BusEc2_2013 Fundamental Concepts

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Business Economics

Topic 2: Some fundamental Economicconcepts

Associate Professor Sarath Divisekera

17/07/2013

Business Economics Dr SarathDivisekera 2

Lecture Outline

Some fundamental Economic Concepts

Marginal Principle

Marginal Analysis & Economic Optimisation

Basic rules of optimisation

Comments on calculus

Some Fundamental Economic

Concepts

Some Fundamental Economic

Concepts

Equilibrium Analysis

Economic Agents areEpitomisers

Assumption of Rationality

Ceteris Paribus and MarginalAnalysis

Constrained Choices

17/07/2013 3Business Economics D r Sarath Divisekera


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Equilibrium AnalysisEquilibrium Analysis

Equilibrium Defined.

A situation where there is no tendency forchange.

What do we mean by a stable equilibrium?

We frequently assume market are inequilibrium.

Is this true? If not, why make the assumption?

Why do we make this assumption?

Induction/ changes/policy


Optimising Economic AgentsOptimising Economic Agents

What does this mean?

Economic agents (i.e., households, firms,managers, etc.) have an objective thatthey are trying to optimise. Individuals assumed to maximise utility.

For-profit firms maximise profits or

minimise costs. Not-for-profits may maximise output

levels.


Economic OptimisationEconomic Optimisation

This is the goal of Business Economics

Help Businesses/Managers makeoptimal decisions

Once statistical functions areestimated, they can be optimised.

We will eventually do this mathematically.

Start with graphical treatment



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Economic Agents are Typically

Constrained

Economic Agents are Typically

Constrained

Resource constraints Physical and Financial

Legal constraints & Time constraints

Some constraints are binding, others are not.

Example of binding constraint.

Example of non-binding constraint.

May need to include constraints in ourmodels.


Ceteris ParibusCeteris Paribus

What does Ceteris Paribus mean andwhy is it important?

Is the Ceteris Paribus condition met inthe real world?

Can do it conceptually, mathematically,

and statistically


17/07/2013Business Economics A/P Sarath

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Functional Relationships Demand; quantity demanded as a function of price

per unit, Q = D(P)

Inverse demand;P = P(Q)

Revenue; dollars of revenue as a function of quantitysold, TR = R(Q) = PQ = P(Q)Q

Cost; dollars of cost as a function of quantityproduced, TC = C(Q)

Profit; dollars of profit as a function of quantity, =(Q) = P(Q)Q - C(Q)


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Why use Functions?

If we know the functional form associatedwith the particular economic problem (sayfor example, to find the profit maximisingoutput levels), we can easily find theoptimal solution.

This can be done either by enumeration(i.e., by calculating the profits associatedwith each output levels), using calculusand/or Marginal Analysis


17/07/2013Business Economics Dr Sarath

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Functional Relationships

Functional relationships can be displayed Three ways:

TABLES (when data is discretely given)

GRAPHS (2 or 3 dimensional, Cartesian axes)

FUNCTIONS (symbolic and mathematical)

Functions of Interest: Revenue

Recall Profit = R - C, and R = P*Q

Note that the price at which we can sell theproduct depends on the prevailing marketconditions and assume this relationship can beexpressed as

P = 170 - 20Q; So R = P*Q

R = P * Q = (170 - 20Q)*Q = 170Q - 20Q2

We call this Revenue Function



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Functions of Interest - Cost Functions

Similarly assume that the mathematically therelationship between the cost and the outputcan be expressed as

C = 100 - 38Q - the Cost Function

Given revenue and cost functions wederive the Profit Function

= R - C = (170Q - 20Q2 ) - (100 + 38Q)

= -100 +132Q 20Q2


Presentation of Functional Relationships: An example Profit

= -100 +132Q 20Q2

Recall that Profit depends on Q, so simply substitutevalues for Q.

Q = 1; then, = -100 +132*(1) 20(1)2 = 12

Q = 2; then, = -100 +132*(2) 20(2)2 = 84

Q = 3; then, = -100 +132*(3) 20(3)2 = 116

Q = 4; then, = -100 +132*(4) 20(4)

2

= 108 And so on..

