OPPORTUNITY COST AND GAINS FROM TRADE

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OPPORTUNITY COST AND GAINS FROM TRADE

• PRINCIPLES OF MICROECONOMICS

Dr. Fidel Gonzalez Department of Economics and
Intl. Business Sam Houston State University
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OPPORTUNITY COST
MARGINAL ANALYSIS
Elasticity
Elasticity
SUPPLY
DEMAND
MARKET EQUILIBRIUM
CONSUMER SURPLUS PRODUCER SURPLUS AND TOTAL
SURPLUS
MARKET EFFICIENCY
MARKET FAILURE
Pigouvian Taxes Quotas Coase Theorem Command and
control
TAXES
EXTERNALITIES
PUBLIC GOODS
COMMON GOODS
ARTIFICIALLY SCARCE GOODS
GAME THEORY
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Opportunity costs and gains from trade
The economic problem is a problem of scarcity and
equity. Scarcity refers to the fact that we have
a lot of desires and a finite number of
resources. This topic talks about scarcity and
introduces some important concepts. In
particular we will talk about 1) Slope and
equation of the line 2) Opportunity cost 3)
Production possibilities frontier 4)
Efficiency 5) Absolute and comparative
advantage 6) Terms of trade
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Opportunity costs
I will explain this concepts using an
example Consider Rob who lives in a desert
island. For survival Rob can collect coconuts (C)
or bananas (B) If he spends the whole day working
he can collect EITHER 8 coconuts and 0 bananas
(if he spends the day collecting only
coconuts) OR 0 coconuts and 10 bananas (if he
spends the day collecting only coconuts) Note
that he is can NOT collect 10 coconuts and 8
bananas that is impossible.
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So what is the scarce resource In this case
time is scarce there is a fixed number of hours.
If there were more hours then Rob will work
longer and obtain more coconuts and
bananas. Next I will graph the options for Rob.
This point represents zero bananas and eight
coconuts.
C
8
This point represents 10 bananas and zero
coconuts.
10
B
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Now we allow Rob to collect any linear
combination of the two point in the previous
graph. Hence I can draw a straight line between
the two points and any point on the line will be
feasible.
Why we allow Rob to have a linear combination and
not some other kind We do this to keep things
simple. We will relax this assumption later on.
C
For example before only the y and x-intercept
were possible but now Rob can collect 4 coconuts
and 5 bananas. Any point on the line.
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Next lets obtain the slope of the line and the
equation of the line (PLEASE refer to the power
point presentation on how to do this).
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5
10
B
Slope -8/10 0.8 Equation of the line in a
general form is y slopex y-intercept In
this case C -0.8 B 8
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The equation of the previous line is very useful
because it gives me all the possible combinations
of C and B that are feasible (that is the all
possible points on the line). For example if B1
then C 7.2 B6 then C5.2
B4 then C4.8
Imagine that Rob decides to collect the
following C8 and B 0 Eating only coconuts is
very boring so Rob decides to eat one banana
now we have the following C -0.8 (1) 8
7.2 Hence C7.2 and B1 Note that in order to
increase bananas by one unit Rob has to reduce
his consumption of coconuts by 0.8 (from 8 to 7.2
coconuts)
C
8
10
B
What if C4.8 and B4 and Rob decides to increase
bananas by one unit then now he will have
C-0.8(5) 8 4 that is C4 and B5
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In every single case in order to increase the
amount of bananas Rob has to give up 0.8
coconuts. This is the idea behind opportunity
cost. The opportunity cost is the is the value of
the best alternative to any choice. In our
example the opportunity cost of one extra banana
for Rob is 0.8 coconuts. Note that there is a
relationship between opportunity cost of one
banana and the slope of the line in the previous
graph. In both cases we measure how much of C
decreases when B goes up by one unit. Actually
the absolute value of the slope is equal to the
opportunity cost of one extra unit of B in terms
of C. First why did I say the absolute
value Because the slope in the graph is
negative -0.8. The opportunity cost is not
negative. Hence I need to take the absolute
value of the slope. Remember that the absolute
value of any number is the positive value of the
number. The absolute value is denoted by
. For example the absolute value of -10 is 10
the absolute value of 10 is also 10. Think of it
as the positive version of any number. Using the
notation -10 10 -5 5 6 6 etc.
