Managerial Economics - CA Sri Lanka

Managerial EconomicsDr Nihal Hennayake

What is Microeconomics and Macroeconomics ? Ragnor Frisch : Micro means “ Small” and Macromeans “Large”Microeconomics deals with the study of individualbehaviour. It deals with the equilibrium of an individual consumer,producer, firm or industry.Macroeconomics on the other hand, deals with economywide aggregates. Determination of National Income Output, Employment Changes in Aggregate economic activity, known as BusinessCycles Changes in general price level , known as inflation, deflation Policy measures to correct disequilibrium in the economy,Monetary policy and Fiscal policy

What is Managerial Economics?“Managerial Economics is economics applied in decision making.It is a special branch of economics bridging the gap betweenabstract theoryand managerial practice” – WillianWarren Haynes, V.L. Mote, Samuel Paul“Integration of economic theory with business practice for thepurpose of facilitating decision making and forward planning” Milton H. Spencer“Managerial economics is the study of the allocation of scarceresources available to a firm or other unit of management amongthe activities of that unit” Willian WarrenHaynes, V.L. Mote, Samuel Paul“ Price theory in the service of business executives is known as

BUSINESS ADMINISTRATIONDECISION PROBLEMSTRADITIONAL ECONOMICS :THEORY AND METHODOLOGYDECISION SCIENCES :TOOLS AND TECHNICSMANAGERIAL ECONOMICS :INTEGRATION OF ECONOMICTHEORY ANDMETHODOLOGY WITH TOOLSAND TECHNICS BORROWEDFROM OTHER DECIPLINESOPTIMAL SOLUTIONS TOBUSINESS PROBLEMS

Nature, Scope and Significance of Managerial Economics: Managerial Economics – Business Economics Managerial Economics is ‘Pragmatic’ Managerial Economics is ‘Normative’ Universal applicability The roots of Managerial Economics came from MicroEconomics Relation of Managerial Economics to Economic Theory is muchlike that of Engineering to Physics or Medicine to Biology. It is therelation of applied field to basic fundamental disciplineCore content of Managerial Economics : Demand Analysis and forecasting of demandProduction decisions (Input Output Decisions)Cost Analysis (Output Cost relations)Price – Output DecisionsProfit AnalysisInvestment Decisions

1. Demand Analysis :Meaning of demand : No. of units of a commodity thatcustomers are willing to buy at a given price under a set ofconditions.Demand function : Qd f (P, Y, Pr W)Demand Schedule : A list of prices and quantitives and thelist is soarranged that at each price thecorrespondingamount is the quantity purchased atthat priceDemand curve: Slops down words from left to right.Law of demand: inverse relation between price andquantityExceptions to the law of demand :Giffens paradoxPrice expectations

Elasticity : Measure of responsiveness Qd f (P, Y, Pr W)E percentage change in DV/ percentage change in IVConcepts of price, income, and cross elasticityPrice Elasticity :Ep Percentage change in QD/Percentage change in PTypes of price elasticity :1. Perfectly elastic demand Ep 2. Elastic demand Ep 13. Inelastic demand Ep 14. Unit elastic demand Ep 15. Perfectly inelastic demand Ep 0

Elasticity and expenditure : If demand is elastic agiven fall in price causes a relatively larger increase inthe total expenditure. P TR when demand is elastic. P TR when demand is inelastic. P TR remains same when demand is Unit elastic.Measurement of elasticity : Point and Arc elasticity Elasticity when demand is linear Determinants of elasticity : (1) Number and closeness of its substitutes, (2) the commodity’s importance in buyers’ budgets, (3) the number of its uses. Other Elasticity Concepts Income elasticity Cross elasticity

Functions of a Managerial Economists: The main function of a manager is decision making andmanagerialEconomics helps in taking rational decisions. The need for decision making arises only when there are morealternatives courses of action. Steps in decision making : Defining the problem Identifying alternative courses of action Collection of data and analyzing the data Evaluation of alternatives Selecting the best alternative Implementing the decision Follow up of the action

Specific functions to be performed by a managerial Economist :1. Production scheduling2. Sales forecasting3. Market research4. Economic analysis of competing companies5. Pricing problems of industry6. Investment appraisal7. Security analysis8. Advice on foreign exchange management9. Advice on trade10.Environmental forecasting

OPTIMIZATIONManagerial economics is concerned with the ways inwhich managers should make decisions in order tomaximize the effectiveness or performance of theorganizations they manage. To understand how this canbe done we must understand the basic optimizationtechniques.Functional relationships:relationships can be expressed by graphs:

This form can be expressed in an equation:Q f ( P)Though useful, it does not tell us how Q responds to P,but this equation do.Q 200 - 5 pMarginal AnalysisThe marginal value of a dependent variable isdefined as the change in this dependentvariable associated with a 1-unit change in aparticular independent variable. e.g.

units 00marginal profitaverage 156Total profit is maximized when marginal profit shifts from positive to negative.

