REVIEW OF ECONOMICS: TABLE OF CONTENTS
PART I
PAGE
OPPORTUNITY COSTS
2
MARGINAL ANALYSIS
4
PRODUCTION POSSIBILITIES CURVE
8
COMPARATIVE ADVANTAGE
17
REVIEW OF FUNCTIONS AND GRAPHS
19
PART II
PAGE
DEMAND
1
SUPPLY
6
MARKET EQUILIBRIUM
8
CHANGES IN SUPPLY & DEMAND & MARKET EQUILIBRIUM
14
MARKET ANALYSIS: RENT CONTROL
23
PART III
PAGE
CONSUMER TASTES & PREFERENCES
1
THE CONSUMER'S BUDGET CONSTRAINT
6
THE OPTIMUM CONSUMPTION BUNDLE
11
CHANGES IN THE OPTIMUM CONSUMPTION BUNDLE
15
MODEL OF CONSUMER CHOICE: LABOR MARKET EXAMPLE
20
PART IV
PAGE
UTILITY POSSIBILITIES CURVE
1
SOCIAL WELFARE FUNCTION
2
EXAMPLES OF CONCEPTS OF SOCIAL WELFARE
3
Winter 1999
1
OPPORTUNITY COSTS
"Perhaps the most fundamental concept in economics, the
opportunity cost of an action is the value of the foregone alternative
action. Opportunity cost can only arise in a world where the resources
available to meet wants are limited so that all wants cannot be
satisfied. If resources were limitless no action would be at the
expense of any other -- all could be undertaken -- and the opportunity
cost of any single action, the value of the 'next best' alternative, would
be zero. Clearly, in a real world of scarcity opportunity cost is
positive."
"Strictly, cost in economics always refers to opportunity cost and
hence accountant and economist may well define the cost of an action
quite differently. For the accountant what matters are the money
outlays on the various resources required to produce a product. For
the economist, those money prices may themselves be an inaccurate
reflection of the opportunity cost of the resources if for some reason
markets have failed to reflect the value of those resources in their
highest value alternative use. Additionally, the economist will tend to
look at all the benefits sacrificed by taking an action."
(This definition is taken from The Dictionary of Modern Economics,
D.W. Pearce (ed.), (Cambridge, MA: MIT Press), 1983.)
Winter 1999
2
PROBLEM #1: You have a rich uncle who lives in Florida. In 1966 your rich uncle visited San
Luis Obispo. He liked it so much that he bought a piece of land not far from Cal Poly, with the
intention of building a house and moving here someday. At that time your uncle paid $10,000
for the half-acre lot.
After returning to Florida he changed his mind, realizing he preferred hurricanes over
earthquakes. Recently your uncle heard that you are going to school at Cal Poly and that you
intend to find a job and settle in San Luis Obispo after you graduate. Your rich and generous
uncle decides to give you the vacant lot as a graduation present.! You thank your uncle
profusely and continue with your studies.
A couple of years later you have graduated. Congratulations the lot is yours! Next door to
your lot a dentist bought a very similar half-acre lot for $100,000. They have just built and
moved into a brand new 2400 square foot home. After a tour of their new home you become
insanely jealous and are determined to have a new house just like the dentist. You grab your
calculator and figure you would be willing to pay up to $300,000 for a home just like the one
the dentist moved into. Immediately you begin to figure how much it will cost to build a 2,400
square foot house almost identical to the one your neighbors built.
The following list provides the numbers related to your dream house:
•
•
•
•
•
•
•
•
Price your uncle paid more than 30 years ago for the half-acre lot: $10,000
Price your neighbor recently paid for a similar half-acre lot: $100,000
Maximum price you would be willing to pay for your dream house: $300,000
City permits: $12,000;
Architectural design and plans: $10,000;
Size of your dream house is 2400 square feet;
Construction costs: $90 per square foot;
Landscaping costs: $6,000
What is the total cost of building your new dream home? Should you go ahead and build your
dream home on the lot your uncle gave you? Explain your answer using economics.