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In general the opportunity cost of one extra unit
of the variable in the x-axis is equal to the
absolute value of the slope in terms of the y
variable. In our previous example The
opportunity cost of one extra unit of B slope
of C The opportunity cost of one extra unit of B
0.8 of C We have not talked about the
opportunity cost of coconuts. Lets use the
equation of the line first Start at B10 and
C0 now increase C by one unit and obtain the
value of B 1 -0.8 B 8 -7 -0.8B B 8.75
B decreased by 1.25 units What if B 4 and
C4.8 increase C by one unit and obtain B 5.8
-0.8 B 8 -2.2 -0.8 B B 2.75 B decreased
by 1.25 units
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That is in order to get an extra unit of C Rob
has to give up 1.25 units of B. That is the
opportunity cost of one extra unit of C is 1.25
units of B. Notice the 1.25 is the inverse of the
slope. That is In general the opportunity
costs of one extra unit of the variable in the
y-axis is equal to the inverse of the absolute
value of the slope in terms of the variable in
the x-axis. In the Rob example
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Production Possibilities Frontier
Now assume that Rob gets tired as the day passes
by. In the morning Rob is very productive
however in the afternoon Rob is not very
productive because he is tired. These are Robs
new options
In the morning 3C and 0B or 0 C and 6 B
In the afternoon 5 C and 0B or 0 C and 4 C
We can graph the previous information
C
Afternoon Slope-5/4-1.25
Morning Slope-3/6-0.5
C
5
3
6
4
B
B
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Combining the morning and afternoon graph into
one graph
C
C
Morning Slope-3/6-0.5
Afternoon Slope-5/4-1.25
5
3
6
C
C
4
B
8
Morning Slope-3/6-0.5
3
5
Afternoon Slope-5/4-1.25
6
10
B
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Note that the slope changes from the morning to
the afternoon. In fact the slope gets
flatter. This means that the opportunity cost of
B increases from morning to afternoon. In other
words B is getting more expensive in the
afternoon. The opposite is happening to C it
is getting cheaper from morning to afternoon.
Morning Slope-3/6-0.5
C
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Afternoon Slope-5/4-1.25
5
B
10
6
Now imagine that we can reduce the day not in
two parts but in milliseconds. In that case the
previous graph will be a curve
C
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The slope of the curve on the left is always
changing. The slope starts from almost zero at
the origin and gets steeper and steeper and B
increases. In other words the opportunity cost
of B increases as we have more of B.
B
10
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The line that shows all the maximum different
possible production combinations is called the
production possibilities frontier (PPF). The
production possibilities frontier can be a
straight line or a curve like in the previous
graph. If the PPF is a straight line the slope
dos not change along the line and the opportunity
cost is also constant. If the PPF is curved like
in the last graph then the slope increases as
the variable in the x-axis goes up. That means
that the opportunity cost of the variable in the
x-axis increases
In the graph on the left you can see that a
change in the x variable when y is big produces a
very small decrease in the y variable. However
the same change in x when y is big produces a
large change in the y variable. That is in order
to obtain the same extra x you give up of y when
y is higher. Q Why does this happen Imagine
that y is the amount of computers produced and x
is the amount of car (see graph in the next)
y
x
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Computers
When we produce a lot of computers we have
resources that are specialized (cars engineers)
and non-specialized resources (assemblers). When
we increase the production of cars most of the
non-specialized resources moves to the cars
industry. Why Because they have skills that can
be used in either industry. Since most of the
specialized computer workers stays in the
computer industry then the drop in the
production of computers does not change that
much. If we continue increasing the production of
cars we will be taking more and more specialized
computer workers into car production. Therefore
the production of computers will drop more and
more.
Cars
At the end we will be transferring very
specialized computer workers into the production
of cars and the production of computer will drop
significantly.
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Computers
C
We want to know if point on the PPF are
efficient. First we need to defined what is
efficiency. We will use the definition Pareto
efficiency (Pareto was an Italian economist) We
say that an allocation is efficient if in order
to make someone better of we have to make someone
else worse off. In terms of the PPF we say that
an allocation is efficient if in order to
increase the production of one good I have to
reduce the production on another good.
