Econ Dept, UMR
Presents
Scarcity, Efficiency, and
Growth
Starring
‹The 3 Basic Questions, and
‹The Production Possibilities
Model
Featuring
‹ The Invisible Hand Argument for
coping with scarcity
‹ Three Basic Questions
‹ Production Possibilities Model
‹ Marginal Opportunity Cost
‹ Efficiency
Part II
‹ Production Possibilities Model
‹ Marginal Opportunity Cost
‹ Efficiency
Production Possibilities Model
‹ Useful to show implications of scarcity
‹ Assumptions of the model
™ There are only 2 things we want
™ Resources and technology are held
constant
™ The trade-off is represented by
‹Increasing marginal cost, or
‹Constant marginal cost
Concepts Illustrated by the PP
Model
‹ What? (where we choose to produce)
‹ How? (we want to choose a point on
the frontier)
‹ Marginal Opportunity Cost
™ Constant (The PPF is linear)
™ Increasing (The PPF is concave)
‹ Scarcity
‹ Productive Efficiency
‹ Growth
Production Possibilities Table
‹ Production Possibilities Table
- a table
that shows all combinations of goods
and services that can be produced given
the resources of society and the existing
state of technology
‹ For simplicity we assume all we want
are two things: House and All Other
Goods (AOG)
Production Possibilities Table:
A Few Possible Combinations
AOG/t
Houses/t
112
0
98
7
80
13
Production Possibilities Table
(Complete)
All Other Goods/t
Housing/t
112
0
98
7
80
13
60
18
40
22
22
25
8
0
27
28
Production Possibilities
Frontier (Table)
‹ This table let’s us know how much our
economy can produce. Let’s show these
possibilities graphically.
‹ To do this we measure the quantity of
each good on the x and y axes.
Production Possibilities (per
month)
‹ If all resources are used to make AOG
we can produce 112 AOG in one month
and implicitly no Houses.
‹ Let’s say we figure that it’s probably a
good idea to make some Houses. What
resources do we shift from AOG to
House production?
™ To anticipate: shift resources such that the
opportunity cost of the houses is as low as
possible
Production Possibilities
Frontier
AOG/t
120
Note the time
symbols, t
90
60
30
0
7
14
21
28 Housing/t
Production Possibilities
Frontier
AOG/t
120
This is the first row in
the table - where there
are no houses and 112
units of AOG
90
60
30
0
7
14
21
28 Housing/t
Production Possibilities
Frontier
AOG/t
120
90
This is the second row in
the table - where there
are 7 houses and 98 units
of AOG produced
60
30
0
7
14
21
28 Housing/t
Production Possibilities
Frontier
AOG/t
These are all of the
production possibilities
from our table
120
90
60
30
0
7
14
21
28 Housing/t
Production Possibilities
Frontier
AOG/t
When we connect the points
we have the “Production
Possibilities Frontier”
120
90
Note the
general
“concave” or
“bowed out”
shape
60
30
0
7
14
21
28 Housing/t
Opportunity Cost
‹ Opportunity Cost - the benefits
foregone from the next best alternative
when a choice is made
‹ “There is no such thing as a free lunch.”
‹ All costs are benefits, benefits foregone
‹ Thus all costs are subjective, not
objective
‹ And our measurement is not then of
costs, but proxies, i.e., stands ins, for
cost
Opportunity Cost in Our
Economy
‹ When we make 7 houses, we are using
resources
‹ Those resources could have been used
to make something else, specifically,
they could have made 14 units of AOG
‹ Thus the opportunity cost of making
the first 7 houses are the benefits given
up by not having 14 AOGs
Per Unit Opportunity Cost
‹ If the opportunity cost of making 7
houses is 14 AOGs, then the average
opportunity cost of making 1 house
must be 2 AOGs (= 14/7)
‹ Most of the time when we are thinking
about opportunity cost, it is easier to
think of it in “per unit” terms. In other
words, ask yourself “what is the
opportunity cost of doing one more
thing, another house, another hour of
study, etc?”
