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Chapter 33 NAME
Production
Introduction. In this section we explore economywide production pos-
sibility sets. We pay special attention to the principle of comparative
advantage. The principle is simply that efficiency suggests that people
should specialize according to their relative abilities in different activities
rather than absolute abilities.
Example: For simplicity, let us imagine an island with only two people
on it, both of them farmers. They do not trade with the outside world.
Farmer A has 100 acres and is able to grow two crops, wheat and hay.
Each acre of his land that he plants to wheat will give him 50 bushels
of wheat. Each acre of his land that he plants to hay will give him 2
tons of hay. Farmer B also has 100 acres, but his land is not so good.
Each acre of his land yields only 20 bushels of wheat and only 1 ton of
hay. Notice that, although Farmer A’s land is better for both wheat and
hay, Farmer B’s land has comparative advantage in the production of hay.
This is true because the ratio of tons of hay to bushels of wheat per acre
2/50 = .04 for Farmer A and 1/20 = .05 for Farmer B. Farmer A, on the
other hand, has comparative advantage in the production of wheat, since
the ratio of bushels of wheat to tons of hay is 50/2 = 25 for Farmer A
and 20/1 = 20 for Farmer B. The efficient way to arrange production is to
have Farmer A “specialize” in wheat and farmer B “specialize” in hay. If
Farmer A devotes all of his land to wheat and Farmer B devotes all of his
land to hay, then total wheat production will be 5,000 bushels and total
hay production will be 100 tons. Suppose that they decide to produce
only 4,000 bushels of wheat. Given that they are going to produce 4,000
bushels of wheat, the most hay they can possibly produce together will
be obtained if Farmer A devotes 80 acres to wheat and 20 acres to hay
while Farmer B devotes all of his land to hay. Suppose that they decide to
produce 6,000 bushels of wheat. Then they will get the most hay possible
given that they are producing 6,000 bushels of wheat if Farmer A puts
all of his land into wheat and Farmer B puts 50 acres into wheat and the
remaining 50 acres into hay.
33.1 (0) Tip and Spot finally got into college. Tip can write term papers
at the rate of 10 pages per hour and solve workbook problems at the rate
of 3 per hour. Spot can write term papers at the rate of 6 pages per
hour and solve workbook problems at the rate of 2 per hour. Which of
these two has comparative advantage in solving workbook problems?
Spot.
408 PRODUCTION (Ch. 33)
0 20406080100
20
40
60
80
Problems
Pages
120
Spot
Tip
Joint
30
18
12
36 96
(a) Tip and Spot each work 6 hours a day. They decide to work together
and to produce a combination of term papers and workbook problems
that lies on their joint production possibility frontier. On the above graph
plot their joint production possibility frontier. If they produce less than
33.2 (0) Robinson Crusoe has decided that he will spend exactly 8
hours a day gathering food. He can either spend this time gathering
coconuts or catching fish. He can catch 1 fish per hour and he can gather
2 coconuts per hour. On the graph below, show Robinson’s production
possibility frontier between fish and coconuts per day. Write an equation
for the line segment that is Robinson’s production possibility frontier.
NAME 409
04812
16
4
8
12
Fish
Coconuts
16
Utility of 4
Utility of 8
Production
possibility frontier
(a) Robinson’s utility function is U(F, C)=FC,whereFis his daily
fish consumption and Cis his daily coconut consumption. On the graph
above, sketch the indifference curve that gives Robinson a utility of 4,
and also sketch the indifference curve that gives him a utility of 8. How
many fish will Robinson choose to catch per day? 4. How many
coconuts will he collect? 8. (Hint: Robinson will choose a bundle
that maximizes his utility subject to the constraint that the bundle lies
in his production possibility set. But for this technology, his production
possibility set looks just like a budget set.)
(b) Suppose Robinson is not isolated on an island in the Pacific, but is
retired and lives next to a grocery store where he can buy either fish or
coconuts. If fish cost $1 per fish, how much would coconuts have to cost in
order that he would choose to consume twice as many coconuts as fish?
(c) Back on his island, Robinson has little else to do, so he pretends that
he is running a competitive firm that produces fish and coconuts. He
wonders, “What would the price have to be to make me do just what I
am actually doing? Let’s assume that fish are the numeraire and have a
price of $1. And let’s pretend that I have access to a competitive labor
market where I can hire as much labor as I want at some given wage.
