipCHN
LT−shirtCHN
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Outline
1 Basic ModelAssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Preferences
To determine equilibrium, we need to specify the preferencesof workers.For simplicity, suppose there is a “representative agent" in theeconomy who receives utility:
W = U(CChipCHN ,C
T−shirtCHN )
where:CChip
CHN ,CT−shirtCHN are the quantity of chips and T-shirts in China
U is some given functionW is a number that tells you the total utility of therepresentative agent.
I will assume that dU(.)dCChip
CHN> 0 and dU(.)
dCT−shirtCHN
> 0.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Preferences
To determine equilibrium, we need to specify the preferencesof workers.For simplicity, suppose there is a “representative agent" in theeconomy who receives utility:
W = U(CChipCHN ,C
T−shirtCHN )
where:CChip
CHN ,CT−shirtCHN are the quantity of chips and T-shirts in China
U is some given functionW is a number that tells you the total utility of therepresentative agent.
I will assume that dU(.)dCChip
CHN> 0 and dU(.)
dCT−shirtCHN
> 0.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Preferences
To determine equilibrium, we need to specify the preferencesof workers.For simplicity, suppose there is a “representative agent" in theeconomy who receives utility:
W = U(CChipCHN ,C
T−shirtCHN )
where:CChip
CHN ,CT−shirtCHN are the quantity of chips and T-shirts in China
U is some given functionW is a number that tells you the total utility of therepresentative agent.
I will assume that dU(.)dCChip
CHN> 0 and dU(.)
dCT−shirtCHN
> 0.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Indifference curves
We can use the preferences W = U(CChipCHN ,C
T−shirtCHN ) to rank
any consumption combination.That is, if U(CChip
CHN ,CT−shirtCHN ) > U(CChip
CHN , CT−shirtCHN ), then we
know that the representative agent would prefer to consume{CChip
CHN ,CT−shirtCHN } rather than {CChip
CHN , CT−shirtCHN }
The typical way to show this on a diagram is to drawindffierence curves.An indffierence curve is a set of all consumption bundles thatyield the same utility. Formally the indffierence curvecorresponding to utility W is:
IC(W ) = {CChipCHN ,C
T−shirtCHN |U(CChip
CHN ,CT−shirtCHN ) = W }
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Indifference curves
We can use the preferences W = U(CChipCHN ,C
T−shirtCHN ) to rank
any consumption combination.That is, if U(CChip
CHN ,CT−shirtCHN ) > U(CChip
CHN , CT−shirtCHN ), then we
know that the representative agent would prefer to consume{CChip
CHN ,CT−shirtCHN } rather than {CChip
CHN , CT−shirtCHN }
The typical way to show this on a diagram is to drawindffierence curves.An indffierence curve is a set of all consumption bundles thatyield the same utility. Formally the indffierence curvecorresponding to utility W is:
IC(W ) = {CChipCHN ,C
T−shirtCHN |U(CChip
CHN ,CT−shirtCHN ) = W }
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Indifference curves
We can use the preferences W = U(CChipCHN ,C
T−shirtCHN ) to rank
any consumption combination.That is, if U(CChip
CHN ,CT−shirtCHN ) > U(CChip
CHN , CT−shirtCHN ), then we
know that the representative agent would prefer to consume{CChip
CHN ,CT−shirtCHN } rather than {CChip
CHN , CT−shirtCHN }
The typical way to show this on a diagram is to drawindffierence curves.An indffierence curve is a set of all consumption bundles thatyield the same utility. Formally the indffierence curvecorresponding to utility W is:
IC(W ) = {CChipCHN ,C
T−shirtCHN |U(CChip
CHN ,CT−shirtCHN ) = W }
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Indifference curves
We can use the preferences W = U(CChipCHN ,C
T−shirtCHN ) to rank
any consumption combination.That is, if U(CChip
CHN ,CT−shirtCHN ) > U(CChip
CHN , CT−shirtCHN ), then we
know that the representative agent would prefer to consume{CChip
CHN ,CT−shirtCHN } rather than {CChip
CHN , CT−shirtCHN }
The typical way to show this on a diagram is to drawindffierence curves.An indffierence curve is a set of all consumption bundles thatyield the same utility. Formally the indffierence curvecorresponding to utility W is:
IC(W ) = {CChipCHN ,C
T−shirtCHN |U(CChip
CHN ,CT−shirtCHN ) = W }
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Indifference curves
[Class question]: Why are the indifference curves curved likethey are?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Indifference curves
[Class question]: Why are the indifference curves curved likethey are?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Types of indifference curves
