Comparative advantage

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Comparative advantagethe basis for
specialization and trade
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A primitive economy

• There are two goods, bread and meat, and two
  people, Alice and Bob.
• Alice and Bob both work 12 hours per day.
• It takes 2 hours for Alice to make a loaf of
  bread and 4 hours to catch a rabbit.
• It takes 4 hours for Bob to make a loaf of bread
  and 2 hours to catch a rabbit.

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Alice alone

• Alice has not yet met Bob. She divides her time
  between making bread and catching rabbits. What
  is possible for her?
• How long does it take to make B loaves of bread
  and R rabbits?
• 2B4R
• In 12 hours, Alice can produce any combination
  such that 2B4R12

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Possible Consumptions for Alice Alone
Rabbits
For Alice, possibilities are given by the
equation 2B4R12. If she only made bread, she
could have 6 loaves. If she only caught rabbits,
shed catch 3.
3
6
Bread
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Alice diversifies
Rabbits
Alice prefers to have some of each good, rather
than to eat only bread. So she spends some time
on each. Suppose she wants equal amounts of
bread and rabbits. Then 2B4R12 and BR.
Solution is BR2
3
2
6
2
Bread
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Bob alone

• Bob divides his time between making bread and
  catching rabbits. It takes 4 hours to make a
  loaf of bread and 2 hours to catch a rabbit.
• How long does it take to make B loaves of bread
  and R rabbits?
• 4B2R
• In 12 hours, Bob can produce any combination
  such that 4B2R12

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Possible Consumptions for Bob Alone
Rabbits
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For Bob, possibilities are given by the
equation 4B2R12. If he made only bread, he
could have 3 loaves. If she only caught rabbits,
hed catch 6.
3
Bread
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Bob diversifies
Suppose Bob wants equal amounts of bread
and rabbits. Then 4B2R12 and BR.
Solution is BR2
Rabbits
6
2
3
2
Bread
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Alice meets Bob

• Suppose that Alice meets Bob and they decide to
  trade. Why might this work?
• Alice is relatively good at bread and Bob is
  relatively good at rabbits.
• What if they specialize?
• Alice could spend all day making bread.
• Bob could spend all day catching rabbits.

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Gains from Trade

• If Alice makes bread all day, she will make 6
  loaves.
• If Bob hunts all day, he will catch 6 rabbits.
• What if they trade?
• Alice could give Bob 3 loaves and Bob give Alice
  3 rabbits.
• Each would have 3 loaves and 3 rabbits to
  consume.
• Alone, each consumes 2 loaves and 2 rabbits.

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Why did trade work?

• Because they had different relative skills in
  producing things they both want.
• They specialized according to comparative
  advantage.
• What would have happened if Bob specialized in
  bread and Alice in rabbits?
• Not so good. Total output would be just 3 of
  each.

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The Sources of the Wealth of Nations.

• Specialization and division of labor according to
  comparative advantage.
• THE GREATEST improvement in the productive
  powers of labour, and the greater part of the
  skill, dexterity, and judgment with which it is
  any where directed, or applied, seem to have been
  the effects of the division of labour. Adam
  Smith, 1776

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Comparative advantage

• It takes Alice twice as long to catch a rabbit as
  to make a loaf of bread.
• It takes Bob twice as long to make a loaf of
  bread as to catch a rabbit.
• Alice is good at bread-making (compared to Bob)
• Bob is good at at rabbit-catching(compared to
  Alice)
• We say Alice has comparative advantage in bread
  and Bob has comparative advantage in rabbits.

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Comparative and Absolute Advantage

• In this example, Bob can catch more rabbits per
  day than Alice and Alice can make more loaves of
  bread per day than Bob.
• We say Bob has both comparative and absolute
  advantage in rabbits and Alice has both
  comparative and absolute advantage in bread.

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Comparative not absolute

• But what if Alice is better at both activities.
• Suppose that she can catch a rabbit in 1 hour
  and make a loaf of bread in 1 hour.
• It takes Bob 4 hours to make a loaf of bread and
  2 hours to catch a rabbit.
• Still Bob has comparative advantage in
  rabbit-catching. (It takes him half as long to
  catch a rabbit as to make a loaf of bread.)
• Alice has comparative advantage in bread.