Winter 1999
3
PROBLEM #2: You are a computer programmer with IBM earning $102,000 per year. You very
much want to quit your job and start your own computer software company. You make the
following calculations based on a fifteen-year business plan:
Annual Projected Revenue = $600,000
Annual Projected Costs:
Costs of Labor:
Rent on Plant
Facilities:
Rent on equipment:
Cost of Materials:
$200,000
$100,000
$100,000
$100,000
In order to finance your new company you will have to sell your $80,000 in IBM shares which
have making a 10% rate of return. Should you go ahead and sell your IBM shares, quit your
job and start your new company? Explain why or why not.
Winter 1999
4
PROBLEM #3: Suppose that you are a rancher capable of producing beef or lamb. Over the
years you have maintained records regarding your total production of both types of meat.
Furthermore assume that the only reason beef relative to lamb production has changed is
because of your desire to produce the combination of beef and lamb that produces the
highest profit for the ranch.
Assume that you have made full and efficient use of your resources.
Your production levels are listed in the table below.
Meat Production Data ((000’s of
Pounds)
YEAR
BEEF
LAMB
1988
200
500
1989
220
460
1990
160
580
1991
190
520
1992
240
420
1993
245
410
1994
230
440
What is the opportunity cost of a pound of beef? What is the opportunity cost of a pound of
lamb?
Winter 1999
6
MARGINAL ANALYSIS
Marginal analysis is the examination of the consequences of making small changes in the
current state of affairs. Marginal benefit is the added value received when making a small
change in some activity. Marginal cost is the added cost incurred when making a small
change in some activity.
Decisions are made at the margin when a decision maker compares the marginal benefit of a
small change in a particular activity to the marginal cost. If the marginal benefit exceeds the
marginal costs, then the decision maker goes ahead with the change.
PROBLEM: Suppose your boyfriend or girlfriend buys you a CD player and the table below
indicates the maximum price you would be willing to pay for each additional disk.
NUMBER OF DISKS
MARGINAL
BENEFIT
NET BENEFIT
Case “a”
Your favorite disk
Your 2nd favorite disk
“ 3rd
“
“
th
“ 4
“
“
“ 5th
“
“
th
“ 6
“
“
th
“ 7
“
“
Case “b”
$19
15
11
9
7
6
4
a.
If the price of a disk is $10 how many will you buy?
b.
If as a result of a 50% sale the price is cut to $5 how many disks will you buy?
c.
Suppose the only way you could get 50% off is by joining a Music club with a
membership fee of $12. How many disks would you buy?
Winter 1999
Case “c”
6
PROBLEM: You are trying to calculate how many hours per week you should study for this
economics course. Your marginal benefit of studying economics during one week is
represented by the graph below. Suppose the next best use of your time is working at SLO
Brewing Co. for $8 per hour. If you apply marginal analysis how many hours should you
study per week?
Marginal
Benefit
12
10
8
6
MB
4
2
0
Winter 1999
1
2
3
4
5
6
7
8
9
10
Hours of Study per Week
7
PRODUCTION POSSIBILITIES CURVE
I.
The production possibilities curve shows the maximum possible output of one good that
can be produced with the available resources (land, labor and capital) and technology
while holding constant the output of an alternative good.
II. The feasible production set consists of all of the possible combinations of goods that can
be produced with the available resources and technology.
A Production Possibilities Curve
Clothing (boxes)
30
25
20
15
10
5
Food
(tons)
0
Winter 1999
5
10
15
20
25
30
35
40
8
PROBLEM: The nation of New Bispo produces two products: grapes, from the numerous
vineyards in the countryside, and “Wizzer” T-Shirts, for the numerous fans of this “ excellent”
rock group. The table below presents the production schedule for New Bispo. Use this
information to answer the following two questions.
POINT
GRAPES
T-SHIRTS
A
B
C
D
E
(tons)
0
25
40
50
55
(boxes)
4,000
3,000
2,000
1,000
0
OPPORTUNITY COST OF EACH TON OF
GRAPES
QUESTION: In the table below fill-in the column for the opportunity cost of each ton of
grapes.
