1、,DEMAND ANALYSIS,OVERVIEW of Chapter 3 Demand Relationships Demand Elasticities Income Elasticities Cross Elasticities of Demand Appendix 3A: Indifference Curves,Health Care & Cigarettes,Raising cigarette taxes reduces smoking In Canada, $4 for a pack of cigarettes reduced smoking 38% in a decade Bu
2、t cigarette taxes also helps fund health care initiatives The issue then, should we find a tax rate that maximizes tax revenues? Or a tax rate that reduces smoking?,Demand Analysis,An important contributor to firm risk arises from sudden shifts in demand for the product or service. Demand analysis s
3、erves two managerial objectives: (1) it provides the insights necessary for effective management of demand, and (2) it aids in forecasting sales and revenues.,Demand Curves,Individual Demand Curve the greatest quantity of a good demanded at each price the consumers are Willing to Buy, ceteris paribu
4、s.,Willing to Buy,Unwilling to Buy,$/Q,Q/time unit,The Market Demand Curve is the horizontal sum of the individual demand curves.The Demand Function includes all variables that influence the quantity demanded,4 3 7,Sam Diane Market,Q = f( P, Ps, Pc, I, W, E),+ + - ? ? +,Supply Curves,Firm Supply Cur
5、ve - the greatest quantity of a good supplied at each price the firm is profitably able to supply, ceteris paribus.,$/Q,Q/time unit,Able to Produce,Unable to Produce,The Market Supply Curve is the horizontal sum of the firm supply curves.The Supply Function includes all variables that influence the
6、quantity supplied,4 3 7,Acme Universal Market,Q = g( P, W, R, TC),+ - - +,Equilibrium: No Tendency to Change,Superimpose demand and supply If No Excess Demand and No Excess Supply No tendency to change,D,S,Pe,willing & able,Q,P,Downward Slope,Reasons that price and quantity are negatively related in
7、clude: income effect-as the price of a good declines, the consumer can purchase more of all goods since his or her real income increased. substitution effect-as the price declines, the good becomes relatively cheaper. A rational consumer maximizes satisfaction by reorganizing consumption until the m
8、arginal utility in each good per dollar is equal: Optimality Condition is MUA/PA = MUB/PB = MUC/PC = .If MU per dollar in A and B differ, the consumer can improve utility by purchasing more of the one with higher MU per dollar.,Comparative Statics and the Supply-Demand Model,Suppose a shift in Incom
9、e, and the good is a “normal” good Does Demand or Supply Shift? Suppose wages rose, what then?,D,S,e1,P,Q,Elasticity as Sensitivity,Elasticity is measure of responsiveness or sensitivity Beware of using Slopes,bushels hundred tons,price price per per bu. bu,Slopes change with a change in units of me
10、asure,Price Elasticity,E P = % change in Q / % change in P Shortcut notation: E P = %Q / %P A percentage change from 100 to 150 A percentage change from 150 to 100 Arc Price Elasticity - averages over the two points,D,arc price elasticity,Arc Price Elasticity Example,Q = 1000 at a price of $10 Then
11、Q= 1200 when the price was cut to $6 Find the price elasticity Solution: E P = %Q/ %P = +200/1100 - 4 / 8 or -.3636. The answer is a number. A 1% increase in price reduces quantity by .36 percent.,Point Price Elasticity Example,Need a demand curve or demand function to find the price elasticity at a
12、 point.E P = %Q/ %P =(Q/P)(P/Q)If Q = 500 - 5P, find the point price elasticity at P = 30; P = 50; and P = 80 E QP = (Q/P)(P/Q) = - 5(30/350) = - .43 E QP = (Q/P)(P/Q) = - 5(50/250) = - 1.0 E QP = (Q/P)(P/Q) = - 5(80/100) = - 4.0,Price Elasticity (both point price and arc elasticity ),If E P = -1, u
13、nit elastic If E P -1, inelastic, e.g., - 0.43 If E P -1, elastic, e.g., -4.0,price,elastic regionunit elastic inelastic region,Straight line demand curve,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 ,