[Class question] Suppose that:
U(CChipCHN ,C
T−shirtCHN ) = CChip
CHN + βCT−shirtCHN
What will the indifference curves look like?Answer:
W = CChipCHN + βCT−shirt
CHN =⇒ CChipCHN = W − βCT−shirt
CHNso that the indifference curves will be straight lines withintercept W and slope −β.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Types of indifference curves
[Class question] Suppose that:
U(CChipCHN ,C
T−shirtCHN ) = CChip
CHN + βCT−shirtCHN
What will the indifference curves look like?Answer:
W = CChipCHN + βCT−shirt
CHN =⇒ CChipCHN = W − βCT−shirt
CHNso that the indifference curves will be straight lines withintercept W and slope −β.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Types of indifference curves
[Class question] Suppose that:
U(CChipCHN ,C
T−shirtCHN ) = CChip
CHN + βCT−shirtCHN
What will the indifference curves look like?Answer:
W = CChipCHN + βCT−shirt
CHN =⇒ CChipCHN = W − βCT−shirt
CHNso that the indifference curves will be straight lines withintercept W and slope −β.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Types of indifference curves
What do the indifference curves like?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Types of indierence curves
[Class question] Supposethat:U(CChip
CHN ,CT−shirtCHN ) = min{(CChip
CHN , βCT−shirtCHN }
What will the indierence curves look like?Answer:
The key thing to note if you consume CChipCHN , then the utility
will be the same if you consume βCT−shirtCHN or βCT−shirt
CHN + x foranyx > 0Hence these preferences (known as “Leontief” preferences) willhave a “kink” at {x ;βx}
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Types of indierence curves
[Class question] Supposethat:U(CChip
CHN ,CT−shirtCHN ) = min{(CChip
CHN , βCT−shirtCHN }
What will the indierence curves look like?Answer:
The key thing to note if you consume CChipCHN , then the utility
will be the same if you consume βCT−shirtCHN or βCT−shirt
CHN + x foranyx > 0Hence these preferences (known as “Leontief” preferences) willhave a “kink” at {x ;βx}
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Types of indierence curves
[Class question] Supposethat:U(CChip
CHN ,CT−shirtCHN ) = min{(CChip
CHN , βCT−shirtCHN }
What will the indierence curves look like?Answer:
The key thing to note if you consume CChipCHN , then the utility
will be the same if you consume βCT−shirtCHN or βCT−shirt
CHN + x foranyx > 0Hence these preferences (known as “Leontief” preferences) willhave a “kink” at {x ;βx}
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Types of indifference curves
What do the indifference curves like?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Outline
1 Basic ModelAssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Autarkic equilibrium
We can now (nally!) define the autarkic equilibrium.[Class question]: What are the exogenous model parameters?
Answer: Productivities LChipCHN and LT−shirt
CHN , population LCHN ,and preferences U(.) (and the same for USA).
[Class question]: What are the endogenous model outcomes?Answer:Production QChip
CHN and QT−shirtCHN , consumption CChip
CHN
and CT−shirtCHN , and relative prices pChip
CHNpT−shirt
CHN(and the same for
USA).
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Autarkic equilibrium
We can now (nally!) define the autarkic equilibrium.[Class question]: What are the exogenous model parameters?
Answer: Productivities LChipCHN and LT−shirt
CHN , population LCHN ,and preferences U(.) (and the same for USA).
[Class question]: What are the endogenous model outcomes?Answer:Production QChip
CHN and QT−shirtCHN , consumption CChip
CHN
and CT−shirtCHN , and relative prices pChip
CHNpT−shirt
CHN(and the same for
USA).
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Autarkic equilibrium
We can now (nally!) define the autarkic equilibrium.[Class question]: What are the exogenous model parameters?
Answer: Productivities LChipCHN and LT−shirt
CHN , population LCHN ,and preferences U(.) (and the same for USA).
[Class question]: What are the endogenous model outcomes?Answer:Production QChip
CHN and QT−shirtCHN , consumption CChip
CHN
and CT−shirtCHN , and relative prices pChip
CHNpT−shirt
CHN(and the same for
USA).
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Autarkic equilibrium
DefinitionFor any set of productivities LChip
CHN and LT−shirtCHN , population LCHN ,
and preferences U(.), equilibrium is defined as a set of productionQChip
CHN and QT−shirtCHN , consumption CChip
CHN and CT−shirtCHN , and
relative prices pChipCHN
pT−shirtCHN
such that...