POINT
GRAPES
T-SHIRTS
A
B
C
D
E
(tons)
0
25
40
50
55
(boxes)
4,000
3,000
2,000
1,000
0
Winter 1999
OPPORTUNITY COST OF EACH TON OF
GRAPES
9
ANSWER:
POINT
GRAPES
T-SHIRTS
A
B
C
D
E
(tons)
0
25
40
50
55
(boxes)
4,000
3,000
2,000
1,000
0
Winter 1999
OPPORTUNITY COST OF EACH TON
OF GRAPES
40 t-shirts/ton of grapes
66.7 t-shirts/ton of grapes
100 t-shirts/ton of grapes
200 t-shirts/ton of grapes
10
QUESTION: Draw the graph for the production possibilities curve of New Bispo.
“Wizzer” t-shirts (000’s of boxes)
6
5
4
3
2
1
Grapes
(tons)
0
Winter 1999
10
20
30
40
50
60
70
80
11
ANSWER:
“Wizzer” t-shirts (000’s of boxes)
6
5
A
4
B
3
C
2
D
1
Grapes
(tons)
E
0
•
10
20
30
40
50
60
70
80
Production efficiency is attained when the maximum possible output of any one good is
produced given the output of other goods. At an efficient production point it is not
possible to increase the output of a particular good without decreasing the output of some
other good.
Winter 1999
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QUESTION: Which output combinations satisfy the condition for economic efficiency?
“Wizzer” t-shirts (000’s of boxes)
6
5
4
3
2
1
Grapes
(tons)
0
Winter 1999
10
20
30
40
50
60
70
80
13
ANSWER: All of the output combinations on the production possibility curve satisfy the
condition for production efficiency.
“Wizzer” t-shirts (000’s of boxes)
6
5
4
3
2
1
Grapes
(tons)
0
Winter 1999
10
20
30
40
50
60
70
80
14
•
The law of increasing opportunity cost states that as more of a particular good is produced
its opportunity cost per unit will increase.
•
The slope of the production possibility curve is equal to the opportunity cost of the good on
the x-axis.
“Wizzer” t-shirts (000’s of boxes)
6
5
A
4
B
3
C
2
D
1
Grapes
(tons)
E
0
Winter 1999
10
20
30
40
50
60
70
80
15
•
Economic growth results from an increase in the quantity and productivity of economic
resources. Economic growth results in the expansion of the feasible production set.
•
Economic growth is represented by an outward expansion of the production possibilities
curve.
“Wizzer” t-shirts (000’s of boxes)
6
5
4
3
2
1
Grapes
(tons)
0
Winter 1999
10
20
30
40
50
60
70
80
16
COMPARATIVE ADVANTAGE
Comparative advantage is the ability to produce something at a lower opportunity cost than
other producers.
The law of comparative advantage states that the producer with the lowest opportunity cost of
producing a particular good should specialize in producing that good.
PROBLEM: Suppose the U.S. and Japan produce only two goods: automobiles and computers.
The table below indicates the value of resources needed to produce autos and computers in
each of these countries.
Country
U.S.
Japan
Value of Resources Needed for Production of Autos and
Computers
Autos
Computers
12,000 $/auto
1,200 $/computer
8,000 $/auto
1,000 $/computer
QUESTION: What is the opportunity cost of autos and computers in each of these countries?
Country
Opportunity Cost in the Production of Autos and Computers
Autos
Computers
U.S.
Japan
Winter 1999
17
ANSWER:
Country
U.S.
Japan
Opportunity Cost in the Production of Autos and Computers
Autos
10 computers/auto
8 computers/auto
Computers
1/10 auto/computer
1/8 auto/computer
QUESTION: Which country has a comparative advantage in the production of autos? Which
country has a comparative advantage in the production of computers?
Winter 1999
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REVIEW OF FUNCTIONS AND GRAPHS
I. Functions
A.
A variable is a quantity that changes in value.
B.
A constant or parameter is a quantity that does not change in value.
C.
A function is a relationship between two or more variables, in which one variable
depends on the value of the other variables. If X and Y are two variables and if the value
of Y depends on the value of X, but X does not depend on Y, then Y is said to be a
function of X. In this case, X is called the independent variable, and Y is called the
dependent variable.