There is a constant returns to scale technology. An hour’s labor produces
410 PRODUCTION (Ch. 33)
one fish or 2 coconuts. At wages above $ 1per hour, I wouldn’t
produce any fish at all, because it would cost me more than $1 to produce
a fish. At wages below $ 1per hour, I would want to produce
infinitely many fish since I would make a profit on every one. So the
only possible wage rate that would make me choose to produce a positive
33.3 (0) We continue the story of Robinson Crusoe from the previous
problem. One day, while walking along the beach, Robinson Crusoe saw
a canoe in the water. In the canoe was a native of a nearby island. The
native told Robinson that on his island there were 100 people and that
they all lived on fish and coconuts. The native said that on his island, it
takes 2 hours to catch a fish and 1 hour to find a coconut. The native said
that there was a competitive economy on his island and that fish were
the numeraire. The price of coconuts on the neighboring island must
have been $.50. The native offered to trade with Crusoe at these
prices. “I will trade you either fish for coconuts or coconuts for fish at
the exchange rate of 2coconuts for a fish,” said he. “But you
will have to give me 1 fish as payment for rowing over to your island.”
Would Robinson gain by trading with him? No. If so, would he buy
(a) Several days later, Robinson saw another canoe in the water on the
other side of his island. In this canoe was a native who came from a
different island. The native reported that on his island, one could catch
only 1 fish for every 4 hours of fishing and that it takes 1 hour to find a
coconut. This island also had a competitive economy. The native offered
to trade with Robinson at the same exchange rate that prevailed on his
own island, but said that he would have to have 2 fish in return for rowing
between the islands. If Robinson decides to trade with this island, he
NAME 411
04812
16
4
8
12
Fish
Coconuts
16
Utility of 4
Utility of 8
Production
possibility frontier
(b) Write an equation for Crusoe’s “budget line” if he specializes appro-
priately and trades with the second trader. If he does this, what bundle
33.4 (0) The Isle of Veritas has made it illegal to trade with the outside
world. Only two commodities are consumed on this island, milk and
wheat. On the north side of the island are 40 farms. Each of these
farms can produce any combination of non-negative amounts of milk and
wheat that satisfies the equation m=60−6w. On the south side of the
island are 60 farms. Each of these farms can produce any combination
of non-negative amounts of milk and wheat that satisfies the equation
m=40−2w. The economy is in competitive equilibrium and 1 unit of
wheat exchanges for 4 units of milk.
(a) On the diagram below, use black ink to draw the production possibility
set for a typical farmer from the north side of the island. Given the
equilibrium prices, will this farmer specialize in milk, specialize in wheat,
412 PRODUCTION (Ch. 33)
0204060
80
20
40
60
Wheat
Milk
80
Black line
Blue line
Red line
Pencil line
15
10
(b) On the diagram below, use black ink to draw the production possibility
set for a typical farmer from the south side of the island. Given the
equilibrium prices, will this farmer specialize in milk, specialize in wheat,
0204060
80
20
40
60
Wheat
Milk
80
Black line
Blue line
Red line
Pencil line
(c) Suppose that peaceful Viking traders discover Veritas and offer to
exchange either wheat for milk or milk for wheat at an exchange rate of
NAME 413
1 unit of wheat for 3 units of milk. If the Isle of Veritas allows free trade
with the Vikings, then this will be the new price ratio on the island. At
(d) On the first of the two graphs above, use red ink to draw the budget
for northern farmers if free trade is allowed and the farmers make the
right choice of what to produce. On the second of the two graphs, use
red ink to draw the budget for southern farmers if free trade is allowed
and the farmers make the right choice of what to produce.
(e) The council of elders of Veritas will meet to vote on whether to accept
the Viking offer. The elders from the north end of the island get 40
votes and the elders from the south end get 60 votes. Assuming that
everyone votes in the selfish interest of his end of the island, how will
(f) Suppose that instead of offering to make exchanges at the rate of 1 unit
of wheat for 3 units of milk, the Vikings had offered to trade at the price
of 1 unit of wheat for 1 unit of milk and vice versa. Would either type
to sketch the budget line for each kind of farmer at these prices if he
makes the right production decision. How will the northerners vote now?
In favor. How will the southerners vote now? Depends
33.5 (0) Recall our friends the Mungoans of Chapter 2. They have a
strange two-currency system consisting of Blue Money and Red Money.
Originally, there were two prices for everything, a blue-money price and
a red-money price. The blue-money prices are 1 bcu per unit of ambrosia
and 1 bcu per unit of bubble gum. The red-money prices are 2 rcu’s per
unit of ambrosia and 4 rcu’s per unit of bubble gum.
414 PRODUCTION (Ch. 33)
(a) Harold has a blue income of 9 and a red income of 24. If it has to
pay in both currencies for any purchase, draw its budget set in the graph
below. (Hint: You answered this question a few months ago.)
