Production Possibility Frontier
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
1
The Production Possibilities
Frontier
 Let’s
introduce the Production
Possibilities Frontier
– better known as the PPF.
 The
PPF is a basic workhorse in
economics.
 Important for understanding some basic
issues in economics.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
2
The PPF
 Great
application is with international
trade theory.
 Helps one understand and distinguish
between comparative advantage and
absolute advantage.
 An important historical figure in all this is
David Ricardo.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
3
David Ricardo
 Famous
19th century British economist.
 Some consider him the grandfather of
international trade theory.
 Very influential in pioneering the theory of
comparative advantage, inter alia.
 Very interesting, very bright guy.
 Had a lot of say about the “corn laws” in
England.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
4
The Production Possibility
Frontier - What Is It?
 The
description of the best possible
combinations of two goods to produce
using all of the available resources.
 Shows the trade-off between more of
one good in terms of the other.
 Assumes: input endowments given,
technology given, time given and
efficient production.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
5
Opportunity Cost
 The
opportunity cost of an activity is the value of
the resources used in that activity when they are
measured by what they would have produced
when used in their next best alternative.
 The slope of the Production Possibility Frontier
measures the marginal opportunity cost of
producing one good in terms of the amount of
the other good foregone.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
6
A Typical PPF Picture
The marginal
opportunity cost of
guns in terms of
butter is
increasing as we
move down the
PPF!
Butter
just attainable
inefficient
unattainable
just attainable
The PPF is
typically bowedout or linear.
It is not bowed-in
Guns
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
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Comparative Advantage
 The
person with the lower marginal
opportunity cost of an activity has the
comparative advantage at that activity.
 This means that the person with the
comparative advantage can produce
the activity by giving up the smallest
amount of the alternative activity.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
8
The Idea of Comparative
Advantage and Trade
 Specialization
and free trade will benefit
all trading parties, even when some are
“absolutely” more efficient producers
than others.
 Need to understand absolute vs.
comparative advantage.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
9
Absolute vs. Comparative
Advantage Applied to Trade





Absolute advantage: if your country uses fewer resources
to produce a given unit of output than the other country.
Comparative advantage: if your country can produce the
output at a lower marginal cost in terms of other goods
foregone than the other country.
Every country (or person, or economy) has a comparative
advantage at some activity.
Absolute advantage is not important and may not always
happen. Sometimes people or countries have the absolute
advantage in nothing! Yet trade possibilities still exist.
It’s all about comparative advantage.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
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PPFs and Comparative
Advantage
Maximum Production Rates
Production P
Random Relative Price Relative Price
Access
of RAM (kg of Corn Meal
Corn meal Memory (k
corn per k
(k chips per
Producer (kg/day) chips/day)
chips)
kg corn meal)
Juanita
12
4
3.00
0.33
Julio
8
2
4.00
0.25




In this example, there are two goods being produced: Corn meal and RAM.
Juanita has an absolute advantage at both: she can produce more of each than
Julio.
Juanita has a comparative advantage at producing RAM compared to Julio: she
gives up 3.00 kg/day of corn meal to make an additional 1k of chips.
Julio has a comparative advantage at producing corn meal compared to Juanita: he
gives up 0.25 k chips to make an additional kg of corn meal.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
11
Production Possibilities

When we draw the
production possibilities
for Juanita and Julio,
there is a kink at 8
kg/day corn meal and
4.00 k chips/day RAM.
The chart shows who
specializes in corn
meal and RAM at each
production level.
Production Possibilities (2)
8.00
7.00
6.00
RAM (k chips/day)

Julio varies production of both while Juanita stays
specialized in RAM. Slope equals Julio's price of corn
meal in terms of RAM = -0.25 k chips/kg corn meal.
Juanita varies production
of both while Julio stays
specialized in corn meal.
Slope equals Juanita's
price of corn meal in
terms of RAM = -0.33 k
chips/kg corn meal.
5.00
4.00
3.00
2.00
1.00
0.00
0 1 2 3 4 5 6 7 8 9 10 111213 141516 171819 202122 232425 262728 2930
Corn m eal (kg/day)
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
12
Adding a Third Producer
Maximum Production Rates
Production P
Random Relative Price Relative Price
Access
of RAM (kg of Corn Meal
Corn meal Memory (k
corn per k
(k chips per
Producer (kg/day) chips/day)
chips)
kg corn meal)
Juanita
12
4
3.00
0.33
Julio
8
2
4.00
0.25
Sergio
2
1
2.00
0.50


