Unit 1. Fundamentals of Managerial Economics (Chapter 1)

Unit 1. Fundamentals of

Managerial Economics (Chapter 1)

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 (2nd)

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.

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 Choices (examples)

Output quantityOutput qualityOutput mixOutput priceMarketing and advertising

Production processes (input mix)Input quantityProduction locationProduction incentivesInput procurement

Michael Porter’s “Five Competitive Forces”

=Decision-making constraints=Factors that influence the sustainability of

firm profits1. market entry conditions for new firms2. Market power of input suppliers3. Market power of product buyers4. Market rivalry amongst current firms5. Price and availability of related products including both ‘substitutes’ and ‘complements’

Marginal Analysis

Analysis of ‘marginal’ costs and ‘marginal’ benefits due to a changeMarginal = additional or incrementalCosts and benefits that are constant (i.e. fixed, don’t change) are excluded from the analysisChanges occurring at ‘the margin’ are all that matter

Marginal Analysis(Examples)

Y XIncremental 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

New Beer Sales Resulting from Amounts Spent 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

Example of a Business (Economic) Decision Resolved with ‘Marginal’

Analysis

Goal: max dollar sales of a productConstraint: advertising budget

‘Marginal’ decision rule: incremental dollar sales generated per incremental dollar spent should be the same for each alternative type of advertising

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-levelmanagement more fully the relationship between thecompany’s price and the resulting number of units ofproduct sold.

Variable RelationshipsExample 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 RelationshipsExample of Alternative Ways of

Depicting

Graphical

Variable RelationshipsExample of Alternative Ways of

Depicting

Mathematical

Q = 700 – 100P

P = 7 – 0.01Q

Common Math Terms Used in Economic Analysis

Term DefinitionVariable 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 DefinitionSpecific 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 FormName of Function Graph of Function

Y = a0 Constant Horizontal straight line with slope = 0

Y = a0 + a1x

(or y = mx + b)

Linear Straight line with slope = a1 (or = m)

Y=a0+a1x+a2x2 Quadratic Parabola (u-shaped curve) with either minimum or maximum value

Y=a0+a1x+a2x2+a3x3 Cubic Curved line (e.g. slope changes from getting flatter to steeper

Y=a0x-n Hyperbola Curved line (u-shaped) bowed towards origin

E X P O N E N T R U L E S E X A M P L E S

1 . x n = x m u lt ip lie d b y itse lf n tim e s x 3 = x x xx 1 = x

2 . x 0 = 1

3 . x -a = 1

x ax -2 = 1 /x2

4 . x a xb = x a+ b x 2 x 3 = x 5

x 2 x -1 = x2-1 = 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 = th e a th roo t o f x x 1/2 x

= w h a t n um b e r m u ltip l ied b yit se lf "a " tim e s = x 81 /3 = 2 (b e ca u se 2 2 2 = 8 )

7 . x a ya = (x y)a x 2y 2 = (xy )2

8 . (x a)b = x ab (x 2) 3 = x 6

9 . (x y)1 /a = x 1/a y 1/a (x y)1 /2 = x . y

3 . x -a = 1

x ax -2 = 1 /x2

4 . x a xb = 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 = th e a th roo t o f x x 1/2 x

9 . (x y)1 /a = x 1/a y 1/a (x y)1 /2 = x . y

Y = a + b1X1 + …bnXn=> 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

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 = Y/X = (Y2-Y1)/(X2-X1)

2. Given values at one pt for Y, X, and b, solve for a (e.g. a = Y1 – bX1)

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 dependentvariable.

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)= Y/X = 1st derivative (in calculus)= Y/ X 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

y

x

rise

run

y y

x x2 1

2 1

Slope Calculation Rules(slope = Y/ X = dy / dx)

Rule Example

1. Slope of a constant = 0 If y=6, slope = 0

2. ‘power rule’ => slope of a function y = axn is (n)(a)xn-1

If y=3x2, slope = (2)(3)x2-

1=6xIf y=x, slope = (1)x1-1=1

3. ‘Sum of functions rule’ = slope of the sum of two functions is the sum of the two functions’ slopes

If y = x + 3x2, 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 BusinessHow to compare or evaluate two different dollar amounts at two different time periods?

0 t1 t2 t3

$Y$X

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

FV1 = PV + PV(r)= PV(1+r)

FV2 = FV1+FV1(r)

= FV1(1+r)= PV(1+r)(1+r)= PV(1+r)2

••••FVn = PV(1+r)n

Time Value ProblemsFVn = PV(1+r)n

Given Solve For

PV,r,n FVn = PV(1+r)n = ‘compounding’

FVn,r,n PV=FVn[1/(1+r)n] = ‘discounting’

FVn,PV,n r (1+r)n=FVn/PV ( find in ‘n’ row)

FVn,PV,rn (1+r)n=FVn/PV ( find in ‘r’ column)

r(%)Borrow or save today (= PV)

Pay back or collect in 1 yr (=

FV)$

interest8 1.00 _____ _____

8 _____ 1.00 _____

9 1.00 _____ _____

9 _____ 1.00 _____

r PV _____ _____

r _____ FV _____

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 resultsin a NPV = 0

Payback Period

=an investment analysis alternative=period of time required for the sum

of net cash flows to equal the initialcost

=value of n such that

i

n

iNCF C

1

Firm ValuationThe value of a firm equals the present value of all its future profits

PV itt / ( )1

If profits grow at a constant rate, g<I, then:

PV i i g 0 01( ) / ( ).current profit level.

Maximizing Short-Term ProfitsIf 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.

FVn = PV (1+r)n where

PV = present value of price, cost, etc.r = estimated annual rate of increasen = number of yearsFV = future value of price, cost, etc.