[Class question]: Any guesses as to what the equilibriumconditions are?
The utility of the representative agent is maximized.Workers maximize their revenue.Consumption is equal to production.
[Class question]: Which of the three equilibrium conditionswill change when we introduce trade?
Answer: the last one.Denfing the equilibrium:Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Autarkic equilibrium
DefinitionFor any set of productivities LChip
CHN and LT−shirtCHN , population LCHN ,
and preferences U(.), equilibrium is defined as a set of productionQChip
CHN and QT−shirtCHN , consumption CChip
CHN and CT−shirtCHN , and
relative prices pChipCHN
pT−shirtCHN
such that...
[Class question]: Any guesses as to what the equilibriumconditions are?
The utility of the representative agent is maximized.Workers maximize their revenue.Consumption is equal to production.
[Class question]: Which of the three equilibrium conditionswill change when we introduce trade?
Answer: the last one.Denfing the equilibrium:Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Autarkic equilibrium
DefinitionFor any set of productivities LChip
CHN and LT−shirtCHN , population LCHN ,
and preferences U(.), equilibrium is defined as a set of productionQChip
CHN and QT−shirtCHN , consumption CChip
CHN and CT−shirtCHN , and
relative prices pChipCHN
pT−shirtCHN
such that...
[Class question]: Any guesses as to what the equilibriumconditions are?
The utility of the representative agent is maximized.Workers maximize their revenue.Consumption is equal to production.
[Class question]: Which of the three equilibrium conditionswill change when we introduce trade?
Answer: the last one.Denfing the equilibrium:Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Autarkic equilibrium
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Autarkic Equilibrium Recap
Equilibrium prices are “pinned-down” by the productiontechnology: pChip
CHNpT−shirt
CHN= LChip
CHNLT−shirt
CHN
[Class question]: Will this always be the case?Answer: No, but if it is not the case, the country willcompletely specialize in the production of one good.
Total quantity produced is determined by the point where theindierence curve lies tangent to the production possibilityfrontier.
This depends on preferences.
Consumption is simply equal to production.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Autarkic Equilibrium Recap
Equilibrium prices are “pinned-down” by the productiontechnology: pChip
CHNpT−shirt
CHN= LChip
CHNLT−shirt
CHN
[Class question]: Will this always be the case?Answer: No, but if it is not the case, the country willcompletely specialize in the production of one good.
Total quantity produced is determined by the point where theindierence curve lies tangent to the production possibilityfrontier.
This depends on preferences.
Consumption is simply equal to production.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Autarkic Equilibrium Recap
Equilibrium prices are “pinned-down” by the productiontechnology: pChip
CHNpT−shirt
CHN= LChip
CHNLT−shirt
CHN
[Class question]: Will this always be the case?Answer: No, but if it is not the case, the country willcompletely specialize in the production of one good.
Total quantity produced is determined by the point where theindierence curve lies tangent to the production possibilityfrontier.
This depends on preferences.
Consumption is simply equal to production.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Autarkic Equilibrium Recap
Equilibrium prices are “pinned-down” by the productiontechnology: pChip
CHNpT−shirt
CHN= LChip
CHNLT−shirt
CHN
[Class question]: Will this always be the case?Answer: No, but if it is not the case, the country willcompletely specialize in the production of one good.
Total quantity produced is determined by the point where theindierence curve lies tangent to the production possibilityfrontier.
This depends on preferences.
Consumption is simply equal to production.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Outline
1 Basic ModelAssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
“Comparative static” example
Consider the China in autarky. (“Autarky” means in theabsence of trade).A comparative static tells us how an equilibrium objectchanges as we change model fundamentals.These make good exam questions.
For example: if we decrease the productivity of chip, whathappens to relative prices and the equilibriumproduction/consumption of chip and T-shirt?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
“Comparative static” example
Consider the China in autarky. (“Autarky” means in theabsence of trade).A comparative static tells us how an equilibrium objectchanges as we change model fundamentals.These make good exam questions.
For example: if we decrease the productivity of chip, whathappens to relative prices and the equilibriumproduction/consumption of chip and T-shirt?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
“Comparative static” example
Consider the China in autarky. (“Autarky” means in theabsence of trade).A comparative static tells us how an equilibrium objectchanges as we change model fundamentals.These make good exam questions.