Try the same with Revenue & Cost Functions


Presentation: Profit Function as a Table

Qquantity

Price

P = 170 -

20Q

Revenue

R = P*Q

R = 170Q -

20Q2

Cost

C = 100 - 38Q

Profit

R-C

1 150 150 138 12

2 130 260 176 84

3 110 330 214 116

4 90 360 252 108

5 70 350 290 60

6 50 300 328 -28

7 30 210 366 -156

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150

100

50

0

-50

-100

-1500 1 2 3 4 5 6 7 8

Total Profit (Thousands of Dollars)

2Q20Q132100

Profit Function as a Graph

Q

Qquantit

y

Profit

1 12

2 84

3 116

4 108

5 60

6 -28

7 -156


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Decision Problems

How many Gadgets should we produce?

Using what input combinations?

How to price our Gadgets?

Should we expand our capacity?

How to protect our markets from erosion?

Should we invest in R&D? What projects?

How to assess and deal with uncertainties?

How to decide how much to produce?

Well, you are the CEO of the GadgetsInternational (GI).

Naturally, you want to maximise profitand your problem is to decide how muchto produce.

Assume at present the weekly productionis 2 units (1 unit of Q = 50,000).

Should GI increase, decrease, or leave unchangedits weekly production of Gadgets?



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Finding the Maximum Output

Recall that if we know the functional formassociated with the particular economicproblem (say for example, to find the profitmaximising output levels), we can easilyfind the optimal solution.

This can be done either by

(a)enumeration (i.e., by calculating theprofits associated with each output levels),

(b) using calculus and/or

Marginal Analysis


What is Marginal Analysis

MA is thee process of consideringsmall changes in a decision (controlvariable) and determining whether agiven change will improve the ultimateobjective


The Control Variable

To do marginal analysis, we canchange a variable, such as the:

quantity of a good you buy,

the quantity of output youproduce, or

the quantity of an input you use.

This variable is called thecontrol/decision variable .



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Key Procedure for Using Marginal

Analysis

Remember to look only at thechanges in total benefits andtotal costs.

If a particular cost or benefitdoes not change, IGNORE IT !


Marginal Concepts

Marginal analysis looks at the change in anyset target (say profit) from making a smallchange in the decision/control variable

Marginal Profit (MP) = in profit/ inoutput/sales

MP is the change in profit resulting from asmall in crease in output

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01

01

QQQofitPrinalargM

output/lesChangeinSa

ofitPrChangeinofitPrinalargM

Business Economics D r Sarath Divisekera

Marginal Revenue (MR)

MR = in Revenue/ inoutput/sales

MR is the amount of additionalrevenue that comes with a unitincrease in output/sales

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01

01

QQ

RR

Q

R)MR(venueReinalargM


venueReChangein)MR(inalRvenueargM



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Marginal Cost (MC)

MC = in cost/ in output

MC is the additional cost ofproducing an extra unit of output.

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01

01

QQ

CC

Q

C)MC(inalCostargM


stChangeinCo)MC(inalCostargM



Divisekera 32

Another way to look at:Marginal value as a slope

Marginal Value is the the slope of thecorresponding function

Marginal Profit is the slope of Profit function

Marginal Revenue is the slope of Revenuefunction

Marginal Cost is the slope of the total costfunction

Marginal Concepts: An example

17/07/2013 Business Economics Dr Sarath Divisekera 33

P Q TR(P*Q)

MR TC MC ProfitTR-TC

MP

150 1 150 138 12130 2 260 110 176 38 84 72110 3 330 70 214 38 116 32

90 4 360 30 252 38 108 -870 5 350 -10 290 38 60 -4850 6 300 -50 328 38 -28 -88

30 7 210 -80 366 38 -156 -128


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150

100

50

0

-50

-100

-1500 1 2 3 4 5 6 7 8

Total Profit (Thousands of Dollars)

Marginal Concept as a slope

Q = 1

= 32

Marginal Profit

321

32

23

84116ProfitMarginal

ProfitMarginal

utSales/OutpinChange

ProfitinChangeProfitMarginal

01

01

Q

QQQ


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Marginal Revenue (MR)

MR = in Revenue/ inoutput/sales

MR is the amount of additionalrevenue that comes with a unitincrease in output/sales

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01

01

QQ

RR

Q

R)MR(venueReinalargM


venueReChangein)MR(inalRvenueargM


MR is the slope of the TR function



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Marginal Cost (MC)

MC = in cost/ in output

MC is the additional cost ofproducing an extra unit of output.

