1 © 2006 by Nelson, a division of Thomson Canada Limited Christopher Michael Trent University Department of Economics LECTURE 3 ECON 340 MANAGERIAL ECONOMICS Demand Theory and Analysis

2 © 2006 by Nelson, a division of Thomson Canada Limited Topics Demand Relationships Demand Elasticities Income Elasticities Cross Elasticities of Demand Combined Effects of Elasticities Indifference Curve Analysis

3 © 2006 by Nelson, a division of Thomson Canada Limited Markets, Demand & Supply and Equilibrium Prices > Equilibrium lead to surpluses Prices < Equilibrium lead to shortages

4 © 2006 by Nelson, a division of Thomson Canada Limited Shifts and Movements in Demand Movement along demand curve? »If the price of a good increases, or decreases and everything else remains the same there is a movement along the demand curve and a change in the quantity demanded. Shift in the demand curve? »If the price of a good remains constant but some other influence on buyers' plans changes, there is a change in the demand for that good and the demand curve shifts. Prices of related goods; Expected future prices; Income; Population; Preferences. P Q D Q P D0 D1

5 © 2006 by Nelson, a division of Thomson Canada Limited Health Care & Cigarettes Raising cigarette taxes reduces smoking »In Canada, $4 for a pack of cigarettes reduced smoking 38% in a decade But cigarette taxes also helps fund health care initiatives »The issue then, should we find a tax rate that maximizes tax revenues? »Or a tax rate that reduces smoking?

6 © 2006 by Nelson, a division of Thomson Canada Limited Demand Analysis An important contributor to firm risk arises from sudden shifts in demand for the product or service. Demand analysis serves two managerial objectives: (1) it provides the insights necessary for effective management of demand, and (2) it aids in forecasting sales and revenues.

7 © 2006 by Nelson, a division of Thomson Canada Limited Individual Demand Curve the greatest quantity of a good demanded at each price the consumers are willing to buy, holding other influences constant $/Q Q /time unit $5 20 Demand Curves

8 © 2006 by Nelson, a division of Thomson Canada Limited The Market Demand Curve is the horizontal sum of the individual demand curves. The Demand Function includes all variables that influence the quantity demanded Sam +Diane = Market Q = f( P, P s, P c, Y, N W, P E ) ? + ? + P is price of the good P S is the price of substitute goods P C is the price of complementary goods Y is income, N is population, W is wealth, and P E is the expected future price

9 © 2006 by Nelson, a division of Thomson Canada Limited Reasons that price and quantity are negatively related include: » income effect — as the price of a good declines, the consumer can purchase more of all goods since one’s real income increased. » substitution effect — as the price declines, the good becomes relatively cheaper. A rational consumer maximizes satisfaction by reorganizing consumption until the marginal utility in each good per dollar is equal. Why is the Demand Curve Downward Sloping????

10 © 2006 by Nelson, a division of Thomson Canada Limited Responsiveness in the QD of a commodity to a change in its price Beware of using Slopes bushelshundred bushels price per bu. Slopes change with a change in units of measure Elasticity as Sensitivity

11 © 2006 by Nelson, a division of Thomson Canada Limited E D = % change in Q / % change in P Shortcut notation: E D = %  Q / %  P A percentage change from 100 to 150 is 50% A percentage change from 150 to 100 is -33% For arc elasticities, we use the average as the base, as in 100 to 150 is +50/125 = 40%, and 150 to 100 is -40% Arc Price Elasticity -- averages over the two points D arc price elasticity E D =  Q/ [(Q 1 + Q 2 )/2]  P/ [(P 1 + P 2 )/2] Average price Average quantity Price Elasticity

12 © 2006 by Nelson, a division of Thomson Canada Limited Arc Price Elasticity Example Q = 1000 when the price is $10 Q= 1200 when the price is reduced to $6 Find the arc price elasticity Solution: E D = %  Q / %  P = +200/ / 8 or The answer is a number. A 1% increase in price reduces quantity by 0.36 percent.

