1. © 2009, 2006 South-Western, a part of Cengage Learning Demand Analysis Chapter 4

2. © 2009, 2006 South-Western, a part of Cengage Learning Chapter 4 OVERVIEW   Utility Theory   Indifference Curves   Budget Constraints   Individual Demand   Optimal Consumption   Demand Sensitivity Analysis: Elasticity   Price Elasticity of Demand   Price Elasticity and Marginal Revenue   Price Elasticity and Optimal Pricing Policy   Cross-price Elasticity of Demand   Income Elasticity of Demand

3. © 2009, 2006 South-Western, a part of Cengage Learning Chapter 4 KEY CONCEPTS   utility   nonsatiation principle   indifference   ordinal utility   cardinal utility   utility function   utils   market baskets   marginal utility   law of diminishing marginal utility   indifference curves   substitutes   complements   perfect substitutes   perfect complements   budget constraint   income effect   substitution effect   price-consumption curve   income-consumption curve   Engle curve   normal goods   inferior goods   optimal market basket   revealed preference   marginal rate of substitution   consumption path

4. © 2009, 2006 South-Western, a part of Cengage Learning Utility Theory   Assumptions About Consumer Preferences More is better. Consumers rank-order desirability of products.   Utility functions relate well-being to consumption.   Marginal utility shows added benefit of a small increase in consumption. Marginal utility is usually positive, MU>0.   Law of Diminishing Marginal Utility Marginal utility eventually declines for everything.

5. © 2009, 2006 South-Western, a part of Cengage Learning Chapter 4: Demand Analysis Where does the demand curve come from? The demand curve is based on economics preferences for goods and services that bring them the most utility per dollar. U = f(Goods, Services) Utility is a function of the goods and services consumed. The more goods and services the higher the utility.

6. © 2009, 2006 South-Western, a part of Cengage Learning

7. Indifference Curves A simple numerical example of indifference curves. Marginal utility is the change in utility when goods or services change. MU = ∆TU / ∆Q Consumer base their purchasing decision on the marginal utility they receive per dollar spent. MU / PRICE

8. © 2009, 2006 South-Western, a part of Cengage Learning

9. Mathematical proof of why the slope of the indifference curve is equal to the marginal rate of substitution (MRS).

10. © 2009, 2006 South-Western, a part of Cengage Learning Indifference Curves   Basic Characteristics Higher indifference curves are better. Indifference curves do not intersect. Indifference curves slope downward. Indifference curves are concave to origin.   Perfect substitutes are products that satisfy the same need, e.g., car models.   Perfect complements are products consumed together, e.g., cars and tires.

11. © 2009, 2006 South-Western, a part of Cengage Learning

13. Budget Constraints   Basic Characteristics Show affordable combinations of X and Y. Slope of –P X /P Y reflects relative prices.   Effects of Changing Income and Prices Budget increase (decrease) causes parallel outward (inward) shift. Relative price change alters budget slope.   Income and Substitution Effects Income effect changes overall consumption. Substitution effect alters relative consumption.

14. © 2009, 2006 South-Western, a part of Cengage Learning

16. Optimal Consumption   Marginal Rate of Substitution (MRS) MRS XY = -MU X /MU Y and equals indifference curve slope. MRS XY shows tradeoff between X and Y consumption, holding utility constant. MRS XY diminishes as substitution of X for Y increases.   Utility maximization requires P X /P Y = MU X /MU Y, or MU X /P X = MU Y /P Y.

17. © 2009, 2006 South-Western, a part of Cengage Learning Individual Demand   Price-consumption curve shows consumption impact of price changes. Reflects movement along demand curve.   Income-consumption curve shows consumption impact of income changes. Reflects shift from one demand curve to another.   Engle curves plot income and consumption. Normal good consumption rises with income. Inferior good consumption falls with income (rare).

18. © 2009, 2006 South-Western, a part of Cengage Learning

19. The Relationship between income and goods and services consumed. Consumption Path When income increases, do you buy more of both goods? What does this mean? As I  demand for good X . X is an inferior good.

20. © 2009, 2006 South-Western, a part of Cengage Learning

23. Demand Sensitivity Analysis: Elasticity   Elasticity measures sensitivity.   Point elasticity shows sensitivity of Y to small changes in X. ε X = ∂Y/Y ÷ ∂X/X.   Arc elasticity shows sensitivity of Y to big changes in X. E X = (Y 2 – Y 1 )/(Y 2 +Y 1 ) ÷ (X 2 -X 1 )/(X 2 +X 1 ).