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01

01

QQ

CC

Q

C)MC(inalCostargM


stChangeinCo)MC(inalCostargM


MC is the slope of the TC function


Back to the Question: ShouldGI increase, decrease, or

leave unchanged its weeklyproduction of Gadgets?

We can determine the profitmaximizing Q* even if all weknow is the table for Marginal

Profit


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Marginal Rule for ProfitMaximisation

To maximize profit, keep producingGadgets as long as your marginal profitfrom the last Gadget remains positive.

If your marginal profit from the lastGadget produced is negative, cut backproduction until a positive marginalprofit is restored.


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Basic Rules of Optimisation

Profit Maximisation

Maximum profit isattained at the outputlevel at whichMarginal profit = 0.

To maximise profit, keep

producing as long as

your marginal profit fromthe last unitproduced/sold remainspositive.

If your marginal profitfrom the last unitproduced is negative, cutback production until apositive marginal profit isrestored.

Alternatively, when MR =

MC, The Equi-Marginal Principle

150

100

50

0

-50

-100

-1500 1 2 3 4 5 6 7 8

Profit is at a maximum when MP = 0

MP = /Q = 0


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Implication of the MarginalRule: The Equi-Marginal Principle

Since (Q) = R(Q) - C(Q)

Therefore = R - C

SoM= MR -MC

IfMR is a decreasing function of Q, or ifMCis an

increasing function of Q, and if these curves

eventually cross [as is typical]

Then the Marginal Rule for Profit Maximization

implies: produce Q* to the point where MR still

just exceeds (or becomes equal to)MC.


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Finding Marginal Values

If we have a Table (say Profit) we can

calculate the marginal values (profit)

Alternatively, if we have the corresponding

Graph, we can find the point at which the

slope is zero.

What if we are given only the mathematical

form of the function?

Finding Marginal Values

Principle: If we knowthe mathematicalfunction associated withany economicrelationship, then thecorresponding Marginalfunction can beobtained bydifferentiating theoriginal function

Example = -100 + 132Q - 20Q2

To find the profitmaximising output,use the rule M = 0

M = 132 - 40Q =0

132 = 40Q; Q = 3.3.


Q40132dQ

dM


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Divisekera 46

Remember!Calculus is a Friend, not a foe

A very convenient Language

A superbly efficient tool for calculating

marginal quantities, and for finding the

maxima and minima of functions

You already know what you need to know (I

guess).

If you have forgotten year 10 math, dont

worry, Everything needed will be taught.


Divisekera 47

Comment on Calculus

The slope of the graph of a function is called derivative of the

function

If we want to find the slope, we differentiate that function.

There are seven rules of differentiation

dx

dy

x

y


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Rules of Differentiation: A quick review

Type of function Rule Example

Constant Y = c dY/dX = 0 Y = 5

dY/dX = 0

Line Y = cX dY/dX = c Y = 5X

dY/dX = 5

Power Y = cXb dY/dX = bcX b-1 Y = 5X2

dY/dX = 10X


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How to find a derivativeHow to find a derivative

a . Derivative ofconstants If the dependent

variable Y is aconstant, its derivativew.r.t. X (independentvariable) is alwayszero.

Example: y = 2

y = f(x) = 2;

dy/dx = 00


x

y = 2

y

How to find a derivative of power

functions

Let y = axb ;

Rule: The derivative of a power function,(y = axb ) is equal to the exponent (b)multiplied by the coefficient (a) times thevariable (x) raised to the power b-1'.

dy/dx = b.a.x(b-1)

Example; Let b = 2 and a = 3, (y = 3x2 ) then,dy/dx = 2.3.x(2-1) = 6x

Let b = 4, then, dy/dx = 4.3.x(4-1) = 12x3


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