How to Find Per Unit
Opportunity Cost
‹ A simple way to find the per unit
opportunity cost is to use the following
equation:
™ Opportunity Cost of a Good or Service
Produced =
Units of Good or Service Forgone
Units of a Good or Serve Produced
Opportunity Cost and the PPF
AOG/t
120
Amount of AOG/t
Given Up
90
60
Amount of
Houses/t Gained
30
7
0
14
21
28
Houses/t
Opportunity Cost and the PPF
AOG/t
120
90
Amount of AOG/t
Given Up
60
Amount of
Houses/t Gained
30
0
7
14
21
28 Houses/t
Opportunity Cost and the PPF
‹ We know that the per unit opportunity
cost of Houses is AOG given up
divided by Houses gained
‹ Graphically, that is the same thing as
the vertical change divided by the
horizontal change (if we ignore the
negative sign).
Slope and Marginal Cost
‹ When the PPF is concave throughout
you measure the slope at a point by
drawing a tangent at that point
‹ The slope of that tangent is the
opportunity cost in the limit (economists
call it Marginal Cost of the good on the x
or, horizontal axis)
‹ The inverse of that slope is the Marginal
Cost of the good on the y, or vertical,
axis
Slope, Tangent and MC
At point A, we have 72 AOG and
17 Houses per month. The
marginal cost of a house at A is the
slope of the tangent at A, 4 units of
AOG. The MC of an AOG is the
A inverse of the slope of the tangent
at A, 1/4 house.
AOG/t
120
90
72
60
MCHA = rise/run = 72/18
=4
30
MCAOGA = run/rise =
= 18/72 = 1/4
rise
0
7
14 17 21
28
run
35 Houses/t
Increasing Opportunity Cost
‹ Opportunity Cost increases because we
picked resources that were best at
making Houses to make Houses first.
We kept choosing the best carpenters
and resources that are best suited for
house production. As we make more
houses the resources left become less
apt at making houses. So, per unit cost
of houses increase.
The Realism of Increasing
Opportunity Cost
‹ Different resources in our economy are
better suited for making different things.
Some people are better carpenters, some
are better at sales, and some are better at
administration. When starting to produce
something we are going to want to make it
as cheaply as possible. In other words giving up as little as possible of other
things. The first houses have the lowest
opportunity cost, because we select the best
carpenters from our set of resources.
Increasing Marginal
Opportunity Cost
‹ Note that generally as we make more
and more of a good, the opportunity
cost of making an additional unit
increases. This is called “Increasing
Marginal Opportunity Cost.”
‹ Increasing MC implies the PPF is
concave, and concavity of the PPF
implies increasing MC
Slope, Tangent and MC
AOG/t
120
B
A
Notice the concavity of the PPF
implies increasing marginal cost
of production. As we increase
the production of houses, the
MC of houses increases.
MCHC > MCHA > MCHB
90
Also,
72
60
MCAOGC < MCAOGA < MCAOGB
C
30
0
7
14 17 21
28
35 Houses/t
Constant Opportunity Cost
‹ If all resources are equally skilled at
making AOG and Houses, then there
are Constant Opportunity Costs
‹ This means that the slope of the PPF is
constant that is, the PPF is linear.
Constant Opportunity Cost
AOG/t
120
The opportunity cost of
making a house is 6 AOGs
(=120/20). This is true
regardless of what
combination of goods is
produced.
90
60
30
0
7
14 20 21
28 Houses/t
A Math Representation of the
PP Model--Linear PPF
‹ Assume two goods, Y and X, and two
resources, L and K, technology is fixed,
and opportunity cost is constant
‹ Y = f(X, L, K, technology)
‹ Y = a - bX + cL + dK where a….d are
parameters to be estimated and
marginal opportunity cost is assumed
to be constant, i.e., the PPF is linear
The Production Function
‹ Y = a - bX + cL + dK
“a” summarizes all factors that contribute
to Y other than X, L, and K
™ “c” and “d” are the estimates that tell us
how much Y would increase if L or K were
to increase by one unit, c.p.