13 © 2006 by Nelson, a division of Thomson Canada Limited Need a demand curve or demand function to find the price elasticity at a point. E D = %  Q / %  P =(  Q/  P)(P/Q) If Q = P, find the point price elasticity at P = 30; P = 50; and P = 80 1.E D = (  Q/  P)(P/Q) = - 5(30/350) = E D = (  Q/  P)(P/Q) = - 5(50/250) = E D = (  Q/  P)(P/Q) = - 5(80/100) = Price Point Elasticity Example

14 © 2006 by Nelson, a division of Thomson Canada Limited Elasticity If E D = -1, unit elastic If E D > -1, inelastic, e.g., If E D < -1, elastic, e.g., price elastic region unit elastic inelastic region Straight line demand curve example quantity

15 © 2006 by Nelson, a division of Thomson Canada Limited Price Elasticity (both point price and arc elasticity ) Price per unit ($) Elastic range: > 1 = 1 = Point of unitary elasticity Inelastic range: < 1 Quantity demanded per time period Demand curve |  p | approaches–  as the demand curve approaches the Y-axis approaches 0 as the demand curve approaches the X-axis |  p |

16 © 2006 by Nelson, a division of Thomson Canada Limited Two Extreme Examples Perfectly Elastic | E D | = ∞ and Perfectly Inelastic |E D | = 0 D D’ D D’

17 © 2006 by Nelson, a division of Thomson Canada Limited TR and Price Elasticities If you raise price, does TR rise? Suppose demand is elastic, and raise price. TR = PQ, so, %  TR = %  P + %  Q If elastic, P, but Q a lot Hence TR FALLS !!! Suppose demand is inelastic, and we decide to raise price. What happens to TR and TC and profit?

18 © 2006 by Nelson, a division of Thomson Canada Limited Elastic portion of demand curve as price increases TR decreases, since small changes in price has a large impact on quantity. Inelastic portion of the demand curve, as price increases, TR increases, since a small change in price has a small impact on quantity. Elastic Unit Elastic Inelastic TR QQQQ

19 © 2006 by Nelson, a division of Thomson Canada Limited MR and Elasticity Marginal revenue is  TR  Q To sell more, often price must decline, so MR is often less than the price.  MR = P ( 1 + 1/E D ) For a perfectly elastic demand, E D = -∞. Hence, MR = P. If E D = -2, then MR = 0.5P, or is half of the price.

20 © 2006 by Nelson, a division of Thomson Canada Limited Determinants of the Price Elasticity The availability and the closeness of substitutes »more substitutes, more elastic The more durable is the product »Durable goods are more elastic than non-durables The percentage of the budget »larger proportion of the budget, more elastic The longer the time period permitted »more time, generally, more elastic »consider examples of business travel versus vacation travel for all three above.

21 © 2006 by Nelson, a division of Thomson Canada Limited E Y = %  Q / %  Y = (  Q/  Y)( Y/Q) point income arc income elasticity: »suppose dollar quantity of food expenditures of families of $20,000 is $5,200; and food expenditures rises to $6,760 for families earning $30,000. »Find the income elasticity of food »%  Q / %  Y = (1560/5980)÷(10,000/25,000) =0.652 »With a 1% increase in income, food purchases rise 0.652% E Y =  Q/ [(Q 1 + Q 2 )/2] arc income  Y/ [(Y 1 + Y 2 )/2] elasticity Income Elasticity

22 © 2006 by Nelson, a division of Thomson Canada Limited Income Elasticity Definitions If E Y >0, then it is a normal good »some goods are Luxuries: E Y > 1 with a high income elasticity (luxuries are also called superior goods) »some goods are Necessities: E Y < 1 with a low income elasticity If E Y is negative, then it’s an inferior good Consider these examples: 1.Expenditures on new automobiles 2.Expenditures on new Chevrolets 3.Expenditures on 1996 Chevy Cavaliers with 150,000 km Which of the above is likely to have the largest income elasticity? Which of the above might have a negative income elasticity?