Sergio has no absolute advantage; however, he has a
comparative advantage over both Juanita and Julio in the
production of RAM.
He sacrifices 2.00 kg of corn meal to make an additional 1k of
chips.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
13
Adding a Fourth Producer
Maximum Production Rates
Producti
Random Relative Price Relative Price
Access
of RAM (kg
of Corn Meal
Corn meal Memory (k
corn per k (k chips per kg
Producer (kg/day) chips/day)
chips)
corn meal)
Juanita
12
4
3.00
0.33
Julio
8
2
4.00
0.25
Sergio
2
1
2.00
0.50
Maria
8
1
8.00
0.13

Question: What is Maria’s comparative advantage with
respect to each of the other three producers?
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
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Comparative Advantage and
Specialization


As more and more
producers enter the
economy, the
production possibility
curve gets more and
more bowed out
(concave).
Along any segment,
most of the producers
are fully specialized.
Only one producer is
producing both goods
along any segment.
Production Possibilities (All)
8.00
7.00
6.00
RAM (k chips/day)

5.00
4.00
3.00
2.00
1.00
0.00
0 1 2 3 4 5 6 7 8 9 1011 1213 141516 1718 192021 2223 242526 2728 2930
Corn m eal (kg/day)
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
15
The Supply Curve from the
PPF

At each relative
price of RAM in
terms of foregone
corn meal, we
can determine
the market supply
Maximum Production Rates
Producti
Random Relative Price Relative Price
Access
of RAM (kg
of Corn Meal
Corn meal Memory (k
corn per k (k chips per kg
Producer (kg/day) chips/day)
chips)
corn meal)
Juanita
12
4
3.00
0.33
Julio
8
2
4.00
0.25
Sergio
2
1
2.00
0.50
Maria
8
1
8.00
0.13
Supply Curve for RAM

The table shows
how much is
supplied and who
is producing.
Quantity
of RAM (k
Chips)
0
1
5
7
8
Relative
Price of RAM
(kg corn/k
RAM)
0.00
2.00
3.00
4.00
8.00
Who is Producing RAM
Chips
No one
Sergio
Sergio, Juanita
Sergio, Juanita, Julio
Sergio, Juanita, Julio, Maria
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
16
The Supply Curve for RAM
Relative Price (kg corn
m eal/k chips)
Supply Curve for RAM
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
0
1
2
3
4
5
6
7
8
9
10
RAM (k chips/day)

The graph shows the supply curve for RAM based on the data in the previous table.
Each additional supplier is shown above the segment where that supplier
determines the relative price.

The supply curve of RAM is rising, reflecting the increasing opportunity cost (also
called marginal cost) of RAM in terms of foregone corn meal.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
17
Supply Curve for Corn Meal
 Do
the exact same thing...
 But in reverse!
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
18
Supply Curve for Corn Meal:
Graph
Relative Price (k chips/kg
m eal)
Supply Curve for Corn Meal
0.700
0.600
0.500
0.400
0.300
0.200
0.100
0.000
0 1
2 3 4 5
6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35
Corn Meal (kg/day)
The supply curve for corn meal is shown above.
 The new producer along each segment is
indicated above.

Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
19
International Trade
Maximum Production Rates
Random
Relative Price Relative Price
Access
of RAM (kg
of Corn Meal
Corn meal Memory (k
corn per k (k chips per kg
Producer
(kg/day)
chips/day)
chips)
corn meal)
Country U
12
4
3.00
0.33
Country M
8
2
4.00
0.25
International price
3.50
0.29



All the facts are the same as in the previous example except that now we
are talking about countries that can trade at an international price.
The international price is between the relative prices that prevail in each
country when no trade is permitted.
There are many countries in the market in addition to the two shown so that
a country can buy or sell as much as it wants or produces at the
international price.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
20
Country U’s Production and
Gains from Trade



Country U has a comparative
advantage in RAM
production.
The blue line shows its
production possibilities
without trade. Slope = –0.33.
The red line shows the
possibilities at the
international price of 0.29 k
chips per kg corn (or 3.50
kg corn/ k chips RAM).
Slope = –0.29.
The gain to trade is the
distance between the two
production possibility curves.
Country U Production Possibilities
RAM (k
chips/day) no
Trade
4.00
3.50
RAM (k chips/day)

3.00
RAM (k
chips/day) with
Trade
2.50
2.00
1.50
1.00
0.50
0.00
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Corn Meal (kg/day)
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
21
Country M’s Production and
Gains from Trade



Country M has a comparative
advantage in corn meal
production.
The blue line shows its
production possibilities
without trade. Slope = –0.25.
The red line shows the
possibilities at the
international price of 0.29 k
chips/ kg corn (or 3.50 kg
corn/ k chips RAM). Slope =
–0.29.
The gain to trade is the
distance between the two
production possibility curves.
Country M Production Possibilities
RAM (k
chips/day) no
Trade
2.50
2.00
RAM (k chips/day)

