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Business Economics
Topic 2: Some fundamental Economicconcepts
Associate Professor Sarath Divisekera
17/07/2013
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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
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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
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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.
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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.
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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
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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
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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
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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
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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
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What is Marginal Analysis
MA is thee process of consideringsmall changes in a decision (controlvariable) and determining whether agiven change will improve the ultimateobjective
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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 !
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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
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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
RR
Q
R)MR(venueReinalargM
output/lesChangeinSa
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
CC
Q
C)MC(inalCostargM
output/lesChangeinSa
stChangeinCo)MC(inalCostargM
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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
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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
RR
Q
R)MR(venueReinalargM
output/lesChangeinSa
venueReChangein)MR(inalRvenueargM
Business Economics D r Sarath Divisekera
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
CC
Q
C)MC(inalCostargM
output/lesChangeinSa
stChangeinCo)MC(inalCostargM
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MC is the slope of the TC function
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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.
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Q40132dQ
dM
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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.
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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
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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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