Managerial Economics and Organizational Architecture, 5e Managerial Economics and Organizational Architecture, 5e Chapter 4: Demand McGraw-Hill/Irwin Copyright © 2009 by The McGraw-Hill Companies, Inc All Rights Reserved Managerial Economics and Organizational Architecture, 5e 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 Managerial Economics and Organizational Architecture, 5e 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 Managerial Economics and Organizational Architecture, 5e Variable Values Suppose the variables have the following values: P = $30 Ps = $50 Pr = $40 I = $50,000 How many tickets will PTC sell? 4-4 Managerial Economics and Organizational Architecture, 5e 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 Managerial Economics and Organizational Architecture, 5e Graphing the Demand Curve $ $ Ticket price (in dollars) Income = 51,000 61 60 60 Income = $50,000 D1 D D0 Q Q 400 Quantity of PTC tickets Quantity of PTC tickets 406.0 4-6 Managerial Economics and Organizational Architecture, 5e 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 Managerial Economics and Organizational Architecture, 5e Demand Elasticity The price elasticity of demand is given by %Q %P 4-8 Managerial Economics and Organizational Architecture, 5e 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 Managerial Economics and Organizational Architecture, 5e Calculating Elasticity Arc Price Elasticity Q (Q1 Q2 ) Q (Q Q ) 2 P P ( P1 P2 ) ( P1 P2 ) 4-10 Managerial Economics and Organizational Architecture, 5e Arc Price Elasticity $ Ticket price in dollars η = -[ΔQ/(Q1 + Q2)/2] ÷ [ΔP/(P1 + P2)/2] 60 =-[-67/(200+133)/2] ÷ [10/(30+40)/2] = 1.4 (133, $40) P2 (200, $30) P1 D Q2 Q1 Quantity of PTC tickets 400 4-11 Managerial Economics and Organizational Architecture, 5e 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) n=1 30 Inelastic demand (n < 1) Q Total revenue (in dollars) $ 6,000 20 Quantity of PTC tickets 4-16 Q Managerial Economics and Organizational Architecture, 5e Other Demand Influences • Complements versus substitutes – Cross price elasticity of demand Qx Qx1 Qx xy Py Py1 Py 4-17 Managerial Economics and Organizational Architecture, 5e Cross Price Elasticity • For substitutes, ηXY > • If the price of Pepsi rises, the demand for Coke rises • For complements, ηXY < • If the price of peanut butter rises, the demand for jelly falls 4-18 Managerial Economics and Organizational Architecture, 5e Income • Income elasticity of demand Q x Qx1 Qx I I I1 I • Normal goods – demand rises as income increases (>0) • Inferior goods – demand falls as income increases (