™ since L and K are given we may rewrite as
™
‹ Y = a’ - b’X where a’ = a + cL + dK
‹ MC of X is given by b’ and the MC of Y
by 1/b’
Y = a’ - b’X = 100 - 4X
Y/t
Linear PPF, Constant MC
100
MCX = 4Y;
25
X/t
MCY = (1/4)*X
A Math Representation of the
PP Model--Concave PPF
‹ Assume two goods, Y and X, and two
resources, L and K, technology is fixed,
and opportunity cost increases with
production
‹ Y = f(X, L, K, technology)
‹ Y = a - bXe + cL + dK where a….d and e
are parameters to be estimated and
marginal opportunity cost is assumed
to be increasing, i.e., the PPF is concave
The Production Function
‹ Y = a - bXe + cL + dK
“a” summarizes all factors that contribute
to Y other than X, L, and K
™ “c” and “d” are the estimates that tell us
how much Y would increase if L or K were
to increase by one unit, c.p.
™ since L and K are given we may rewrite as
™
‹ Y = a’ - b’Xe where a’ = a + cL + dK
‹ MC of X is given by eb’X(e-1) and the MC
of Y by 1/eb’X(e-1)
e
Y = a’ - b’X
Y/t
2
= 100 - 4X
Concave PPF, Increasing MC
100
MCX = 10X; MCY = (1/10)*X
A
50
~3.5
At point A, MCX = slope at A =
~35.4Y, and MCY = inverse of
the slope at A = ~0.03X
5
X/t
A Review, Scarcity and the PP
Model
Since we have scarce resources, we
are limited in what we can produce.
We cannot make 60 AOG and 28
Houses.
AOG/t
120
90
60
30
0
7
14
21
28 Houses/t
A Review, “What”, “How”
and the PP Model
AOG/t
Somewhere on the frontier allocating
resources to their best (efficient)
120
90
60
30
0
7
14
21
28 Houses/t
Productive Efficiency and the
PP Model
‹ To produce efficiently, our economy
must not be able to produce more of one
good without producing less of another.
In other words, we must be on the PPF.
If we are inside of the PPF, we could
produce more of one good without
producing less of another.
‹ Consider the 3 points on the following
graph:
Productive Efficiency
AOG/t
Point A cannot be
efficient since we can
increase production of
Houses from 7 to 18
while still producing
60 AOG
120
90
60
A
B
C
30
0
7
14
21
28 Houses/t
Points on and off the PPF
‹ All points, such as B, are efficient since if
we want to increase production of either
good we must decrease our production of
the other good
‹ All points, such as A, are inefficient since
we can have more of one good without
giving up any of the other
‹ All points, such as C, are unattainable with
our present technology, resources,
institutions, traditions and customs.
Being on the PPF is not
inevitable. We will be in the
interior if we have
‹ Unemployment - The condition in
which a resource is unable to find a use
to produce things we want
‹ Underemployment - The condition in
which some units of resources are not
employed in their most productive, i.e.,
valued, uses
Shifting the PPF Outward
‹ Resources available to the nation
increase
‹ There is an improvement in the
technology with which the nation
employs its resources
™ Both are achieved if the county chooses to
produce more capital, both physical and
human capital, and less consumer goods
™ Technology is introduced through newer
capital and a better educated labor force
‹ Changes in institutions,
traditions/customs, and economic
policy
Growth
AOG/t
120
New PPF
Increased immigration,
technological advance,
change in social mores
about the role of
women, etc.
90
60
Old PPF
30
0
7
14
21
28
Houses/t
Technological change doesn’t
have to be neutral: Here it
affects just Housing
AOG/t
120
New PPF
90
60
30
0
7
14
21
28
Houses/t
Growth and Changing
Marginal Cost
‹ Note that the slope of the PPF may
change at any given level of House
production - implying the opportunity
cost changed
‹ This is because it now takes less
resources to make a house, which
means we are giving up less AOG each
time we make a house
The End
In chapter 3, you will begin to see how
the forces of Supply and Demand
interact to give answers to our three
basic questions: How, What, and For
Whom