(In these notes I will use Y to represent a dependent variable and X to represent an
independent variable.)
e.g. Let A represent the area of a circle and R the radius of a circle. Both of these quantities,
A and R, are variables since they can change in value. Suppose we specify A as a function of
R. We can represent this function using an algebraic equation. In general form this function
may be represented as:
A = f(R)
The equation representing the specific functional relationship between A and R is:
A = π R2
where π (π
π =3.14 ...) and 2 are constants or parameters since they do not change in value.
(In these notes I will use capital letters to represent variables and small letters to represent
constants.)
Winter 1999
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D.
The equation representing the specific functional relationship between two or more
variables may take on many different forms. Here we describe three different forms.
1.
In a linear function the independent variables are raised to the first power only.
The general form of a linear function between two variables is:
Y=a+bX
2.
In a quadratic function one or more independent variables are raised to the
second power. The general form of a quadratic function between two variables
is:
Y = a + b X + c X2
3.
In an exponential function a parameter is raised to a variable power, such as:
Y = a + bX
Winter 1999
20
II. Graphs
A.
Whereas algebraic equations are used to represent functions mathematically, graphs
are used to represent functions between two variables visually.
(It is also possible to represent functions involving three variables using graphs, but
unfortunately your instructor does not possess the artistic skill required to draw three
dimensional graphs.)
B.
The Cartesian coordinate system is constructed by drawing two lines perpendicular to
each other. In math the horizontal line is often labeled as the X-axis and reserved for
the independent variable; the vertical line is labeled as the Y-axis and is reserved for the
dependent variable. The system results in four separate areas called quadrants. A
point is located numerically by the pair of X and Y values associated with the point:
(X,Y).
C.
A positive or direct relationship exists between two variables if an increase in the value
of one variable is associated with an increase in the value of the other variable. When
two variables are positively related the graph of the relationship is upward sloping.
D.
A negative or inverse relationship exists between two variables if an increase in the
value of one variable is associated with a reduction in the value of the other variable.
When two variables are negatively related the graph of the relationship is downward
sloping.
E.
The intercept is the value of the dependent variable when the independent variable is
set equal to zero. Or in terms of graphs, the intercept is the value of the Y variable at
the point where the graph of the relationship intersects the Y-axis.
F.
The slope of a line or curve representing a function between two variables measures the
rate of change of the dependent variable with respect to changes in the independent
variable. That is, it indicates the magnitude of the change in the dependent variable
resulting from a change in the independent variable.
Winter 1999
21
G.
H.
Steps in graphing a function between two variables
1.
Construct a table of the values of the dependent variable for various values of the
independent variable
2.
Draw the two perpendicular axes
3.
Mark X and Y values along the axes in equally spaced increments
4.
Plot each pair of numbers in the table on the graph
5.
Draw the line or curve which joins together the points plotted on the graph
Graphs of a linear function between two variables
1.
The graph of a linear function is always a straight line.
2.
The slope of the graph of a linear function is a constant. If ∆ Y is the change in the
dependent variable resulting from a change in the independent variable equal to
∆X, then the slope is equal to ∆Y/∆
∆X.
(You may remember from high school algebra that the slope is equal to the "rise
over the run." Relating these terms to the ones used here the rise is equal to ∆ Y
and the run is equal to the ∆X.
Winter 1999
22
PROBLEM 1: In the space below construct a graph for the linear relationship between the time
it takes to type a paper (T) and the number of pages in the paper (P):
T = 10 + 5 P
T
P
1
2
3
4
5
T
Slope = __________
30
20
10
Intercept = __________
0
Winter 1999
1
2
3
4
5
P
23
3.
Earlier we found that the general form of a linear function between two variables
can be written as Y = a + b X . Given only this general form we know that the
graph of this function is a straight line; the slope is equal to "b", the coefficient of
the independent variable; and the intercept is equal to "a", the constant term.
PROBLEM 2: What is the slope and the intercept of the following linear relationship?
Y = 8 + 0.5 X
Slope = __________
Winter 1999
Intercept = __________
24
I. Graphs of a nonlinear function between two variables
1.
The graph of a nonlinear function is always a curve.