For example: if we decrease the productivity of chip, whathappens to relative prices and the equilibriumproduction/consumption of chip and T-shirt?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
“Comparative static” example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
“Comparative static” example
So reducing the productivity of chips:Reduces the equilibrium consumption and production of chips.Increases the relative price of chips to T-shirts.
[Class question]what about the effect on the equilibriumconsumption and production of T-shirt?
It depends.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
“Comparative static” example
So reducing the productivity of chips:Reduces the equilibrium consumption and production of chips.Increases the relative price of chips to T-shirts.
[Class question]what about the effect on the equilibriumconsumption and production of T-shirt?
It depends.
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Outline
1 Basic ModelAssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example
As above:China has population of workers LCHN .Workers produce chips and T-shirts with unit labor costs LChip
CHNand LT−shirt
CHN , respectively.
Suppose workers havepreferences::U(CChip
CHN ,CT−shirtCHN ) = (CChip
CHN)α(CT−shirtCHN )1−α}
α ∈ (0, 1). These preferences are known as Cobb-Douglaspreferences.One of my go-to preferences for exams (other go-to: Leontief).
Question: What is the equilibrium quantity of chips andT-shirts consumed per worker?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example
As above:China has population of workers LCHN .Workers produce chips and T-shirts with unit labor costs LChip
CHNand LT−shirt
CHN , respectively.
Suppose workers havepreferences::U(CChip
CHN ,CT−shirtCHN ) = (CChip
CHN)α(CT−shirtCHN )1−α}
α ∈ (0, 1). These preferences are known as Cobb-Douglaspreferences.One of my go-to preferences for exams (other go-to: Leontief).
Question: What is the equilibrium quantity of chips andT-shirts consumed per worker?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example
As above:China has population of workers LCHN .Workers produce chips and T-shirts with unit labor costs LChip
CHNand LT−shirt
CHN , respectively.
Suppose workers havepreferences::U(CChip
CHN ,CT−shirtCHN ) = (CChip
CHN)α(CT−shirtCHN )1−α}
α ∈ (0, 1). These preferences are known as Cobb-Douglaspreferences.One of my go-to preferences for exams (other go-to: Leontief).
Question: What is the equilibrium quantity of chips andT-shirts consumed per worker?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Production
Step #1(a): We calculate the PPF. From above, recall thatlabor can be used either to produce chips or T-shirts.
QChipCHNLChip
CHN + QT−shirtCHN LT−shirt
CHN = LCHN
Can then write the quantity produced of chips as a function ofT-shorts.
QChipCHN = LCHN
LChipCHN
− QT−shirtCHN
LT−shirtCHNLChip
CHN
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Production
Step #1(a): We calculate the PPF. From above, recall thatlabor can be used either to produce chips or T-shirts.
QChipCHNLChip
CHN + QT−shirtCHN LT−shirt
CHN = LCHN
Can then write the quantity produced of chips as a function ofT-shorts.
QChipCHN = LCHN
LChipCHN
− QT−shirtCHN
LT−shirtCHNLChip
CHN
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Production
Step #1(b): We calculate the relative price. In autarky, therelative price of chips to T-shirts is equal to the (negative) ofthe slope of the PPF:
pT−shirtCHNpChip
CHN= − dQChip
CHNdQT−shirt
CHN
[Class question]: What is the intuition? Is this true withtrade?In this linear case, we then have (as we found above) that:
pChipCHN
pT−shirtCHN
= − LChipCHN
LT−shirtCHN
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Production
Step #1(b): We calculate the relative price. In autarky, therelative price of chips to T-shirts is equal to the (negative) ofthe slope of the PPF:
pT−shirtCHNpChip
CHN= − dQChip
CHNdQT−shirt
CHN
[Class question]: What is the intuition? Is this true withtrade?In this linear case, we then have (as we found above) that:
pChipCHN
pT−shirtCHN
= − LChipCHN
LT−shirtCHN
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Consumption
Step #2(a): We calculate the wage of a worker.Assume the price of T-shirts is 1 [Why is this okay?].WA worker can produce 1
LT−shirtCHN
. Hence her wage is:
wCHIN = pT−shirtCHN
LT−shirtCHN
= 1LT−shirt
CHN
[Class question] what would happen if I had calculatedwagOverivew of the trade in China and Worldes using herchips production?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Consumption
Step #2(a): We calculate the wage of a worker.Assume the price of T-shirts is 1 [Why is this okay?].WA worker can produce 1
LT−shirtCHN
. Hence her wage is:
wCHIN = pT−shirtCHN
LT−shirtCHN
= 1LT−shirt
CHN
[Class question] what would happen if I had calculatedwagOverivew of the trade in China and Worldes using herchips production?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Consumption
Step #2(b): We calculate the equilibrium consumption of aworker.
