Production Possibility Frontier

Prof. John M. Abowd and Jennifer P. Wissink, Cornell University 1

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Production Possibility Frontier


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oThe 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.


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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.


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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.


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oThe 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.


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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.


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A Typical PPF Picture

Guns

Butter

unattainable

inefficient just attainable

just attainable

The marginal opportunity cost of guns in terms of butter is increasing as we move down the PPF!

The PPF is typically bowed-out or linear.

It is not bowed-in


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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.


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oThe 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.


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oAbsolute 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.


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oPPFs and Comparative Advantage

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.

Maximum Production Rates Production Possibilities (2)

ProducerCorn meal (kg/day)

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Memory (k chips/day)

Relative Price of RAM (kg corn per k

chips)

Relative Price of Corn Meal (k chips per

kg corn meal)Juanita 12 4 3.00 0.33Julio 8 2 4.00 0.25


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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)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 1 2 3 4 5 6 7 8 9 10 111213 141516 171819 202122 232425 262728 2930

Corn meal (kg/day)

RA

M (

k c

hip

s/d

ay) 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.

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.


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Adding a Third Producer

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.



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chips)

Relative Price of Corn Meal (k chips per

kg corn meal)Juanita 12 4 3.00 0.33Julio 8 2 4.00 0.25Sergio 2 1 2.00 0.50


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Adding a Fourth Producer

Question: What is Maria’s comparative advantage with respect to each of the other three producers?



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chips)

Relative Price of Corn Meal

(k chips per kg corn meal)

Juanita 12 4 3.00 0.33Julio 8 2 4.00 0.25Sergio 2 1 2.00 0.50Maria 8 1 8.00 0.13


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oComparative 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)

0.00

1.00

2.00

3.00

4.00

5.00

6.00

7.00

8.00

0 1 2 3 4 5 6 7 8 9 1011 1213 141516 1718 192021 2223 242526 2728 2930

Corn meal (kg/day)

RA

M (

k c

hip

s/d

ay)


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oThe Supply Curve from the PPF

At each relative price of RAM in terms of foregone corn meal, we can determine the market supply

The table shows how much is supplied and who is producing.

Supply Curve for RAM Supply Curve of Corn Meal

Quantity of RAM (k

Chips)

Relative Price of RAM

(kg corn/k RAM)

Who is Producing RAM Chips

0 0.00 No one1 2.00 Sergio5 3.00 Sergio, Juanita7 4.00 Sergio, Juanita, Julio8 8.00 Sergio, Juanita, Julio, Maria



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chips)



Juanita 12 4 3.00 0.33Julio 8 2 4.00 0.25Sergio 2 1 2.00 0.50Maria 8 1 8.00 0.13


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The Supply Curve for RAM

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.

Supply Curve for RAM

0.001.002.003.004.005.006.007.008.009.00

10.00

0 1 2 3 4 5 6 7 8 9 10

RAM (k chips/day)

Re

lati

ve P

rice

(k

g c

orn

m

eal

/k c

hip

s)

The supply curve of RAM is rising, reflecting the increasing opportunity cost (also called marginal cost) of RAM in terms of foregone corn meal.


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Supply Curve for Corn Meal

Do the exact same thing... But in reverse!


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oSupply Curve for Corn Meal: Graph

The supply curve for corn meal is shown above. The new producer along each segment is

indicated above.

Supply Curve for Corn Meal

0.000

0.100

0.200

0.300

0.400

0.500

0.600

0.700

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)

Re

lati

ve P

rice

(k

ch

ips

/kg

m

eal

)


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International Trade

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.

Maximum Production Rates Country U


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chips)



Country U 12 4 3.00 0.33Country M 8 2 4.00 0.25International price 3.50 0.29


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oCountry 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

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Corn Meal (kg/day)

RA

M (

k ch

ips/

da

y)

RAM (kchips/day) noTrade

RAM (kchips/day) withTrade


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oCountry 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

0.00

0.50

1.00

1.50

2.00

2.50

0 1 2 3 4 5 6 7 8 9 10

Corn Meal (kg/day)

RA

M (

k ch

ips/

da

y)




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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?


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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

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Corn Meal (kg/day)

RA

M (

k ch

ips/

da

y)




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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?


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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

0.00

0.50

1.00

1.50

2.00

2.50

0 1 2 3 4 5 6 7 8 9 10

Corn Meal (kg/day)

RA

M (

k ch

ips/

da

y)




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oThe 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.

RAM (K chips/day)

Relative Price (kg corn meal/k chips)

Most Efficient Producers

Least Efficient Producers

Demand


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oThe Sources ofComparative 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.


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oThe Sources ofComparative Advantage Edward Leamer of UCLA’s five biggies:

– Natural resources

– Knowledge capital

– Physical capital

– Land

– Skilled and unskilled labor


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oOther Explanations forObserved Trade Flows Product differentiation and competitive

markets Acquired comparative advantage Natural comparative advantages Economies of scale Trading Environments Openness of Economy


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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:England Portugal

1 yd. of cloth 2 hours 1 hour1 barrel of wine 40 hours 10 hours

England Portugal1 hour of labor in cloth .5 yd. of cloth 1 yd. of cloth1 hour of labor in wine 1/40 bl. of wine 1/10 a bl. of wine


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oAbsolute Advantage and Comparative Advantage

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?

England Portigal1 yd. of cloth 2 hours 1 hour

1 barrel of wine 40 hours 10 hours

England Portigal1 hour of labor in cloth .5 yd. of cloth 1 yd. of cloth1 hour of labor in wine 1/40 bl. of wine 1/10 a bl. of wine


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oFrom 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.


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PPF Gymnastics

Guns

Butter

PPF old

PPF new

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.

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Production Possibility Frontier

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