0 5 10 15 20
5
10
15
Ambrosia
Bubble gum
20
Part j budget set
(12,9)
9
12
6
9
Part a budget set
(b) The Free Choice party campaigns on a platform that Mungoans should
be allowed to purchase goods at either the blue-money price or the red-
money price, whichever they prefer. We want to construct Harold’s bud-
get set if this reform is instituted. To begin with, how much bubble gum
could Harold consume if it spent all of its blue money and its red money
(c) How much ambrosia could it consume if it spent all of its blue
(d) If Harold were spending all of its money of both colors on bubble gum
and it decided to purchase a little bit of ambrosia, which currency would
(e) How much ambrosia could it buy before it ran out of that color money?
(f) What would be the slope of this budget line before it ran out of that
2.
NAME 415
(g) If Harold were spending all of its money of both colors on ambrosia
and it decided to purchase a little bit of bubble gum, which currency
(h) How much bubble gum could it buy before it ran out of that color
(i) What would be the slope of this budget line before it ran out of that
(j) Use your answers to the above questions to draw Harold’s budget set
in the above graph if it could purchase bubble gum and ambrosia using
either currency.
408 PRODUCTION (Ch. 33)
0 20406080100
20
40
60
80
Problems
Pages
120
Spot
Tip
Joint
30
18
12
36 96
(a) Tip and Spot each work 6 hours a day. They decide to work together
and to produce a combination of term papers and workbook problems
that lies on their joint production possibility frontier. On the above graph
plot their joint production possibility frontier. If they produce less than
33.2 (0) Robinson Crusoe has decided that he will spend exactly 8
hours a day gathering food. He can either spend this time gathering
coconuts or catching fish. He can catch 1 fish per hour and he can gather
2 coconuts per hour. On the graph below, show Robinson’s production
possibility frontier between fish and coconuts per day. Write an equation
for the line segment that is Robinson’s production possibility frontier.
NAME 409
04812
16
4
8
12
Fish
Coconuts
16
Utility of 4
Utility of 8
Production
possibility frontier
(a) Robinson’s utility function is U(F, C)=FC,whereFis his daily
fish consumption and Cis his daily coconut consumption. On the graph
above, sketch the indifference curve that gives Robinson a utility of 4,
and also sketch the indifference curve that gives him a utility of 8. How
many fish will Robinson choose to catch per day? 4. How many
coconuts will he collect? 8. (Hint: Robinson will choose a bundle
that maximizes his utility subject to the constraint that the bundle lies
in his production possibility set. But for this technology, his production
possibility set looks just like a budget set.)
(b) Suppose Robinson is not isolated on an island in the Pacific, but is
retired and lives next to a grocery store where he can buy either fish or
coconuts. If fish cost $1 per fish, how much would coconuts have to cost in
order that he would choose to consume twice as many coconuts as fish?
(c) Back on his island, Robinson has little else to do, so he pretends that
he is running a competitive firm that produces fish and coconuts. He
wonders, “What would the price have to be to make me do just what I
am actually doing? Let’s assume that fish are the numeraire and have a
price of $1. And let’s pretend that I have access to a competitive labor
market where I can hire as much labor as I want at some given wage.
There is a constant returns to scale technology. An hour’s labor produces
410 PRODUCTION (Ch. 33)
one fish or 2 coconuts. At wages above $ 1per hour, I wouldn’t
produce any fish at all, because it would cost me more than $1 to produce
a fish. At wages below $ 1per hour, I would want to produce
infinitely many fish since I would make a profit on every one. So the
only possible wage rate that would make me choose to produce a positive
33.3 (0) We continue the story of Robinson Crusoe from the previous
problem. One day, while walking along the beach, Robinson Crusoe saw
a canoe in the water. In the canoe was a native of a nearby island. The
native told Robinson that on his island there were 100 people and that
they all lived on fish and coconuts. The native said that on his island, it
takes 2 hours to catch a fish and 1 hour to find a coconut. The native said
that there was a competitive economy on his island and that fish were
the numeraire. The price of coconuts on the neighboring island must
have been $.50. The native offered to trade with Crusoe at these
prices. “I will trade you either fish for coconuts or coconuts for fish at
the exchange rate of 2coconuts for a fish,” said he. “But you
will have to give me 1 fish as payment for rowing over to your island.”
