Finance 510: Microeconomic Analysis

1. Finance 510: Microeconomic Analysis Consumer Demand Analysis

2. Suppose that you observed the following consumer behavior P(Bananas) = $4/lb. P(Apples) = $2/Lb. Q(Bananas) = 10lbs Q(Apples) = 20lbs Choice A P(Bananas) = $3/lb. P(Apples) = $3/Lb. Q(Bananas) = 15lbs Q(Apples) = 15lbs Choice B What can you say about this consumer? Is strictly preferred to Choice B Choice A How do we know this?

3. Consumers reveal their preferences through their observed choices! Q(Bananas) = 10lbs Q(Apples) = 20lbs Q(Bananas) = 15lbs Q(Apples) = 15lbs P(Bananas) = $4/lb. P(Apples) = $2/Lb. Cost = $80 Cost = $90 P(Bananas) = $3/lb. P(Apples) = $3/Lb. Cost = $90 Cost = $90 B Was chosen even though A was the same price!

4. What about this choice? Choice C Cost = $90 P(Bananas) = $2/lb. P(Apples) = $4/Lb. Q(Bananas) = 25lbs Q(Apples) = 10lbs Q(Bananas) = 15lbs Q(Apples) = 15lbs Cost = $90 Choice B Q(Bananas) = 10lbs Q(Apples) = 20lbs Cost = $100 Choice A Is strictly preferred to Is choice C preferred to choice A? Choice C Choice B

5. Is strictly preferred to Choice B Choice A Is strictly preferred to Choice C Choice B C > B > A Is strictly preferred to Choice C Choice A Rational preferences exhibit transitivity

6. Consumer theory begins with the assumption that every consumer has preferences over various consumer goods. Its usually convenient to represent these preferences with a utility function Set of possible choices “Utility Value”

7. Using the previous example (Recall, C > B > A) Choice A Q(Bananas) = 10lbs Q(Apples) = 20lbs Choice B Q(Bananas) = 15lbs Q(Apples) = 15lbs Choice C Q(Bananas) = 25lbs Q(Apples) = 10lbs

8. We only require a couple restrictions on Utility functions • For any two choices (X and Y), either U(X) > (Y), U(Y) > U(X), or U(X) = U(Y) (i.e. any two choices can be compared) • For choices X, Y, and Z, if U(X) > U(Y), and U(Y) > U(Z), then U(X) > U(Z) (i.e., the is a definitive ranking of choices) • However, we usually add a couple additional restrictions to insure “nice” results • If X > Y, then U(X) > U(Y) (More is always better) • If U(X) = U(Y) then any combination of X and Y is preferred to either X or Y (People prefer moderation to extremes)

9. Suppose we have the following utility function U = 20 Imagine taking a “cross section” at some utility level.

10. The “cross section” is called an indifference curve (various combinations of X and Y that provide the same level of utility) Any two choices can be compared There is a definite ranking of all choices A C B

11. The “cross section” is called an indifference curve (various combinations of X and Y that provide the same level of utility) More is always better! C A B

12. The “cross section” is called an indifference curve (various combinations of X and Y that provide the same level of utility) People Prefer Moderation! A C B

13. The marginal rate of substitution (MRS) measures the amount of Y you are willing to give up in order to acquire a little more of X + = 0 Suppose you are given a little extra of good X. How much Y is needed to return to the original indifference curve?

14. The marginal rate of substitution (MRS) measures the amount of Y you are willing to give up in order to acquire a little more of X + = 0 Now, let the change in X become arbitrarily small

15. The marginal rate of substitution (MRS) measures the amount of Y you are willing to give up in order to acquire a little more of X Marginal Utility of X Marginal Utility of Y

16. The marginal rate of substitution (MRS) measures the amount of Y you are willing to give up in order to acquire a little more of X If you have a lot of X relative to Y, then X is much less valuable than Y MRS is low)!

17. An Example

18. The elasticity of substitution measures the curvature of the indifference curve

19. An Example

20. Consumers solve a constrained maximization – maximize utility subject to an income constraint. As before, set up the lagrangian…

21. First Order Necessary Conditions

25. Suppose that we raise the price of X Can we be sure that demand for x will fall?

26. Suppose that we raise the price of X, but at the same time, increase your income just enough so that your utility is unchanged Substitution effect

27. Now, take that extra income away… Income effect

28. Demand Curves present the same information in a different format D

29. Demand Curves present the same information in a different format

30. Elasticity of Substitution vs. Price Elasticity

31. Perfect Complements vs. Perfect Substitutes (Almost)

33. Suppose that we raise the price of Y… Substitution effect (+) Income effect (-) Net Effect = ????

34. Cross Price Elasticity

35. Income and Substitution effects cancel each other out!!

36. Suppose that we raise Income Substitution effect = 0 Income effect (-)

37. Income Elasticity

39. Willingness to pay Suppose that we have the following demand curve $100 A demand curve tells you the maximum a consumer was willing to pay for every quantity purchased. $50 D 100 For the 100th sale of this product, the maximum anyone was willing to pay was $50

40. Willingness to pay Suppose that we have the following demand curve $100 $75 $50 D 50 100 For the 50th sale of this product, the maximum anyone was willing to pay was $75

41. Consumer Surplus Consumer surplus measures the difference between willingness to pay and actual price paid $100 $75 Whoever purchased the 50th unit of this product earned a consumer surplus of $25 $50 D 50 100 For the 50th sale of this product, the maximum anyone was willing to pay was $75

42. Consumer Surplus Consumer surplus measures the difference between willingness to pay and actual price paid $100 If we add up that surplus over all consumers, we get: CS = (1/2)($100-$50)(100-0)=$2500 $2500 $50 Total Willingness to Pay ($7500) $5000 - Actual Amount Paid ($5000) D Consumer Surplus ($2500) 100

43. A useful tool… In economics, we are often interested in elasticity as a measure of responsiveness (price, income, etc.)

44. Estimating demand curves Given our model of demand as a function of income, and prices, we could specify a demand curve as follows:

45. High Elasticity Linear demand has a constant slope, but a changing elasticity!! Low Elasticity

46. Estimating demand curves We could, instead, use a semi-log equation:

47. Estimating demand curves We could, instead, use a semi-log equation:

48. Estimating demand curves The most common is a log-linear demand curve: Log linear demand curves are not straight lines, but have constant elasticities!

49. If we assumed that this was the maximization problem underlying a demand curve, what form would we use to estimate it?

50. Estimating demand curves Suppose you observed the following data points. Could you estimate the demand curve? D