Managerial Economics eighth edition Thomas Maurice Chapter 6

Managerial Economics eighth edition Thomas Maurice Chapter 6 Elasticity and Demand Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

Managerial Economics 2 Price Elasticity of Demand (E) • • • P & Q are inversely related by the law of demand so E is always negative • The larger the absolute value of E, the more sensitive buyers are to a change in price 2 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

3 Managerial Economics Price Elasticity of Demand (E) Table 6. 1 Elasticity Responsiveness E Elastic Unitary Elastic Inelastic 3 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

4 Managerial Economics Price Elasticity of Demand (E) • Percentage change in quantity demanded can be predicted for a given percentage change in price as: • % Qd = % P x E • Percentage change in price required for a given change in quantity demanded can be predicted as: • % P = % Qd ÷ E 4 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

5 Managerial Economics Price Elasticity & Total Revenue Table 6. 2 5 Elastic Unitary elastic Inelastic Q-effect dominates No dominant effect P-effect dominates Price rises TR falls No change in TR TR rises Price falls TR rises No change in TR TR falls Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

6 Managerial Economics Factors Affecting Price Elasticity of Demand • Availability of substitutes • The better & more numerous the substitutes for a good, the more elastic is demand • Percentage of consumer’s budget • The greater the percentage of the consumer’s budget spent on the good, the more elastic is demand • Time period of adjustment • The longer the time period consumers have to adjust to price changes, the more elastic is demand 6 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

7 Managerial Economics Calculating Price Elasticity of Demand - Tues • Price elasticity can be calculated by multiplying the slope of demand ( Q/ P) times the ratio of price to quantity (P/Q) 7 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

8 Managerial Economics Calculating Price Elasticity of Demand • Price elasticity can be measured at an interval (or arc) along demand, or at a specific point on the demand curve • If the price change is relatively small, a point calculation is suitable • If the price change spans a sizable arc along the demand curve, the interval calculation provides a better measure 8 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

9 Managerial Economics Computation of Elasticity Over an Interval • When calculating price elasticity of demand over an interval of demand, use the interval or arc elasticity formula 9 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

10 Managerial Economics Let’s Try an Interval E • Say Price drops from $18 to $16 • This causes a increase in quantity demanded of 200 • What is the price elasticity of demand over this interval? 10 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

11 Managerial Economics Computation of Elasticity at a Point • When calculating price elasticity at a point on demand, multiply the slope of demand ( Q/ P), computed at the point of measure, times the ratio P/Q, using the values of P and Q at the point of measure • Method of measuring point elasticity depends on whether demand is linear or curvilinear 11 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

Managerial Economics 12 Point Elasticity When Demand is Linear 12 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

13 Managerial Economics Point Elasticity When Demand is Linear • Compute elasticity using either of the two formulas below which give the same value for E 13 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

14 Managerial Economics Point Elasticity When Demand is Curvilinear • Compute elasticity using either of two equivalent formulas below 14 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

15 Managerial Economics Let’s try a point E • If we want to calculate a point elasticity at the point where price = $5 and quantity = 90 • The line equation y = 100 – 2 p or Q = 100 – 2 p • We can use 15 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

16 Managerial Economics Elasticity (Generally) Varies Along a Demand Curve • For linear demand, price and E vary directly • The higher the price, the more elastic is demand • The lower the price, the less elastic is demand • For curvilinear demand, no general rule about the relation between price and quantity 16 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

17 Managerial Economics Constant Elasticity of Demand (Figure 6. 3) 17 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

18 Managerial Economics Computation of Elasticity Over an Interval • Marginal revenue (MR) is the change in total revenue per unit change in output • Since MR measures the rate of change in total revenue as quantity changes, MR is the slope of the total revenue (TR) curve 18 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

19 Managerial Economics Demand & Marginal Revenue (Table 6. 3) 19 TR = P Q MR = TR/ Q Unit sales (Q) Price 0 $4. 50 1 4. 00 $4. 00 2 3. 50 $7. 00 $3. 00 3 3. 10 $9. 30 $2. 30 4 2. 80 $11. 20 $1. 90 5 2. 40 $12. 00 $0. 80 6 2. 00 $12. 00 $0 7 1. 50 $10. 50 $-1. 50 Mc. Graw-Hill/Irwin $ 0 -- Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

20 Managerial Economics Demand, MR, & TR Panel A 20 Mc. Graw-Hill/Irwin (Figure 6. 4) Panel B Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

21 Managerial Economics Demand & Marginal Revenue • When inverse demand is linear, = A + BQ P • Marginal revenue is also linear, intersects the vertical (price) axis at the same point as demand, & is twice as steep as demand MR = A + 2 BQ 21 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

22 Managerial Economics Linear Demand, MR, & Elasticity (Figure 6. 5) 22 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

23 Managerial Economics MR, TR, & Price Elasticity Table 6. 4 Marginal Total revenue MR > 0 TR increases as Q increases MR = 0 TR is maximized MR < 0 23 Mc. Graw-Hill/Irwin Price elasticity of demand Elastic ( E > 1) 1) Unit elastic ( E = 1) 1) TR decreases as Inelastic Q increases ( E < 1) 1) Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

24 Managerial Economics Marginal Revenue & Price Elasticity • For all demand & marginal revenue curves, the relation between marginal revenue, price, & elasticity can be expressed as 24 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

25 Managerial Economics Income Elasticity • Income elasticity (EM) measures the responsiveness of quantity demanded to changes in income, holding the price of the good & all other demand determinants constant • Positive for a normal good • Negative for an inferior good 25 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

26 Managerial Economics Cross-Price Elasticity • Cross-price elasticity (EXY) measures the responsiveness of quantity demanded of good X to changes in the price of related good Y, holding the price of good X & all other demand determinants for good X constant • Positive when the two goods are substitutes • Negative when the two goods are complements 26 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

27 Managerial Economics Interval Elasticity Measures • To calculate interval measures of income & cross-price elasticities, the following formulas can be employed 27 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

Managerial Economics 28 Point Elasticity Measures 28 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.

29 Managerial Economics Homework • Read Chapter 6 • Do Technical Problems: 1, 2, 3, 4, 5, 7, 9, 10, 12, 13, 15, 16 • Do Applied Problems: 1, 3, 4, 6, 8, 29 Mc. Graw-Hill/Irwin Copyright © 2005 by the Mc. Graw-Hill Companies, Inc. All rights reserved.