Unit1

Unit 1.
Fundamentals of Managerial
Economics

Unit 1. Learning Outcomes =>
you should be able to:
1. Explain and apply marginal economic analyses to
making decisions
2. Calculate the slope (incremental change) of both linear
and nonlinear functions mathematically and graphically
3. Derive and interpret a linear equation for an economic
relationship
4. Understand and apply rules of exponents to economic
problems
5. Explain and apply time value of money concepts to
decisions having long-run impacts
6. Understand how microeconomic concepts are important
factors in making good decisions
7. Apply mathematical slopes to economic problems
Drive Rental Car or Co. Car?
Sue has been asked by her boss to
attend a business meeting 125 miles
away. She has two alternatives for
getting to the meeting and back: 1)
rent a car for $50 plus fuel costs or 2)
drive a company-owned car. Her boss
has asked her to choose the cheapest
form of transportation for the company.
What should Sue do?
Buy New Book or Used Book?
Joe has signed up to take an Econ class
which is about to begin. His instructor
expects him to read material from the
textbook and to access/use on-line
supplements. Joe has two alternatives: 1)
buy a new book for $120 which gives him the
supplements at no additional charge or 2)
buy a used book for $70 which does not
include the supplements so they would have
to be purchased separately for $35. What
should Joe do?
Fuel Once or Twice?
Suppose an airline company has a round trip
flight from Houston to Cancun to Houston.
Soaring oil prices have airlines scrambling to
save money on fuel. The company has
noticed fuel prices are 17 cents per gallon
less in Houston vs Cancun. Rather than
refueling in Cancun, the airline is thinking
about buying enough fuel for the whole trip
in Houston before departure. What are the
„marginal‟ analysis considerations in this case?
How Much to Spend on TV and Radio
Advertising?

Total Spent
New Beer Sales Generated
(in barrels per year)
TV Radio
$0 0 0
$100,000 4,750 950
$200,000 9,000 1,800
$300,000 12,750 2,550
$400,000 16,000 3,200
$500,000 18,750 3,750
$600,000 21,000 4,200
$700,000 22,750 4,550
$800,000 24,000 4,800
$900,000 24,750 4,950
$1,000,000 25,000 5,000
Max B(T,R)
Subject to: T + R = 1,000,000
What Is the Additional Revenue?
Suppose a statistician in your firm‟s research
department has given you his/her
mathematical estimate of your company‟s
sales (total revenue = TR and Q = quantity of
output) as follows:
TR = 7Q - .01Q
2

What will be the added revenue of selling
another unit of output? If the added cost of
producing another unit of output is constant
at $2.00, at what level of output is the
additional revenue generated from that
output just equal to the added cost?
Purchase Agreement – Good or
Bad?
With short-term interest rates at 7%, Amcott‟s CEO
(Ralph) decided to use $20 million of the company‟s most
recent annual retained earnings to purchase the rights to
Magicword, a software package that converts French text
word files into English. The purchase agreement is for the
next three years. Ralph has projected Amcott will earn an
additional $7 million net profits annually for each of the
next three years as a result of the agreement. After
learning of Ralph‟s decision, some members of Amcott‟s
board have been critical of Ralph‟s decision and are
considering firing Ralph. Is the board‟s criticism of Ralph‟s
decision justified?
Putting Saturn in Orbit
Microeconomic analysis was particularly
important to GM when it started selling its
line of Saturn cars in 1991. In producing and
selling Saturns, GM tried drastically new
approaches. GM spent an estimated $5
billion to get Saturn going. What were the
major changes implemented by GM and were
they well founded based on economic
considerations?
Deal or No Deal
Reports have it that the native
Americans who originally owned
Manhattan Island sold it in 1626 for
$24. Meanwhile, in 1984 it was
estimated that the value of that
property was $23 billion. Was selling
the land for $24 in 1626 a mistake?
“It‟s easy to identify successful
strategies (and the reasons for their
success) or failed strategies (and the
reasons for their failures) in retrospect.
It‟s much more difficult to identify
successful or failed strategies before
they succeed or fail.”
Luke Frueb and Brian McCann
Managerial Economics (2008)
While there is no doubt that luck, both good
and bad, plays a role in determining the
success of firms, we believe that success is
often no accident. We believe that we can
better understand why firms succeed or fail
when we analyze decision making in terms of
consistent principles of market economics and
strategic action.
Besanko, et. Al
Economics of Strategy (2
nd
)
Common Causes of Failed
Strategies
1. Relevant information
a. Not enough
b. Enough BUT either ignored or
used/analyzed incorrectly