RAM (k
chips/day) with
Trade
1.50
1.00
0.50
0.00
0
1
2
3
4
5
6
7
8
9
10
Corn Meal (kg/day)
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
22
Question
 If
country U chooses to consume 7
kg/day of corn meal, what is the gain to
trade from specializing in RAM
production, measured in k chips/day of
RAM?
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
23
Answer


The vertical distance
between the blue and
red PPFs at a corn meal
consumption of 7 kg/day
measures country U’s
gain to trade in k chips
RAM/day.
The point on the blue
PPF is the best country
U can do without trade.
With trade country U can
consume more RAM per
day, up to the point on
the red PPF.
Country U Production Possibilities
RAM (k
chips/day) no
Trade
4.00
3.50
RAM (k chips/day)

3.00
RAM (k
chips/day) with
Trade
2.50
2.00
1.50
1.00
0.50
0.00
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
Corn Meal (kg/day)
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
24
Question
 What
is country M’s gain if it chooses to
consume 1.5 k chips per day, measured
in kg/day of corn meal?
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
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Answer


The horizontal distance
between the red and blue
PPFs measures country
M’s gain to trade at a
RAM consumption of 1.5
k chips/day.
The blue PPF is the best
that country M can do
without trade.
Trade allows country M
to specialize in the
production of corn meal
and still benefit from a
higher consumption of
RAM.
Country M Production Possibilities
RAM (k
chips/day) no
Trade
2.50
2.00
RAM (k chips/day)

RAM (k
chips/day) with
Trade
1.50
1.00
0.50
0.00
0
1
2
3
4
5
6
7
8
9
10
Corn Meal (kg/day)
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
26
The International Supply
Curve for RAM


The international supply
curve for RAM is a rising
function of the opportunity
cost of RAM in terms of
foregone corn meal.
Which countries actually
produce RAM for the
international market will
depend upon where the
demand curve crosses
this supply curve.
Relative Price (kg corn meal/k chips)
Least Efficient
Producers
Most Efficient
Producers
Demand
RAM (K chips/day)
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
27
The Sources of
Comparative Advantage

The Heckscher-Ohlin Theorem is a theory that
explains the existence of a country’s comparative
advantage by its factor endowments.
– Factor endowments: the quantity and quality of
labor, land, and natural resources of a country.
– From Sweden in the early 1900s

According to the H-O theorem, a country has a
comparative advantage in the production of a
product if that country is relatively well endowed
with inputs used intensively in the production of
that product.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
28
The Sources of
Comparative Advantage

Edward Leamer of UCLA’s five biggies:
– Natural resources
– Knowledge capital
– Physical capital
– Land
– Skilled and unskilled labor
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
29
Other Explanations for
Observed Trade Flows
 Product
differentiation and competitive
markets
 Acquired comparative advantage
 Natural comparative advantages
 Economies of scale
 Trading Environments
 Openness of Economy
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
30
Note of Caution


Information on comparative advantage is often given in
many other forms - pay careful attention to the
information you are given.
Two more ways to present the same kind of information:
1 yd. of cloth
1 barrel of wine
England
2 hours
40 hours
Portugal
1 hour
10 hours
England
Portugal
1 hour of labor in cloth .5 yd. of cloth
1 yd. of cloth
1 hour of labor in wine 1/40 bl. of wine 1/10 a bl. of wine
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
31
Absolute Advantage and
Comparative Advantage
1 yd. of cloth
1 barrel of wine
England
2 hours
40 hours
Portigal
1 hour
10 hours
England
Portigal
1 hour of labor in cloth .5 yd. of cloth
1 yd. of cloth
1 hour of labor in wine 1/40 bl. of wine 1/10 a bl. of wine




Portugal has the A.A. in both wine and cloth.
England has the C.A. in cloth.
Portugal has the C.A. in wine.
Can you figure out the marginal opportunity cost for
each output in each country?
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
32
From Opportunity Cost to
Marginal Cost




The concept of marginal cost is the most important
concept in the theory of producer supply behavior.
Marginal cost is the additional cost associated with
increasing production by one unit.
In our production possibility examples, marginal cost
is the value of the activity that is reduced when the
other activity is increased by one unit.
Marginal cost is, therefore, the same thing as
marginal opportunity cost.
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
33
PPF Gymnastics

Butter


PPF new


PPF old

The PPF is also useful
for many other types of
questions.
Questions about
efficiency.
Questions about equity.
Questions about tax
and transfer policy.
Questions about
composition of output.
Questions about growth
and productivity.
Guns
Prof. John M. Abowd and Jennifer P. Wissink, Cornell University
34