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Cora can catch 4 rabbits per hour and Don can
catch 1. Cora can bake 4 loaves of bread per
hour and Don can bake 2.

1. Cora has comparative advantage in both
   activities.
2. Don has comparative advantage in bread-baking and
   Cora has comparative advantage in rabbit-catching
3. Don has comparative advantage in rabbit-catching
   and Cora has comparative advantage in
   bread-baking.
4. Don has comparative advantage in both activities.

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Why is that?

• In an hour Don can bake 2 loaves of bread or
  catch 1 rabbit. The ratio of Dons productivity
  at bread-baking to his productivity at
  rabbit-catching is 2/12
• In an hour Cora can bake 4 loaves of bread for
  every 4 rabbits she catches. The ratio of her
  productivity at bread-baking to her productivity
  at rabbit-catching is 4/41.
• Since 2gt1, Don has comparative advantage in
  bread.

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Continued

• The ratio of Dons productivity at
  rabbit-catching to his productivity at
  bread-baking is ½.
• The ratio of Coras productivity at
  rabbit-catching to her productivity at
  bread-baking is 4/41.
• Since 1gt1/2, Cora has comparative advantage in
  rabbit-catching.

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Farmers Alf and Barney can plant wheat or hay.
Alfs land yields 60 bushels of wheat per acre
and Barneys yields 30. Alfs land yields 3
tons of hay per acre and Barneys yields 2

1. Alf has comparative advantage in both crops.
2. Barney has comparative advantage in hay.
3. Barney has comparative advantage in wheat.

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Why is that?

• The ratio of Alfs productivity in hay to his
  productivity in wheat is
• 3 tons/ 60 bushels 1/20 tons/bushel
• The ratio of Barneys productivity in hay to his
  productivity in wheat is
• 2 tons/30 bushels1/15 tons/bushel
• 1/15gt1/20 so Barney has comparative advantage in
  hay.

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Alf has 100 acres. He can get 60 bushels of wheat
per acre or 3 tons of hay per acre. The following
equation shows the combinations of bushels of
wheat (W) and tons of hay (H) that he can grow
on his farm.

• 60W3H100
• (W/60)(H/3)100
• 3W60H
• 60W3H

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Why is that?

• He gets 60 bushels of wheat from every acre
  planted in wheat and three tons of hay from every
  acre in hay.
• To get W bushels of wheat he needs to plant
  W/60 acres in wheat. To get H tons of hay, he
  needs to plant H/3 acres in hay.
• He has 100 acres to plant in one or the other so
  he can choose any combination where
• (W/60)(H/3)100.

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The ratio of productivity in hay to productivity
in wheat for Alf is 1/20 ton per bushel, and for
Barney it is 1/15 ton per bushel. The price of
wheat is 1 per bushel. If the price of hay is
18 per ton

1. Alf will specialize in wheat and Barney in hay.
2. Both will produce wheat.
3. Both will produce hay.
4. Alf will specialize in hay and Barney in wheat.

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Why is that?

• By switching his cropland from hay to wheat, Alf
  gets 20 bushels of wheat for every ton of hay he
  gives up. 20 bushels of wheat are worth 20. A
  ton of hay is worth 18.
• By switching cropland from wheat to hay, Barney
  gets 1 ton of hay for every 15 bushels of wheat
  that he gives up. 15 bushels of wheat are worth
  15. A ton of hay is worth 20.

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.
Alfs Options
Gold line shows production possibilities. 1 ton
of hay costs 20 bushels of wheat.
6000 bushels
Pink line shows combinations Attainable by
specializing in wheat And trading at price 18
per ton for Hay and 1 per ton for wheat. .
5400 bushels
Dotted pink line shows Combinations available to
Alf If he specializes in Hay. (Bad Choice)
H
333.3
300 tons
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..
Barneys Options
W
3600
The green line shows combinations of Hay and
wheat that Barney could produce On his 100 acre
farm.
3000 bushels
The pink line shows combinations he Could obtain
by specializing in hay And trading at world
price of 18/per Ton of hay, 1 per bushel of
wheat.
Dotted pink line shows combos Available by
specializing in wheat (Bad idea)
H
200 tons
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