2. Objectives
1. Understand the components of the standard trade model,
production possibilities frontiers, isovalue lines, and indifference
curves.
2. Determine an optimal combination production and consumption
under autarky on the standard trade model.
3. Introduction
• Standard trade model is a general model that includes Ricardian,
specific factors, and Heckscher-Ohlin models as special cases.
– Two goods: food (F) and cloth (C)
– Two countries: Home (H) and Foreign (F)
• Two key relationships in the standard trade model
– Relationship between the production possibility frontier and the optimal
production choice
– Relationship between the preference and the optimal consumption choice
4. Optimal Production Choice
• What a country produces depends on the relative
price of cloth to food PC /PF.
• An economy chooses its production of cloth QC and
food QF to maximize the value of its output V = PCQC
+ PF QF, given the prices of cloth and food.
– The slope of an isovalue line equals –(PC /PF).
– Produce at point where PPF is tangent to isovalue line.
• At Q, an opportunity cost of cloth is equal to the
relative price of shoe (MRT = PC/PF).
– IF MRT < PC/PF then, it can increase profits (value) by
producing more cloth.
– IF MRT > PC/PF then, it can increase profits (value) by
producing less cloth.
Slope = - PC/PF
5. Relative Price and Production Choice
• When a relative price of cloth is low at (PC
/PF)1, a country will produce less cloth
and more food at Q1.
• When a relative price of cloth is high at
(PC /PF)2, a country will produce more
cloth and less food at Q2.
6. Consumption Choice
• Trade will allow country to exchange goods and to choose any points along the
isovalue line.
• Given the preference of consumers, there are one combination of two goods
along the isovalue line which gives the highest utility (satisfaction) to consumers.
• Country’s preference is represented by indifference curves.
– Community indifference curves: Assume that the country’s consumption
decisions may be represented as if they were based on the tastes of a single
representative consumer.
7. Indifference Curves
• Indifference curve: shows the various
combinations of two goods that yield
equal utility (satisfaction) to the country.
– Example: All three combinations of
Cloth and Food (A, B, C) bring the
same utility (satisfaction).
• One indifference curve for each level of
utility. Higher (right=upper) the
indifference curve, greater the utility
(satisfaction).
– Example: Indifference curve2 gives
higher utility (satisfaction) than
Indifference curve1. Cloth Consumption (QC)
Food Consumption (QF)
Indifference curve1
A
B
C
Indifference curve210
10 207
5
15
8. Marginal Rate of Substitution
• Marginal rate of substitution (MRSXY) of
X (cloth) for Y (food): the amount of Y
(food) that a country could give up for
one extra unit of X (cloth) and still remain
on the same indifference curve (same
utility).
• MRS is a slope of indifference curve.
MRS = ΔQF/ΔQC
– Example: At B, MRS = 1
Food Consumption (QF)
B
10
Indifference Curve1
Cloth Consumption (QC)10
5
15
9. Slope of Indifference Curve
• MRS is a ratio of marginal utilities.
MRS = MUC/MUF = (ΔTU/ΔQC)/(ΔTU/ΔQF) = ΔQF/ΔQC
where MUC is marginal utility of consuming one
more unit of cloth and TU is total utility of
consuming QC and QF.
• Indifference curve becomes steeper as it consumes
less cloth (moving toward upper left) and flatter as it
consumes more cloth (moving toward lower right).
– As consumption of cloth increases, MUC decreases
due to diminishing marginal utility, so MRS
decreases.
Cloth Consumption (QC)
Food Consumption (QF)
Indifference Curve1
A
B
C
10
10
10. Optimal Consumption Choice
• There are many combinations of two goods
that a country can choose to consume along
the isovalue line.
• There is one combination of two goods which
brings the highest utility (satisfaction) to a
country.
– Example: Both Point A and B are on the
isovalue line, but Point B on Indifference
curve 1 gives higher utility (satisfaction)
than Point A on Indifference curve 0.
– Point C will bring higher utility
(satisfaction) than Point B, but it cannot be
reached by the given isovalue line.