24. © 2009, 2006 South-Western, a part of Cengage Learning Price Elasticity of Demand   Price Elasticity Formula Point price elasticity, ε P = ∂Q/Q ÷ ∂P/P. In all cases, ε P < 0.   Price Elasticity and Total Revenue Price cut increases revenue if │ε P │> 1. Revenue constant if │ε P │= 1. Price cut decreases revenue if │ε P │< 1.

25. © 2009, 2006 South-Western, a part of Cengage Learning What makes demand more elastic?  Products with close substitutes have elastic demand.  Demand for an individual brand is more elastic than industry aggregate demand.  Products with many complements have less elastic demand.  In the long run, demand curves become more elastic.  As price increases, demand becomes more elastic  The larger the percentage of income required to purchase a good, the more elastic it’s demand.  Luxury goods tend to be more elastic

26. © 2009, 2006 South-Western, a part of Cengage Learning Price Elasticity and Marginal Revenue   Elasticity Varies along Demand Curve As price rises, so too does │ε P │. As price falls, so too does│ε P │.   Price Elasticity and Price Changes MR > 0 if │ε P │> 1. MR = 0 if │ε P │= 1. MR < 0 if │ε P │< 1.

27. © 2009, 2006 South-Western, a part of Cengage Learning

29. Price Elasticity and Optimal Pricing Policy   Optimal Price Formula MR and ε P are directly related. MR = P/[1+(1/ ε P )]. Optimal P* = MC/[1+(1/ ε P )].   Determinants of Price Elasticity Essential goods have low│ε P │. Nonessential goods have high│ε P │.

30. © 2009, 2006 South-Western, a part of Cengage Learning Relationship Between Elasticity and Total Revenue © 2009, 2006 South-Western, a part of Cengage Learning

31. Elasticity- numeric example © 2009, 2006 South-Western, a part of Cengage Learning

32. Point Price Elasticity © 2009, 2006 South-Western, a part of Cengage Learning -3000 x 2 = -6000 = -6.19 = e p 3150 3150 Y = 5,000 – 3,000(2) + 200(2) + 75(10) + 60(50) Y = 5,000 – 6,000 + 400 + 750 + 3000 = 3,150 y = 9150 – 3000P Y if P Y = 1 y = 9150 – 3,000 y = 6150

33. © 2009, 2006 South-Western, a part of Cengage Learning Solving for price elasticity © 2009, 2006 South-Western, a part of Cengage Learning eP Y = -3000 x 1 = -3000 = -.488 6150 6150 Interpreting e < -1elastic -1 < e < 0 inelastic e = -1unit elastic

34. © 2009, 2006 South-Western, a part of Cengage Learning Cross-price Elasticity of Demand   Cross-price elasticity shows demand sensitivity to changes in other prices. ε PX = ∂Q Y /Q Y ÷ ∂P X /P X.   Substitutes have ε PX > 0. E.g., Coke demand and Pepsi prices.   Complements have ε PX < 0. E.g., Coke demand and Fritos prices.   Independent goods have ε PX = 0. E.g., Coke demand and car prices.

35. © 2009, 2006 South-Western, a part of Cengage Learning Cross Price Elasticity © 2009, 2006 South-Western, a part of Cengage Learning Cross Price Elasticity If P X changes, what happens to the demand for Y? Substitutescoke, pepsiP c  D c  B p  + Complements peanut butter, jellyP PB  D PB  D J  - dQ y x P X = e YPx dP x Q Y Y = 5000 – 3000P Y + 200P X + 75I + 60A P Y = 2P X = 2I = 10A = 50 e YPX = 200 x 2 = 400 =.127 3150 3150

36. © 2009, 2006 South-Western, a part of Cengage Learning Income Elasticity of Demand   Income elasticity shows demand sensitivity to changes in income. ε I = ∂Q/Q ÷ ∂I/I.   Normal goods have ε I > 0. Noncyclical normal goods have 0 < ε I < 1, e.g., candy. Cyclical normal goods have ε I > 1, e.g., housing.   Inferior goods have ε I < 0. Very rare.

37. © 2009, 2006 South-Western, a part of Cengage Learning Income Elasticity of Demand © 2009, 2006 South-Western, a part of Cengage Learning If I change what happens to the demand for Y? Normal/Luxury = As I  Y  Inferior Goods = As I  Y  E I = (d Y /d I ) x (I/Y)EI = 75 x (10/3150) = (750/3150) =.24 E I > 0normal E I > 0luxury 0 < e < 0necessity E I < 0normal