2. Irrelevant information used
Microeconomics is the study of how individual
firms or consumers do and/or should make
economic decisions taking into account such
things as:
1. Their goals, incentives, objectives.
2. Their choices, alternatives, problems.
3. Constraints such as inputs, resources, money, time,
technology, competition.
4. All (cash & noncash) incremental or marginal
benefits and costs.
5. The time value of money.
Managerial Economics
Managerial Economics is
microeconomics applied to decisions
made by business managers.
Goals, Incentives, Objectives
A fundamental economic truth is that
individual firms or decision makers
respond to economic incentives. What
these incentives are (i.e. money,
profits, utility, etc.) and how they
influence economic decision making are
key topics for study and analysis in
business (or managerial) economics.
Managerial Goals (examples)
$ sales, total revenue, gross income,
market share
Q sales, Q of output, output per unit of
input (production efficiency)
$ costs, total costs, cost per unit of
output (cost efficiency)
$ profits, total profits, profit per unit of
output
Managerial Choices
(examples)
Output quantity
Output quality
Output mix
Output price
Marketing and
advertising
Production processes
(input mix)
Input quantity
Production location
Production incentives
Input procurement
Michael Porter‟s “Five
Competitive Forces”
= Decision-making constraints
= Factors that influence the sustainability of
firm profits
1. Market entry conditions for new firms
2. Market power of input suppliers
3. Market power of product buyers
4. Market rivalry amongst current firms
5. Price and availability of related products
including both „substitutes‟ and „complements‟
Marginal Analysis
Analysis of „marginal‟ costs and „marginal‟
benefits due to a change
Marginal = additional or incremental
Costs and benefits that are constant (i.e.
fixed, don‟t change) are excluded from the
analysis
Changes occurring at „the margin‟ are all that
matter
Two important dimensions of change:
direction, magnitude
“Good” Economic Decisions
¬Marginal benefits > marginal costs
¬Examples of marginal benefits:
↑ profit
↑ revenue
↓ cost
↑ safety
↓ risk
Marginal costs = opposite of above examples
Marginal Analysis
(Examples)

Y

X
Incremental Y/
Incremental X
TR Units of output MR
TC Units of output MC
TP Units of input MP
TRP Units of input MRP
TC Units of input MFC
TU Units of good MU
Profit Units of output MP
Assume you are a member of your company‟s
Marketing Dept. You believe, and correctly so,
1) the market demand for your firm‟s product is
linear,
2) if your company charges $5.00 for its product,
quantity sold would be 200 units and
3) if your company set price = $3.00, the number of
units sold would be 400.
Develop alternative ways of explaining to upper-level
management more fully the relationship between the
company‟s price and the resulting number of units of
product sold.
Variable Relationships
Example of Alternative Ways of Depicting
Tabular

P Q
$7 0
6 100
5 200
4 300
3 400
2 500
1 600
0 700
Variable Relationships
Example of Alternative Ways of Depicting
Graphical

Variable Relationships
Example of Alternative Ways of Depicting
Mathematical

Q = 700 – 100P

P = 7 – 0.01Q
Common Math Terms Used in
Economic Analysis
Term Definition
Variable Something whose value or magnitude (often Q or $
in Econ) may change (or vary); usually denoted by
letter „labels‟ such as Y, X, TR, TC
Parameter or
Constant
Something whose value does NOT change
General
equation or
function
A mathematical expression that suggests the value
of one variable relates to or depends on the value of
another variable (or set of variables) without
showing the precise nature of that relationship [e.g.
y = f(x)].
Common Math Terms Used in
Economic Analysis
Term Definition
Specific
equation or
function
A mathematical expression that shows precisely how
the value of one variable is related to the value of
another variable (or set of variables) [e.g. y = 10 +
2x].
Inverse
equation or
function
A mathematical expression rewritten so that the
variable previously on the right-hand side of the
equal sign now becomes the variable solved for on
the left-hand side of the equal sign [e.g. y = 2x and
x = 1/2 y are each an inverse equation of the
other].
Common Math Functions Used in
Economics
Function Form
Name of
Function