B
A
PPF
Cars
The point A is below the PPF this means that we
can increase the production of both goods at the
same time so this is clearly and inefficient
point. Allocations below the PPF are
inefficient. The point B is efficient because in
order to increase the production of any good we
have to reduce the production of the other good.
Any allocation on the PPF is efficient. No single
allocation on the PPF is more efficient the
others they are all equally efficient. The point
C is above the PPF this means that this point is
not feasible. We would like to produce at point C
because it represents higher production but our
resources are not enough to reach it. Allocations
above the PPF are desired but unfeasible.
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Trade
Lets go back to our previous example with Rob and
assume the PPF is a straight line. So far we have
Rob is alone in the island. Because Rob has
nobody to trade with everything that he produces
he has to consume it. That is in the absence of
trade production equals consumption WITHOUT
TRADE PRODUCTIONCONSUMPTION Now Sam appears in
the island too. There are only Rob and Sam in the
desert island. Sam can collect 12 coconuts and 0
bananas OR 0 coconuts and 4 bananas Graphing
Sams production possibilities frontier
C
12
Slope -12/4 -3
PPF
4
B
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Hence The opportunity cost of 1 B 3 C The
opportunity cost of 1 C 1/3 C Now imagine they
do not trade and each produce the following Rob
decides to produce 5 B and 4 C Sam decide to
produce 2 B and 6 C
World Production and Consumption without Trade
Total World Production of B is 7 and C is 10
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Graphing the information in the table we obtain
the PPF for Rob and Sam
Sam
Rob
C
C
12
8
6
4
2
4
B
5
10
B
Remember that because there is not trade their
production possibilities frontier also dictates
how much they can consume. None of them can
consume above their PPF when there is not
trade. However they would like to consumer above
their PPF. Both of them will enjoy to consume
more of both goods. Remember points above PPF are
desired but unfeasible without trade.
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Before we move one we need to have some
definitions. Absolute Advantage someone has an
absolute advantage if he is able to produce more
of a good or service with the same amount of
resources. In our previous example Sam has an
absolute advantage in the production of coconuts
and Rob has an absolute advantage in the
production of B. Comparative Advantage someone
(or a country) has an comparative advantage in
the production of a good or service if it has a
lower opportunity cost than the other person
(country) in the production of that good or
service. In our previous example Rob has a
comparative advantage in the production of
bananas (its opportunity cost of one B is 0.8 C
which is lower than Sams 3 C). Sam has a
comparative advantage in the production of
coconuts (its opportunity cost of one C is 1/3
which is lower than Sams 1.25 C). The concept of
comparative advantage is key to understand trade.
Having a comparative advantage in the production
of a good means that it is cheaper for that
person to produce the good. It is cheaper in the
sense that the person has to give up less of the
other good. That is for Rob is cheaper to
produce bananas (in terms of the coconuts he has
to give up) and for Sam is cheaper to produce
coconuts (in terms of the bananas he has to give
up).
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Assume each person specializes in the production
of the good in which they have a comparative
advantage. In the example Sam will specialize
in coconuts and Rob will specialize in
bananas. The following table shows the new world
production
World Production with Specialization
We have just showed the power of specialization
based on comparative advantage. Comparing the
world production with and without specialization
we can see that the world production with
specialization increase the total production of B
by 3 units and the total production of C
increases by 2 units. The theory of comparative
advantage tell us that total production will
increase if producers specialize in the good in
which they have a comparative advantage. Because
no one can have a comparative advantage in all
goods
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However with specialization the production is not
equal to production. Part of the production is
consumed by the producer and the rest is traded
for other goods. WITH SPECIALIZATION (OR WITH
TRADE) CONSUMPTION PRODUCTION Once Rob and
Sam specialize in the production of B and C
respectively they have to trade. The question
now is What is the price at which they will be
willing to trade In other words how many C for
B are they willing to trade. This price is called
terms or trade. Rob will love to have a price
of 1 B for 12 C clearly Sam will not want this.