23 © 2006 by Nelson, a division of Thomson Canada Limited Point Income Elasticity Problem Suppose the demand function is: Q = P + 3Y find the income and price elasticities at a price of P = 2, and income Y = 10 So: Q = 10 -2(2) + 3(10) = 36 E Y = (  Q/  Y)( Y/Q) = 3(10/ 36) = E D = (  Q/  P)(P/Q) = -2(2/ 36) = Characterize this demand curve, which means describe them using elasticity terms.

24 © 2006 by Nelson, a division of Thomson Canada Limited Cross Price Elasticities E X = %  Q A / %  P B = (  Q A /  P B )(P B /Q A ) Substitutes have positive cross price elasticities: butter & margarine Complements have negative cross price elasticities: DVD machines and the rental price of DVDs at Blockbuster When the cross price elasticity is zero or insignificant, the products are not related

25 © 2006 by Nelson, a division of Thomson Canada Limited Find the point price elasticity, the point income elasticity, and the point cross-price elasticity at P=10, Y=20, and P s =9, if the demand function were estimated to be: Q D = ·P + 2·Y + 2·P s Is the demand for this product elastic or inelastic? Is it a luxury or a necessity? Does this product have a close substitute or complement? Find the point elasticities of demand. Problem

26 © 2006 by Nelson, a division of Thomson Canada Limited Answer First find the quantity at these prices and income: Q D = ·P + 2·Y + 2·P s = 90 -8·10 + 2·20 + 2·9 = = 68 E D = (  Q/  P)(P/Q) = (-8)(10/68)= which is elastic E Y = (  Q/  Y)(Y/Q) = (2)(20/68) = which is a normal good, but a necessity E X = (  Q A /  P B )(P B /Q A ) = (2)(9/68) = which is a mild substitute

27 © 2006 by Nelson, a division of Thomson Canada Limited Combined Effect of Demand Elasticities Most managers find that prices and income change every year. The combined effect of several changes are additive. %  Q = E D (%  P) + E Y (%  Y) + E X (%  P R ) »where P is price, Y is income, and P R is the price of a related good. If you knew the price, income, and cross price elasticities, then you can forecast the percentage changes in quantity.

28 © 2006 by Nelson, a division of Thomson Canada Limited Example: Combined Effects of Elasticities Toro has a price elasticity of -2 for snow blowers Toro snow blowers have an income elasticity of 1.5 The cross price elasticity with professional snow removal for residential properties is What will happen to the quantity sold if you raise price 3%, income rises 2%, and professional snow removal companies raise price 1%? »%  Q = E P %  P +E Y %  Y + E X %  P x = -2 3% % % = -6% + 3% + 0.5% »%  Q = -2.5%. We expect sales to decline.

29 © 2006 by Nelson, a division of Thomson Canada Limited Q: Will Total Revenue for your product rise or fall? A: Total revenue will rise slightly (about + 0.5%), as the price went up 3% and the quantity of snow blowers sold will fall 2.5%. Example (concluded): Combined Effects of Elasticities

30 © 2006 by Nelson, a division of Thomson Canada Limited Indifference Curve Analysis of Demand Consumers attempt to maximize happiness, or utility: U(F, E) over food and entertainment Subject to an income constraint : Y = P F F + P E E Graph in 3-dimensions E F U UoUo UoUo

31 © 2006 by Nelson, a division of Thomson Canada Limited Consumer Choice assume consumers can rank preferences, that more is better than less (nonsatiation), that preferences are transitive, and that individuals have diminishing marginal rates of substitution. Then indifference curves slope down, never intersect, and are convex to the origin. F E convex Uo U1 U2 give up 2F for one E

32 © 2006 by Nelson, a division of Thomson Canada Limited F E E Uo U1 a c demand b Indifference Curves We can "derive" a demand curve graphically from maximization of utility subject to a budget constraint. As price falls, we tend to buy more due to (i) the Income Effect and (ii) the Substitution Effect. PEPE

33 © 2006 by Nelson, a division of Thomson Canada Limited Optimal Consumption Point Optimality Condition: MU F / P F = MU E / P E “ the marginal utility per dollar in each use is equal ” Suppose MU 1 = 20, and MU 2 = 50 and P 1 = 5, andP 2 = 25 are you maximizing utility?