Graph of Function
Y = a
0
Constant Horizontal straight line with
slope = 0
Y = a
0
+ a
1
x
(or y = mx + b)
Linear Straight line with slope = a
1
(or
= m)
Y=a
0
+a
1
x+a
2
x
2
Quadratic Parabola (u-shaped curve) with
either minimum or maximum
value
Y=a
0
+a
1
x+a
2
x
2
+a
3
x
3
Cubic Curved line (e.g. slope changes
from getting flatter to steeper
Y=a
0
x
-n
Hyperbola Curved line (u-shaped) bowed
towards origin
EXPONENT RULES EXAMPLES
1. x
n
= x multiplied by itself n times x
3
= x x x
x
1
= x
2. x
0
= 1
3. x
-a
=
1
x
a
x
-2
= 1/x
2
4. x
a
x
b
= x
a+b
x
2
x
3
= x
5
x
2
x
-1
= x
2-1
= x
5.
x
a
x
b
= x
a-b
x
2
/x
3
= x
2
x
-3
= x
-1
= 1/x
6. x
1/a
= the a
th
root of x x
1/2
 x
= what number multiplied by
itself "a" times = x 8
1/3
= 2 (because 2 2 2 = 8)
7. x
a
y
a
= (xy)
a
x
2
y
2
= (xy)
2
8. (x
a
)
b
= x
ab
(x
2
)
3
= x
6
9. (xy)
1/a
= x
1/a
y
1/a
(xy)
1/2
= x . y
3. x
-a
=
1
x
a
x
-2
= 1/x
2
4. x
a
x
b
= x
a+b
x
2
x
3
= x
5
5.
x
a
x
b
= x
a-b
x
2
/x
3
= x
2
x
-3
= x
-1
= 1/x
6. x
1/a
= the a
th
root of x x
1/2
 x
9. (xy)
1/a
= x
1/a
y
1/a
(xy)
1/2
= x . y
Y = a + b
1
X
1
+ …b
n
X
n
=> the value of Y
depends on the values of n different
other variables; a „ceteris paribus‟
assumption => we assume that all X
variable values except one are held
constant so we can look at how the
value of Y depends on the value of the
one X variable that is allowed to change
“Ceteris Paribus”
Given 2 pts on a straight line, how to solve for the
specific equation of that line?

Recall, in general, the equation of a straight line is Y
= a + bX, where b = the slope, and a = the vertical
axis intercept. The specific equation has the values of
„a‟ and „b‟ specified.

Solution procedure:
1. Solve for b = AY/AX = (Y
2
-Y
1
)/(X
2
-X
1
)
2. Given values at one pt for Y, X, and b, solve for a
(e.g. a = Y
1
– bX
1
)
Straight Line Equation
Graphical Concepts (Variable Relationships)
Y axis: a vertical line in a graph along which the
units of measurement represent different
values of, normally, the Y or dependent
variable.

Y axis intercept:
the value of Y when the value of X = 0, or
the value of Y where a line or curve
intersects the Y axis; = „a‟ in Y = a + bX


Graphical Concepts (Variable Relationships)
X axis: a horizontal line in a graph along which
the units of measurement represent
different values of, normally, the X or
independent variable

X axis intercept:
the value of X when the value of Y = 0, or
the value of X where a line or curve
intersects the X axis
Graphical Concepts (Variable Relationships)
Slope:
= the steepness of a line or curve; a +(-) slope =>
the line or curve slopes upward (downward) to the
right
= the change in the value of Y divided by the
change in the value of X (between 2 pts on a line
or a curve)
= cY/ cX = 1
st
derivative (in calculus)
= AY/ AX using algebraic notation
= the „marginal‟ effect, or the change in Y brought
about by a 1 unit change in X
= b if Y = a + bX


„Slope‟ Graphically
¬ = =
÷
÷
A
A
y
x
rise
run
y y
x x
2 1
2 1
Slope Calculation Rules
(slope = AY/ AX = dy / dx)
Rule Example
1. Slope of a constant = 0 If y=6, slope = 0
2. „power rule‟ => slope of a
function y = ax
n
is (n)(a)x
n-1