Sam will love to have a price of 1C for 10 B but
Rob will not like it. So what kind of price is
Rob and Sam willing to accept
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Lets start with Rob Rob can do two things 1) he
can not specialize and trade with himself or 2)
specialize and trade with Sam. If Rob does not
specialize he is fact trading with himself and
the price he is paying is his opportunity cost.
For example imagine that Rob is producing 5
bananas and 4 coconuts. He now wants to have
another coconut. He can figuratively trade with
himself he will do that by increasing the
production of coconuts by one. But this requires
that he lowers the production of bananas by 1.25
bananas. In fact he has traded 1 coconut for
1.25 bananas with himself. The opportunity cost
is the price of trading with himself. Rob will
accept any price that is better than the price of
trading with himself. In other words we will
accept any price that is better than his
opportunity cost. A good to see this is by
using a number line. We will use the number line
that you used in kindergarten.
The number line goes from left to right and
increases from zero to infinity
0
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I will show the opportunity cost in the number
line. Robs opportunity cost 1C 1.25 B Next
put C on the other side
Now graph 1.25 B/C in the number line
B/C
0
1.25
We know that Rob has bananas and wants coconuts
so he will love to have a price of very few
bananas for a lot of coconuts. When B is low and
C is high then B/C will be a low number. That is
Rob prefers small B/C. This implies that Rob
will be better off compared to trading with
himself to the left of the opportunity cost. For
example if the price happens to be 0.5 bananas
for 1 coconut Rob will be better off because if
he trades with himself he would have to give up
1.25 for 1 coconut. As long as the price is to
the left of his opportunity cost Rob will be
better off.
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Robs opp. cost
B/C
0
1.25
Rob is better off to the left of the opp. cost
Now lets consider Sam. His opportunity cost is 1
C 1/3 B Again moving C to the other side
Now let show Sams opportunity cost in the
number line
B/C
0
0.33
Sam has coconuts and wants bananas so he wants
to have a price of very few coconuts for a lot of
bananas. When B is high and C is low then B/C
will be a high number. Sam prefers small B/C..
For example if the price happens to be 2
bananas for 1 coconut Sam will be better off
because if he trades with himself he would have
to give up 3 coconuts for 1 banana. As long as
the price is to the right of his opportunity cost
Sam will be better off.
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Placing both opportunity costs in the same number
line
Sam is better off to the left of his opp. cost
Sams opp. cost
B/C
1.25
0.33
0
Robs opp. cost
Rob is better off to the left of his opp. cost
The place where both Sam and Rob can be better
off is between 0.33 and 1.25
Both better off in this range
B/C
1.25
0.33
0
We really do not know where in the range between
0.33 and 1.25 B/C the real price will be. This
will depend on their negotiations but we know
that for sure that they will trade.
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Lets assume that they decide the price to be 1.
bananas for 1 coconut.
Actual price
B/C
0.5
1.25
0.33
0
Also assume that Rob decides to sell two
bananas. This implies that Sam has to pay 4
coconuts. The final allocation of coconuts and
bananas is the following
World Production with Specialization
World Consumption After Trade
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Finally lets compare consumption with trade and
consumption without trade
World Consumption without Trade
World Consumption After Trade
NOTE THAT WITH TRADE BOTH SAM AND ROB CONSUME
MORE THAN WITHOUT TRADE
We have reached our main conclusion Trade will
be better than no trade for all parties involved
IF AND ONLY IF 1) the parties specialize in the
production of the good in which they have a
comparative advantage AND 2) the terms of
trade are better than their respective
opportunity costs.
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However the advantages of trade are not only that
both can consume more but also they consumer
above the production possibilities frontier. That
brings us to our second main result
If 1) the parties specialize in the production of
the good in which they have a comparative
advantage AND 2) the terms of trade are
better than their respective opportunity
costs. The involved parties will consume above
their production possibilities frontier. A point
that is not feasible (but desired) without trade
The point 8C and 2 B is above the PPF so it is
preferred over any point on the PPF but it is
only available with trade
Rob
Sam
The point 4C and 8 B is above the PPF so it is
preferred over any point on the PPF but it is
only available with trade
C
C
12
8
6
4
2
4
B
5
10
B