Unit 4. Quantitative Demand Analysis (as functions of output level) (Ch. 3, 8)

Revenue Concepts and Output Relationships 1.Graphical 2.Mathematical  Revenue Concept = f(q)

D Curves Facing Individual Firms Case #1:P = a – bX  ‘imperfect’ competition * firm has some control over P (P maker)  significant portion of mkt supply  firm output influences mkt supply * heterogeneous products * difficult mkt entry (& exit) * imperfect info

D Curves Facing Individual Firms Case #2:P = a  ‘perfect’ competition * firm has no control over P (P taker)  insignificant portion of mkt supply  firm output does not impact mkt supply * homogenous products * easy mkt entry (& exit) * perfect info

Revenue Concepts Concept/DefinitionIf P = a – bxIf P = a 1. TR = Total Revenue = total $ sales to firm = gross income = total $ cost to buyers = Px = (a-bx)x = ax-bx 2 = Px = ax 2. AR = Average Revenue = revenue per unit of output = TR/x = (ax-bx 2 )/x = a – bx = P = TR/x = ax/x = a = P 3. MR = Marginal Revenue = additional revenue per unit of additional output = slope of TR curve =  TR/  x =  TR/  x = a – 2bx =  TR/  x =  TR/  x = a

Market & Firm D (Perfect Competition)

Revenue Concepts P = a

Revenue Concepts P=a-bQ

TR Max P-Taking firm No TR max as TR keeps increasing with Q P-Setting firm Max TR where MR = 0  P =a/2

Question If a firm wants to increase its dollar sales of a product, should it  P or  P?

Quote of the Day “Students of Economics need to be taught, in business, sometimes you should raise your price, and sometimes you should lower your price.” CEO of Casey’s

Business managers often want to know: If a D factor affecting sales of their product changes by a given %, what will be the corresponding % impact on Q sold of their product. =“Elasticity of Demand”

Elasticity of D Definition (Meaning) = A measure of responsiveness of D to changes in a factor that influences D Two components 1. Magnitude of change (number) 2. Direction of change (sign) = The number shows the magnitude of how much D will change due to a 1% change in a D factor The sign shows whether the D factor and D are changing in the same or opposite directions +  same direction -  opposite direction

Elasticities of Demand  E Q,F = %  Qd x /%  F = %  Q/%  F where, Qd x = the quantity demanded of X F= a factor that affects Qd x Notes: sign > 0  Qd x & F, ‘directly’ related sign < 0  Qd x & F, ‘indirectly’ related number > 1  %  Qd x >%  F

Elasticity Calculation

Types of Elasticities TypeF E0E0 =own PPXPX ECEC =cross PPYPY EIEI =IncomeI EAEA =advertisingA

Elasticity Value Meanings (e.g.) E 0 = -2  for each 1%  P x,Q d for X will  by 2% in opposite direction E C = +1/2  for each 1%  P Y,Q d for X will  by 1/2% in same direction E I = +.1  for each 1%  I,Q d for X will  by.1% in same direction

Own Price Elasticity of Demand Negative according to the ‘law of demand’

Perfectly Elastic & Inelastic Demand

E 0 Calculation E 0 = E X,Px

E 0 and Linear D (P = a – bx) P x E 0 a/2 > a/2 < a/2

Q d = 10 – 2P Own-Price Elasticity: (-2)P/Q If P=1, Q=8 (since 10 – 2 = 8) Own price elasticity at P=1, Q=8: (-2)(1)/8 = Example of Linear Demand

Factors Affecting Own Price Elasticity Available Substitutes The more substitutes available for the good, the more elastic the demand. Time Demand tends to be more inelastic in the short term than in the long term. Time allows consumers to seek out available substitutes. Expenditure Share Goods that comprise a small share of consumer’s budgets tend to be more inelastic than goods for which consumers spend a large portion of their incomes.

Uses of E 0 1.Calculate % change in P needed to bring about desired % change in Q sold 2.Calculate % change in Q sold that will result from a given % change in P 3.Calculate magnitude of change in TR that will result from a given % change in P

Example 1: Pricing and Cash Flows According to an FTC Report by Michael Wad, AT&T’s own price elasticity of demand for long distance services is – AT&T needs to boost revenues in order to meet it’s marketing goals. To accomplish this goal, should AT&T raise or lower it’s price?

Example 2: Quantifying the Change If AT&T lowered price by 3 percent, what would happen to the volume of long distance telephone calls routed through AT&T?

Answer Calls would increase by percent!

Own-Price Elasticity and Total Revenue Elastic Increase (a decrease) in price leads to a decrease (an increase) in total revenue. Inelastic Increase (a decrease) in price leads to an increase (a decrease) in total revenue. Unitary Total revenue is maximized at the point where demand is unitary elastic.

Change in TR (math) TR 1 =P 1 Q 1 TR 2 =P 2 Q 2 =(P 1 +  P)(Q 1 +  Q) =P 1 Q 1 +  PQ 1 +  QP 1 +  P  Q  TR=TR 2 – TR 1 =  PQ 1 +  QP 1 +  P  Q =  PQ 1 +  QP 1 (  P  Q  0 for small  P and small  Q)

Change in TR Due to  Q (i.e. MR) NOTE: MR = 0 if E is unitary > 0 if E is elastic < 0 if E is inelastic

Change in TR and E 0

Quantifying the Change inTR =($100 mil) (1 – 8.64) (-.03) =(100 mil) (-7.64) (-.03) =$ mil.

Cross Price Elasticity of Demand +Substitutes - Complements

Example 3: Impact of a change in a competitor’s price According to an FTC Report by Michael Ward, AT&T’s cross price elasticity of demand for long distance services is If MCI and other competitors reduced their prices by 4%, what would happen to the demand for AT&T services?

Answer AT&T’s demand would fall by percent!

Income Elasticity +Normal Good -Inferior Good

Demand Functions Mathematical representations of demand curves Example: X and Y are substitutes (coefficient of P Y is positive) X is an inferior good (coefficient of M is negative)

Elasticity Calculation

Specific Demand Functions Linear Demand Own PriceCross PriceIncome ElasticityElasticityElasticity

E X,Px Calculation Given D Function Equation X=10 – 2P x + 3P Y – 2M =10 – 2P x + 3(4) – 2(1)  X=20 – 2P X  P x =10 -.5X

E X,Px at P X = 4 ?

E X,I Calculation Given D Equation X=10 – 2P X + 3P Y – 2I =10 – 2(1) + 3(4) – 2I  X=20 – 2I

E X,I at I = 2 ?

Log-Linear Demand Own Price Elasticity:  X Cross Price Elasticity:  Y Income Elasticity:  M

Summary Elasticities are tools you can use to quantify the impact of changes in prices, income, and advertising on sales and revenues. Given market or survey data, regression analysis can be used to estimate: Demand functions Elasticities A host of other things, including cost functions Managers can quantify the impact of changes in prices, income, advertising, etc.

Use of Elasticities Pricing Managing cash flows Impact of changes in competitors’ prices Impact of economic booms and recessions Impact of advertising campaigns And lots more!