If y=3x
2
, slope = (2)(3)x
2-1
=6x
If y=x, slope = (1)x
1-1
=1
3. „Sum of functions rule‟ = slope
of the sum of two functions is the
sum of the two functions‟ slopes
If y = x + 3x
2
, slope = 1 + 6x
Mathematics of „Optimization‟
„Optimization‟ ¬ a decision maker wishes
to either MAXimize or MINimize a goal
(i.e. objective function)

For a function to have a maximum or
minimum value, the corresponding
graph will reveal a nonlinear curve that
has either a „peak‟ or a „valley‟
Mathematics of „Optimization‟
The mathematical equation of the function to be optimized will
have THE VERTICAL AXIS VARIABLE ON THE LEFT-HAND SIDE
OF THE EQUATION (e.g. Y = f(x) ¬ Y is the vertical axis
variable)

the slope of a curve at either a peak or a valley will = 0; in math
terms, the slope is the first derivative (I.e. dY/dX = 0)

„Constrained optimization‟ ¬ do the best job of maximizing (or
minimizing) a function given constraints; the „Lagrangian
Multiplier Method‟ is a mathematical procedure for solving these
kinds of problems
Typical „Time Value of Money‟
Problems in Business
How to compare or evaluate two
different dollar amounts at two different
time periods?
0
t
1
t
2
t
3

$Y
$X
Assume x = $900, y = $1000, r = 6%, t
1
= 3, t
2
= 5
Time Value of Money
(Basic Concept)
A dollar is worth more (or less) the sooner (later) it is
received or paid due to the ability of money to earn
interest.
¬ present value
+ interest earned
= future value
Or
¬ future value
- interest lost
= present value
Time Value of Money
(Applications/Uses)
1. To evaluate business decisions where
at least some of the cash flows occur
in the future
2. To project future dollar amounts such
as cash flows, incomes, prices
3. To estimate equivalent current-period
values based on projected future
values
Time Value of Money Concepts
PV = present value
= the number of $ you will be able to
borrow [or have to save] presently in
order to payback [or collect] a given
number of $ in the future
FV = future value
= the number of $ you will have to pay back
[or be able to collect] in the future as a
result of having borrowed [or saved] a
given number of $ presently

FV
1
= PV + PV(r)
= PV(1+r)
FV
2
= FV
1
+FV
1
(r)
= FV
1
(1+r)
= PV(1+r)(1+r)
= PV(1+r)
2

•
•
•
•
FV
n
= PV(1+r)
n

Time Value Equation
Time Value Problems
FV
n
= PV(1+r)
n
Given Solve For

PV,r,n FV
n
= PV(1+r)
n
= „compounding‟

FV
n
,r,n PV=FV
n
[1/(1+r)
n
] = „discounting‟

FV
n
,PV,n r ¬ (1+r)
n
=FV
n
/PV (¬ find in „n‟ row)

FV
n
,PV,r n ¬ (1+r)
n
=FV
n
/PV (¬ find in „r‟ column)

Net Present Value (NPV)
= an investment analysis concept
= PV of future net cash flows – initial
cost
= PV of MR‟s – PV of MC‟s
= invest if NPV > 0
= invest if PV of MR‟s > PV of MC‟s
Internal Rate of Return
= an investment analysis
alternative

= value of ‘r’ that results
in a NPV = 0

Payback Period
= an investment analysis alternative
= period of time required for the sum
of net cash flows to equal the initial
cost
= value of n such that


i
n
i
NCF C
=
¿
=
1
Firm Valuation
The value of a firm equals the present value of all its
future profits

PV i
t
t
= ¿ + t / ( ) 1
If profits grow at a constant rate, g<I, then:

PV i i g = + ÷ = t t
0 0
1 ( ) / ( ).
current profit level.

Maximizing Short-Term Profits
If the growth rate in profits < interest rate and both
remain constant, maximizing the present value of all
future profits is the same as maximizing current profits.
Time Value of Money
(Applied to Inflation)
¬Can be used to estimate or forecast
future prices, revenues, costs, etc.

¬FV
n
= PV (1+r)
n
where
PV = present value of price, cost, etc.
r = estimated annual rate of increase
n = number of years
FV = future value of price, cost, etc.