(We say that nonlinear functions have a curvilinear relationship)
2.
A tangent is a straight line that touches the curve at only one point, without
intersecting the curve.
PROBLEM 3: Which of the following graphs depicts a tangent?
Graph A
Graph B
•
Graph C
•
•
•
3.
The slope of a curvilinear relationship at a particular point is equal to the slope of
the tangent at that point. In order to precisely determine the slope of a curve at a
particular point it is necessary to use calculus.
4.
The slope of a curve between two points is approximately equal to the slope of
the line joining the two points. The closer the two points are to each other the
better this approximation will be.
Winter 1999
25
PROBLEM 4: In the space below graph the nonlinear relationship between the area of a circle
and the radius of a circle: A = π R2
A
Point
v
w
x
y
z
R
0
1
2
3
4
A
0
3.14
12.57
28.27
50.27
50
z
40
30
y
20
x
10
v
0
1
2
3
4
5
R
The approximate slope on the curve between points v and x is given by the slope of the line
joining these two points:
Approximate Slope = ∆ A/∆
∆R = 12.57/2 = 6.29
PROBLEM 5: What is the slope on the curve between points x and z?
PROBLEM 6: What is the intercept of this curvilinear relationship between the area and the
radius of a circle?
Winter 1999
26
III. Graphical Relationships Between Total, Marginal & Average
A.
The words “total”, “marginal” and “average” appear repeatedly in
describing variables used in economic models.
1.
In economic analysis the word “total” means aggregate or overall.
For example: total benefit (TB), total cost (TC), total profit (Tπ
π), and
total revenue (TR).
2.
The word “marginal” means added, additional, extra or incremental. In
mathematical terms the word marginal refers to a rate of change
(∆
∆ y/∆
∆x). In graphical terms the word marginal refers to the slope of a
total curve. For example, let Q represent the number of units
consumed or produced and ∆Q represent the change in the number of
units, then: marginal benefit = ∆TB/∆
∆Q, marginal cost = ∆TC/∆
∆Q,
marginal profit = ∆Tπ
π/∆
∆Q and marginal revenue = ∆TR/∆
∆Q.
3.
The word “average” means typical. Average refers to the arithmetic
mean, which is calculated by dividing the total by the quantity of
units. For example: average benefit = TB/Q, average cost = TC/Q,
average profit = Tπ
π/Q and average revenue = TR/Q.
Winter 1999
27
EXAMPLE: Suppose Pete Garcia collects baseball cards. Pete’s evaluation of what his
collection of baseball cards is worth to him is called the total value or total benefit. The total
benefit is a function of the number of cards in Pete’s collection. The table and graphs below
shows the total benefit, marginal benefit and average benefit.
Total Number of Cards
in Pete’s Collection
0
50
100
150
200
250
Total
Benefit
($)
0
250
450
600
700
750
$
Marginal
Benefit
($)
5
4
3
2
1
Average
Benefit
($)
5.00
4.50
4.00
3.50
3.00
$
5
TB
700
600
4
500
3
400
AB
300
2
200
1
100
MB
0
Winter 1999
50
100
150
200
250
Q
0
50
100
150
200
250 Q
28
C.
Not all total benefit, marginal benefit or average benefit curves look like the ones in the
previous two graphs. Each case has to be examined on its own. Fortunately there are
shortcuts that can be used to graph the marginal benefit and average benefit curves.
1.
Winter 1999
To determine the shape of the marginal benefit curve: 1) figure out whether the
slope of the total benefit curve is increasing, decreasing or doing both; 2) if the
slope is increasing draw a curve representing a positive relationship; 3) if the
slope is decreasing draw a curve representing a negative relationship; and 4) if
the slope is doing both draw a curve representing both a positive and negative
relationship making sure to put the two segments in the correct order.
29
EXAMPLE: Look at the total benefit curve in the graph on the left. From Q=0 to Q=20 the
slope of the total benefit curve is positive and increasing. From Q=20 to Q=40 the slope is
positive but decreasing. At Q=40 the slope equals zero. Finally for Q>0 the slope is negative
and decreasing. Based on these observations the marginal benefit curve must have a shape
like the curve in the graph on the right.