Would Robinson gain by trading with him? No. If so, would he buy
(a) Several days later, Robinson saw another canoe in the water on the
other side of his island. In this canoe was a native who came from a
different island. The native reported that on his island, one could catch
only 1 fish for every 4 hours of fishing and that it takes 1 hour to find a
coconut. This island also had a competitive economy. The native offered
to trade with Robinson at the same exchange rate that prevailed on his
own island, but said that he would have to have 2 fish in return for rowing
between the islands. If Robinson decides to trade with this island, he
NAME 411
04812
16
4
8
12
Fish
Coconuts
16
Utility of 4
Utility of 8
Production
possibility frontier
(b) Write an equation for Crusoe’s “budget line” if he specializes appro-
priately and trades with the second trader. If he does this, what bundle
33.4 (0) The Isle of Veritas has made it illegal to trade with the outside
world. Only two commodities are consumed on this island, milk and
wheat. On the north side of the island are 40 farms. Each of these
farms can produce any combination of non-negative amounts of milk and
wheat that satisfies the equation m=60−6w. On the south side of the
island are 60 farms. Each of these farms can produce any combination
of non-negative amounts of milk and wheat that satisfies the equation
m=40−2w. The economy is in competitive equilibrium and 1 unit of
wheat exchanges for 4 units of milk.
(a) On the diagram below, use black ink to draw the production possibility
set for a typical farmer from the north side of the island. Given the
equilibrium prices, will this farmer specialize in milk, specialize in wheat,
412 PRODUCTION (Ch. 33)
0204060
80
20
40
60
Wheat
Milk
80
Black line
Blue line
Red line
Pencil line
15
10
(b) On the diagram below, use black ink to draw the production possibility
set for a typical farmer from the south side of the island. Given the
equilibrium prices, will this farmer specialize in milk, specialize in wheat,
0204060
80
20
40
60
Wheat
Milk
80
Black line
Blue line
Red line
Pencil line
(c) Suppose that peaceful Viking traders discover Veritas and offer to
exchange either wheat for milk or milk for wheat at an exchange rate of
NAME 413
1 unit of wheat for 3 units of milk. If the Isle of Veritas allows free trade
with the Vikings, then this will be the new price ratio on the island. At
(d) On the first of the two graphs above, use red ink to draw the budget
for northern farmers if free trade is allowed and the farmers make the
right choice of what to produce. On the second of the two graphs, use
red ink to draw the budget for southern farmers if free trade is allowed
and the farmers make the right choice of what to produce.
(e) The council of elders of Veritas will meet to vote on whether to accept
the Viking offer. The elders from the north end of the island get 40
votes and the elders from the south end get 60 votes. Assuming that
everyone votes in the selfish interest of his end of the island, how will
(f) Suppose that instead of offering to make exchanges at the rate of 1 unit
of wheat for 3 units of milk, the Vikings had offered to trade at the price
of 1 unit of wheat for 1 unit of milk and vice versa. Would either type
to sketch the budget line for each kind of farmer at these prices if he
makes the right production decision. How will the northerners vote now?
In favor. How will the southerners vote now? Depends
33.5 (0) Recall our friends the Mungoans of Chapter 2. They have a
strange two-currency system consisting of Blue Money and Red Money.
Originally, there were two prices for everything, a blue-money price and
a red-money price. The blue-money prices are 1 bcu per unit of ambrosia
and 1 bcu per unit of bubble gum. The red-money prices are 2 rcu’s per
unit of ambrosia and 4 rcu’s per unit of bubble gum.
414 PRODUCTION (Ch. 33)
(a) Harold has a blue income of 9 and a red income of 24. If it has to
pay in both currencies for any purchase, draw its budget set in the graph
below. (Hint: You answered this question a few months ago.)
0 5 10 15 20
5
10
15
Ambrosia
Bubble gum
20
Part j budget set
(12,9)
9
12
6
9
Part a budget set
(b) The Free Choice party campaigns on a platform that Mungoans should
be allowed to purchase goods at either the blue-money price or the red-
money price, whichever they prefer. We want to construct Harold’s bud-
get set if this reform is instituted. To begin with, how much bubble gum
could Harold consume if it spent all of its blue money and its red money
(c) How much ambrosia could it consume if it spent all of its blue
(d) If Harold were spending all of its money of both colors on bubble gum
and it decided to purchase a little bit of ambrosia, which currency would
(e) How much ambrosia could it buy before it ran out of that color money?
(f) What would be the slope of this budget line before it ran out of that
2.
NAME 415
(g) If Harold were spending all of its money of both colors on ambrosia
and it decided to purchase a little bit of bubble gum, which currency
(h) How much bubble gum could it buy before it ran out of that color
(i) What would be the slope of this budget line before it ran out of that
(j) Use your answers to the above questions to draw Harold’s budget set
in the above graph if it could purchase bubble gum and ambrosia using
either currency.