14、 but Q a lotHence TR FALLS ! Suppose demand is inelastic, and we decide to raise price. What happens to TR and TC and profit?,Another Way to Remember,Linear demand curve TR on other curve Look at arrows to see movement in TR,ElasticUnit ElasticInelastic,TR,QQ,1979 Deregulation of Airfares,Prices dec
15、lined Passengers increased Total Revenue Increased What does this imply about the price elasticity of air travel ?,Determinants of the Price Elasticity,The number of close substitutes more substitutes, more elastic The proportion of the budget larger proportion, more elastic The longer the time peri
16、od permitted more time, generally, more elastic consider examples of business travel versus vacation travel for all three above.,Income Elasticity,E I = %Q/ %I =(Q/I)( I / Q)arc income elasticity: suppose dollar quantity of food expenditures of families of $20,000 is $5,200; and food expenditures ri
17、ses to $6,760 for families earning $30,000. Find the income elasticity of food %Q/ %I = (1560/5980)(10,000/25,000) = .652,Definitions,If E I is positive, then it is a normal or income superior good some goods are Luxuries: E I 1 some goods are Necessities: E I 1 If E QI is negative, then its an infe
18、rior good consider: Expenditures on automobiles Expenditures on Chevrolets Expenditures on 1993 Chevy Cavalier,Point Income Elasticity Problem,Suppose the demand function is:Q = 10 - 2P + 3I find the income and price elasticities at a price of P = 2, and income I = 10 So: Q = 10 -2(2) + 3(10) = 36 E
19、 I = (Q/I)( I/Q) = 3( 10/ 36) = .833 E P = (Q/P)(P/Q) = -2(2/ 36) = -.111 Characterize this demand curve !,Cross Price Elasticities,E X = %Qx / %Py = (Qx/Py)(Py / Qx)Substitutes have positive cross price elasticities: Butter & Margarine Complements have negative cross price elasticities: VCR machine
20、s and the rental price of tapes When the cross price elasticity is zero or insignificant, the products are not related,HOMEWORK PROBLEM: Find the point price elasticity, the point income elasticity, and the point cross-price elasticity at P=10, I=20, and Ps=9, if the demand function were estimated t
21、o be: Qd = 90 - 8P + 2I + 2Ps. 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.,Indifference Curve Analysis Appendix 3A,Consumers attempt to max happiness, or utility: U
22、(X, Y) Subject to an income constraint: I = PxX + PyY Graph in 3-dimensions,Y,X,U,Uo,Uo,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 i
23、ndifference curves slope down, never intersect, and are convex to the origin.,X,Y,5 6 7,97 6,convex,Uo,U1,U2,give up 2X for a Y,X,Y,Y,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 ten
24、d to buy more due to (i) the Income Effect and (ii) the Substitution Effect.,Py,Consumer Choice & Lagrangians,The consumer choice problem can be made into a Lagrangian Max L = U(X, Y) - PxX + PyY - I i) L / X = U/X - Px = 0 MUx = Pxii) L / Y = U/Y - Py = 0 MUy = Pyiii) PxX + PyY - I = 0 Equations i)
25、 and ii) are re-arranged on the right-hand-side after the bracket to show that the ratio of MUs equals the ratio of prices. This is the equi-marginal principle for optimal consumption,Optimal Consumption Point,Rearranging we get the Decision Rule: MUx / Px = MUy / Py = MUz / Pz “the marginal utility
26、 per dollar in each use is equal” Lambda is the marginal utility of moneySuppose MU1 = 20, and MU2 = 50 and P1 = 5, and P2 = 25 are you maximizing utility?,Problem,Max L = 2X + 2Y -.5X2 +XY - .6Y2 - 48 - 4X - 6Y 1. Lx: 2 - X + Y = 4 2. Ly: 2 + X - 1.2Y = 6 3. L: 48 - 4X - 6Y = 0 (1) and (2) yields: X = 1.08Y + .4 (3) can be reduced to X = 12 -1.5Y Together we get: X = 5.256, Y = 4.496 Substitute X and Y into (1) we find = .31,X = 1.08Y + .4,