$
$
TB
0
10
20
30
40
50
Q
0
10
20
30
40
50
Q
MB
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30
2.
Winter 1999
To determine the shape of the average benefit curve: 1) pick several points on
the total benefit curve; 2) draw a line from each of those points to the origin,
these lines are called rays; 3) moving from left to right figure out whether the
slopes of the rays are increasing, decreasing or doing both; 2) if the slopes are
increasing draw a curve representing a positive relationship; 3) if the slopes are
decreasing draw a curve representing a negative relationship; and 4) if the slopes
are doing both draw a curve representing both a positive and negative
relationship making sure to put the two segments in the correct order.
31
EXAMPLE: Look at the total benefit curve in the graph on the left. From the origin to point x
the slopes of the rays are positive and increasing. From point x to point z the slopes are
positive but decreasing. Based on these observations the average benefit curve must have a
shape like the curve in the graph on the right.
$
$
y
z
x
TB
w
v
AB
u
0
D.
10
20
30
40
50
Q
0
10
20
30
40
50
Q
MB
There is a particular relationship between marginal and average. If the marginal is
above the average, then the average must be increasing. If the marginal is below the
average, then the average must be decreasing. Finally if the marginal is equal to the
average, then there is no change in the average.
EXAMPLE: Look at the graph on the right. In the range from Q=0 to Q=30, where the marginal
benefit exceeds average benefit, the average benefit is rising. At Q=0, where the marginal
benefit is equal to the average benefit, the average benefit levels out. In the range beyond
Q=30, where the marginal benefit is less than the average benefit, the average benefit is falling.
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E.
Given information on marginal benefit it is possible to determine the size of total
benefits. Mathematically total benefit is equal to the sum of marginal benefits.
Graphically total benefit is equal to the area under the marginal benefit curve.*
EXAMPLE: Hiroshi Urata collects antique chairs. His marginal benefit for each additional
chair in his collection is depicted in the graph on the left. With a total of six antique chairs in
Hiroshi’s collection his total benefit is equal to the shaded area in the graph.
$
Total Benefit
4000
3000
2000
TB
1000
MB
0
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2
4
6
8
10
Q
33
F.
Given information on average benefit it is also possible to determine the size of total
benefits. Mathematically total benefit is equal to average benefit multiplied by the
number of units (Q). Graphically total benefit is equal to the area of the rectangle with a
height equal to the average benefit and a base equal to Q.
EXAMPLE: Bharati Mukherjee loves to go the San Francisco opera. The average benefit she
receives from her trips to the opera is depicted in the graph on the right. With a total of eight
opera trips Bharati’s total benefit is equal to the shaded area in the graph.
$
Total Benefit
80
60
AB
40
20
0
2
4
6
8
10
Q
*Note, There is one qualification to this method for deriving the total from the marginal curve.
The method works perfectly if the total curve passes through the origin. In other words, the
area under the marginal curve is equal to the total as long as the total is equal to zero when
quantity (Q) is equal to zero.
If however the total curve has a positive vertical intercept, then the total is equal to the area
under the marginal curve plus the value of the positive vertical intercept.
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34
PROBLEM 7: Mwangi Kimenyi lives in Fresno, California, and enjoys traveling to Africa. The
total cost and benefit of his African vacation depends on the number of vacation days. The
graph on the left depicts the relationship between the total cost (TC) of his vacation and the
number of vacation days (Q). The graph on the right depicts the relationship between the
marginal benefit of each additional vacation day (MB) and the number of vacation days (Q).
$
$
500
2800
2400
400
TC
2000
300
1600
1200
200
800
100
400
MB
0
2
4
6
8
10
Q
0
2
4
6
8
10
Q
a.
Does the marginal cost of each additional vacation day increase or decrease with
each additional vacation day? Does the average cost of the vacation increase or
decrease with each additional vacation day? What do the marginal cost and
average cost curves look like?
b.
Using marginal analysis determine the optimal number of vacation days for
Mwangi’s trip to Africa.
c.
Assuming Mwangi chooses the optimal number of days for his vacation, what is
the net gain in dollars that he derives from his vacation?
Winter 1999
35