Average Profit Profit / QPROFITSMAXCB– Profit / Q averageprofitMaximizing averageprofit doesn’tmaximize total profitprofitsQSlope of ray from theorigin:quantity

Marginal Profits / Q Q1 is breakeven (zero profit) maximum marginal profitsoccur at the inflection point(Q2) Max average profit at Q3 Max total profit at Q4 wheremarginal profit is zero So the best place to produceis where marginal profits 0.profits(Figure 2.1)maxQ3Q4Q2Q1QaverageprofitsmarginalprofitsQ

Differential Calculus inManagementA function with one decision variable, X, can be written as:Y f(X)The marginal value of Y, with a small increase of X, isMy Y/ XFor a very small change in X, the derivative is written:dY/dX limit Y/ X X 0

Marginal Slope DerivativeThe slope of line C-Dis Y/ XThe marginal at pointC is Y/ XThe slope at point Cis Y over XThe derivative atpoint C is also thisslopeD YY XCX

Quick Differentiation ReviewNameFunctionDerivativeExampleConstant Y cdY/dX 0FunctionsdY/dX 0Y 5A LineY c X dY/dX cdY/dX 5Y 5XPower Y cXbFunctionsdY/dX b c X b-1 Y 5X2dY/dX 10X

Quick Differentiation ReviewSum of Y G(X) H(X)Functionsexample Y 5X 5X2Product ofdY/dX dG/dX dH/dXdY/dX 5 10XY G(X) H(X)Two Function dY/dX (dG/dX)H (dH/dX)Gexample Y (5X)(5X2 )dY/dX 5(5X2 ) (10X)(5X) 75X2

Quick Differentiation ReviewQuotient of Two Y G(X) / H(X)FunctionsdY/dX (dG/dX) H - (dH/dX) GH2Y (5X) / (5X2) dY/dX 5(5X2) -(10X)(5X)(5X2)2 -25X2 / 25X4 - X-2Chain RuleY G [ H(X) ]dY/dX (dG/dH) (dH/dX) Y (5 5X)2dY/dX 2(5 5X)1(5) 50 50X

Max of xySlope 0the functionY -50 100X - 5X2value of xdy/dx1020i.e.,xValue of Dy/dx when y is maxdY 100 - 10XdXdY 0ifdXX 100Value of dy/dx whichIs the slope of y curvei.e., Y is maximized whenthe slope equals zero.1020xNote that this is not sufficient for maximization or minimization problems.

SinceyMax value of ydYdX 0 at two points, we need anothercondition to distinguish between the maximum andminimum points.Look at theMin value of ydYdXcurve* at point 5 the curve is upward, i.e., its slope ( thesecond derivative (the derivative of the derivative)) ispositive. HencexDy/dxd 2Y 0dX 2value of dy/dxd2y/dx2 0( minimum point )d2y/dx2 0* at point 10 the curve is downward, i.e., its slope isnegative. Henced 2Y 0dX 2x( maximum point )

Optimization RulesMaximization conditions:12-dY 0dXd 2Y 0dX 2Minimization conditions:12-dY 0dXd 2Y 0dX 2

Applications of Calculus in ManagerialEconomicsmaximization problem:A profit function might look like an arch, rising to a peak and thendeclining at even larger outputs. A firm might sell hugeamounts at very low prices, but discover that profits are low ornegative.At the maximum, the slope of the profit function is zero. The firstorder condition for a maximum is that the derivative at that pointis zero.If 50Q Q2,then d /dQ 50 2 Q, using the rules of differentiation.Hence, Q 25 will maximize profitswhere50 2Q 0.

More Applications of Calculusminimization problem: Cost minimizationsupposes that there is a least cost point to produce. Anaverage cost curve might have a U shape. At theleast cost point, the slope of the cost function iszero. The first order condition for a minimum is thatthe derivative at that point is zero.If TC 5Q2 – 60Q,then dC/dQ 10Q 60.Hence, Q 6 will minimize costWhere:10Q 60 0.