Food Consumption (QF)
B
Indifference Curve1
Cloth Consumption (QC)
Indifference Curve2
Indifference Curve0
C
A
Isovalue Line
11. Condition for Optimal Consumption
Combination
• At the optimal (maximum utility)
consumption combination, the isovalue
line is tangent to the indifference curve.
• A slope of isovalue line is equal to a slope
of indifference curve.
PC/PF = MRS
• At B, an additional utility from consuming
an additional unit of cloth is equal to its
relative price.
Food Consumption (QF)
B
Indifference Curve1
Cloth Consumption (QC)
Slope = -PC/PF
12. PPF and Indifference Curves
• A country can choose any
production combination along its
PPF.
• It can reach the highest utility
(satisfaction) at Point A on
Indifference curve 2.
– Point B is possible, but gives less utility
on Indifference Curve 1.
– Point C is impossible because it is
outside of PPF.
Quantity of Food (QF)
A
Indifference Curve2
Quantity of Cloth (QC)
Indifference Curve1
Indifference Curve3
B
C
PPF
13. Optimal Production and Consumption under
Autarky
• Autarky: absence of trade
• In the absence of trade, each
country produces and consumes at
a point where the country’s
production possibility frontier is
tangent to the highest indifference
curve.
• Under autarky, a country produces
what it consumes.
Quantity of Food (QF)
A
Indifference Curve
Quantity of Cloth (QC)
PPF
Slope = -PC/PF
Isovalue Line
14. Optimal Production and Consumption
Condition under Autarky
• At the optimal point, the slope of PPF is equal to the slope of indifference curve.
MRTCF = MRSCF
• At optimal, an opportunity cost of cloth is its value.
– If they are not equal, the country can increase its welfare by producing more
of goods whose value is higher than cost.
• At equilibrium (tangent point)
MRTCF = MRSCF = PC/PF
15. Equilibrium Relative price
• Equilibrium relative price (PC/PF): the slope of line tangent to the
country’s production possibility frontier and indifference curve at the
autarky point of production and consumption.
– The forces of demand and supply in each country determine the equilibrium
relative price.
– Demand is represented by the country’s indifference curves.
– Supply is represented by the country’s production possibility frontier.
16. Difference in PPFs and Equilibrium under
Autarky
• If each country has a PPF with different shape due differences in resources, even with
the same preference across countries (identical indifference curves) each country
chooses a different combination of goods to be produced and consumed under autarky.
Quantity of Food (QF)
AF
Indifference Curve
Quantity of Cloth (QC)
PPFF
Slope = -(PC/PF)F
Quantity of Food (QF)
AH
Indifference Curve
Quantity of Cloth (QC)
PPFH
Slope = -(PC/PF)H
17. Relative Prices across Countries under Autarky
• Under autarky
– Home has more resources to produce cloth, while Foreign has more recourses
to produce food.
– Relative price of cloth is lower in Home than Foreign.
(PC/PF)H < (PC/PF)F
• A difference in relative prices across countries under autarky provides
comparative advantage in each country.
– Home has a comparative advantage in production of cloth, while Foreign has
a comparative advantage in production of food.
18. Difference in Preference and Equilibrium
under Autarky
• If each country has different preference, even with the same resources across
countries (identical PPFs) each country chooses a different combination of goods
to be produced and consumed under autarky.
Quantity of Food (QF)
AH
Indifference Curve
Quantity of Cloth (QC)
PPFH
Slope = -(PC/PF)H
Quantity of Food (QF)
AF
Indifference Curve
Quantity of Cloth (QC)
PPFF
Slope = -(PC/PF)F
19. Relative Prices across Countries under Autarky
• Under autarky
– Home prefer more food than cloth, while Foreign prefer more cloth than
food.
– Relative price of cloth is lower in Home than Foreign.
(PC/PF)H < (PC/PF)F
• A difference in relative prices across countries under autarky provides
comparative advantage in each country.
– Home has a comparative advantage in production of cloth, while Foreign has
a comparative advantage in production of food.
20. 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
