Managerial Economics and Organizational Architecture, 5e Chapter 4: Demand McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc. All Rights Reserved.

Demand Function A mathematical representation of the relationship between the quantity demanded and all factors influencing demand: Q = f(X1, X2,… Xn) where Q is quantity demanded and the Xis are the factors influencing demand 4-2

Demand for PTC Tickets Q = 117 - 6.6P + 1.66Ps - 3.3Pr + 0.00661I where P is PTC ticket price, Ps is price of symphony tickets, Pr is price of nearby restaurant meals, and I is average per capita income 4-3

Variable Values Suppose the variables have the following values: Ps = $50 Pr = $40 I = $50,000 How many tickets will PTC sell? 4-4

The Demand Curve Substitute variable values (except for P) into the equation and simplify: P = 60 - 0.15Q This is the equation for the demand curve. Law of demand – as the price of a good rises, the quantity demanded falls 4-5

Graphing the Demand Curve $ $ Income = 51,000 61 60 60 Income = $50,000 Ticket price (in dollars) D1 D D0 Q Q 400 406.0 Quantity of PTC tickets Quantity of PTC tickets 4-6

Price Elasticity of Demand Measures the responsiveness of quantity demanded to changes in price Often referred to as elasticity of demand Helps firms determine the effect of price changes on total revenue 4-7

Demand Elasticity The price elasticity of demand is given by 4-8

Calculating Elasticity Arc Price Elasticity Information requirements: Quantity demanded before and after the price change Q1 Q2 Price before and after the price change P1 P2 4-9

Calculating Elasticity Arc Price Elasticity 4-10

Arc Price Elasticity $ η = -[ΔQ/(Q1 + Q2)/2] ÷ [ΔP/(P1 + P2)/2] 60 =-[-67/(200+133)/2] ÷ [10/(30+40)/2] = 1.4 Ticket price in dollars (133, $40) P2 (200, $30) P1 D Q2 Q1 400 4-11 Quantity of PTC tickets

Price Changes and Total Revenue If demand is elastic (>1), price and total revenue move in opposite directions If P↑ then TR↓ If P↓ then TR↑ If demand is inelastic (<1), price and total revenue move together If P↑ then TR↑ If P↓ then TR↓ 4-12

Range of Price Elasticities $ $ D η = 0 D η = ∞ Price (in dollars) Price (in dollars) Q Q Quantity Quantity Perfectly nelastic Perfectly lastic 4-13

Determinants of Price Elasticity Availability of substitutes few substitutes for salt many substitutes for milk at the supermarket Size of good in consumer budget paper clips versus a car Time period for consumer adjustment over time consumers find alternative goods 4-14

Price Changes and Total Revenue Total revenue is P x Q For PTC, P=60-.15Q And TR = (60-.15Q)Q=60Q-.15Q2 Marginal revenue, MR, is TR/Q=60-.30Q 4-15

Demand, Total Revenue, & Marginal Revenue $ 60 Elastic demand (n > 1) Ticket price (in dollars) 30 n = 1 Inelastic demand (n < 1) Q $ 6,000 Total revenue (in dollars) Q 4-16 200 Quantity of PTC tickets

Other Demand Influences Complements versus substitutes Cross price elasticity of demand 4-17

Cross Price Elasticity For substitutes, ηXY > 0 If the price of Pepsi rises, the demand for Coke rises For complements, ηXY < 0 If the price of peanut butter rises, the demand for jelly falls 4-18

Income Income elasticity of demand Normal goods – demand rises as income increases (>0) Inferior goods – demand falls as income increases (<0) 4-19

Network Effects Demand for a good increases as the number of users of the good increases fax machines High Definition DVD versus Blu-Ray 4-20

Product Attributes Managers must understand consumer demand What product attributes are important to consumers? price product design packaging promotion 4-21

Product Life Cycle Q Introduction Growth Maturity Decline Industry quantity of output Product life cycle T Time 4-22

Demand Estimation Three general techniques interviews surveys, focus groups, questionnaires price experimentation track changes in sales when prices change statistical analysis must account for omitted variables and other issues 4-23

Omitted Variables Problem   1998 1999 2000 Income (I) $3,000 $4,000 $3,500 Advertising (A) 2 3 2.5 Price (P) 10 Sales (S) 236 284 260 True demand S=120-2P+8A+0.04I Estimated demand S=140+48A 4-24

Estimating Demand The Identification Problem $ Three different equilibriums are not mapping out the demand curve S1 Price (in dollars) S2 P1 D1 P2 D2 S3 P3 D3 Estimated demand Q Q1 Q2 Q3 Quantity 4-25