Competitive Firm: Maximize Profits– where TR - TC P Q - TC(Q)– Use our first order condition:– d /dQ P - dTC/dQ 0.a function of Q– Decision Rule: P MC.Max 100Q - Q2First order 100 -2Q 0 impliesQ 50 and; 2,500

Second Order Condition: one variableIf the second derivative is negative,then it’s a maximum.Problem 1Max 100Q - Q2Problem 2Max 50 5X2First derivativeFirst derivative100 -2Q 0second derivative is: -2impliesQ 50 is a MAX10X 0second derivative is: 10impliesQ 10 is a MIN

e.g.;2Y -1 9X - 6X X3Y 0 at2 9 - 12X 3X 0Quadratic FunctionY aX2 bX cX b b2 4ac2aX 3or X 1the second conditiond 2YdX 2 -12 6Xat X 3d 2YdX 2a 3at X 1b -12d 2YdX 2c 9 2 1thereforefirst conditiondYdXX ( 12) 122 4(9 3)6 -12 6(3) 6 0 ( minimum point) -12 6(1) - 6 0 (maximum point)

Partial DifferentiationEconomic relationships usually involveseveral independent variables.A partial derivative is like a controlledexperiment- it holds the “other” variablesconstantSuppose price is increased, holding thedisposable income of the economy constantas inQ f (P, I )then Q/ P holds income constant.

Sales are a function of advertising innewspapers and magazines ( X, Y)Max S 200X 100Y -10X2 -20Y2 20XYDifferentiate with respect to X and Y and setequal to zero. S/ X 200 - 20X 20Y 0 S/ Y 100 - 40Y 20X 0solve for X & Y and Sales

2 equations & 2 unknowns200 - 20X 20Y 0100 - 40Y 20X 0Adding them, the -20X and 20X cancel, sowe get 300 - 20Y 0, or Y 15Plug into one of them:200 - 20X 300 0, hence X 25To find Sales, plug into equation:S 200X 100Y -10X2 -20Y2 20XY 3,250

PARTIAL DIFFERENTIATION AND MAXIMIZATION OFMULTIVARIATE FUNCTIONS. f (Q1 , Q2 )To know the marginal effect of Q 1 on we hold Q2 constant, andvice versa.In order to do that we use partial derivative ofQ1 denoted by with respect to ( treating Q as constant )2 Q1e.g.; -20 100Q1 80Q2 - 10Q12 - 10Q22 - 5Q1Q2;to find the partial derivative of with respect to Q1 we treat Q2as constant; hence Q1 100 - 20Q1 - 5Q2; Q2 80 - 20Q2 - )derivativesequaltozeroandsolve

100 - 20Q1 - 5Q2 080 - 20Q2 - 5Q1 0multiply by -4 and add- 220 75Q2 0henceQ2 2.933substitute for Q2 at any of the eq. 1100 - 20Q1 - 14.665;henceQ1 4.267.i.e.,profit is maximized when the firm produces 4.267 of Q1 and 2.933 of Q2.

CONSTRAINED OPTIMIZATIONWe assume that the firm can freely produce 4.267 of Q 1 and 2.933of Q2. Quite often this may not be the case.e.g.Minimize TC 4Q12 5Q22 - Q1Q2;subject to:Q1 Q2 30The constraint functionSolution:The lagrangian multiplier:Steps:1 - set the constraint function to zero2 - form the lagrangian function by adding the constraint functionafter multiplication with an unknown factor to the originalfunction.3 - take the partial derivatives and set them equal to zero4 - solve the resulting equations simultaneously

step 1:30 - Q1 - Q2 0step 2:L 4Q12 5Q22 - Q1Q2 ( 30 - Q1 - Q2)step 3: L Q1 L Q2 L 8Q1 - Q2 - -Q1 10Q2 - -Q1 - Q2 30

8Q1 - Q2 - 0(1)-Q1 10Q2 - 0(2)-Q1 - Q2 30(3) 0step 4multiply eq(2) by -1 and subtract from eq(1)9Q1 - 11Q2 0(4)multiply (3) by 9 and add to eq(4)-9Q1 - 9Q2 270 09Q1 - 11Q2 0-20Q2 270 0Q2 270/20 13.5

substituting in eq (3) Q1 16.5the values of Q1 and Q2 that minimizes TC are 16.5 and 13.5respectively.substituting Q1 and Q2 in eq(1) or eq(2) we find that 118.5the interpretation of measures the change in TC if the constraint is to be relaxed by oneunit.i.e., TC will increase ( has a positive sign ) by 118.5 if the constraintbecomes 29 or 31.

Managerial Economics is ‘Normative’ Universal applicability The roots of Managerial Economics came from Micro Economics Relation of Managerial Economics to Economic Theory is much like that of Engineering to Physics or Medicine to Biology. It is the relation of applied field to basic fundamental disciplin