Maximize utility subject to the worker’s budget constraint:
maxCChipCHN ,C
T−shirtCHN
(CChipCHN)α(CT−shirt
CHN )1−α
s.t.CChipCHNpChip
CHN + CT−shirtCHN = wCHN
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Consumption
Step #2(b): We calculate the equilibrium consumption of aworker.
Maximize utility subject to the worker’s budget constraint:
maxCChipCHN ,C
T−shirtCHN
(CChipCHN)α(CT−shirt
CHN )1−α
s.t.CChipCHNpChip
CHN + CT−shirtCHN = wCHN
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Consumption
To solve the problem, we have
CT−shirtCHN = (1− α)wCHN
CChipCHNpChip
CHN = wCHN
Implication: With Cobb-Douglas preferences, always spend aconstant fraction of income on each good, where fractionpinned down by exponent!
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Consumption
To solve the problem, we have
CT−shirtCHN = (1− α)wCHN
CChipCHNpChip
CHN = wCHN
Implication: With Cobb-Douglas preferences, always spend aconstant fraction of income on each good, where fractionpinned down by exponent!
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Equilibrium
Step #3: Combine production and consumption equilibriumrelationships:
Prices: pChipCHN = LChip
CHNLT−shirt
CHN,pT−shirt
CHN = 1Wages:wCHIN = 1
LT−shirtCHN
Consumption: CT−shirtCHN = (1− α)wCHN , CChip
CHNpChipCHN = wCHN .
Answer to the question:
CT−shirtCHN = 1− α
LT−shirtCHN
,CChipCHN = α
LChipCHN
[Class questions] whats the intuition for and the unit costs?Why doesn’t the labor supply affect the production decision?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Equilibrium
Step #3: Combine production and consumption equilibriumrelationships:
Prices: pChipCHN = LChip
CHNLT−shirt
CHN,pT−shirt
CHN = 1Wages:wCHIN = 1
LT−shirtCHN
Consumption: CT−shirtCHN = (1− α)wCHN , CChip
CHNpChipCHN = wCHN .
Answer to the question:
CT−shirtCHN = 1− α
LT−shirtCHN
,CChipCHN = α
LChipCHN
[Class questions] whats the intuition for and the unit costs?Why doesn’t the labor supply affect the production decision?
Weigang Liu International Economics
Basic ModelSummary
AssumptionsProduction Possibility FrontierPrices and SpecializationPreferencesEquilibriumComparative saticsMathematical example
Mathematical example: Equilibrium
Step #3: Combine production and consumption equilibriumrelationships:
Prices: pChipCHN = LChip
CHNLT−shirt
CHN,pT−shirt
CHN = 1Wages:wCHIN = 1
LT−shirtCHN
Consumption: CT−shirtCHN = (1− α)wCHN , CChip
CHNpChipCHN = wCHN .
Answer to the question:
CT−shirtCHN = 1− α
LT−shirtCHN
,CChipCHN = α
LChipCHN
[Class questions] whats the intuition for and the unit costs?Why doesn’t the labor supply affect the production decision?
Weigang Liu International Economics
Basic ModelSummary
Summary
Assumptions of the model is introduced.
PPF is introduced.
How to find the equilibrium in mathematical language.
Weigang Liu International Economics
Basic ModelSummary
Summary
Assumptions of the model is introduced.
PPF is introduced.
How to find the equilibrium in mathematical language.
Weigang Liu International Economics
Basic ModelSummary
Summary
Assumptions of the model is introduced.
PPF is introduced.
How to find the equilibrium in mathematical language.
Weigang Liu International Economics
Basic ModelSummary
Homework #1
Find the equilibrium if the preference is:U(CChip
CHN ,CT−shirtCHN ) = min{(CChip
CHN , βCT−shirtCHN }.
U(CChipCHN ,C
T−shirtCHN ) = log(CChip
CHNβCT−shirtCHN ).
Weigang Liu International Economics
Appendix For Further Reading
Further Reading I
Krugman, Obstfeld, and Melitz.Chapter 3 in International Economics.Pearson Press, 2018.
Weigang Liu International Economics