1. Finance 30210: Managerial Economics
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!
Choice A
Choice B
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 combinations of consumer goods. Its usually convenient to represent these preferences with a utility function
Set of possible consumption 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 require that utility functions satisfy a few basic properties
There is a definite ranking of all choices A C B

9. We require that utility functions satisfy a few basic properties
More is always better! C A B

10. We require that utility functions satisfy a few basic properties
People Prefer Moderation! 15 A C 10 5 B 5 10 15

11. Suppose you are given a little extra of good X
Suppose you are given a little extra of good X. How much Y is needed to return to the original indifference curve?
Marginal Utility of X
Marginal Utility of Y
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

12. 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!

13. The elasticity of substitution measures the curvature of the indifference curve
Elasticity of substitution measures the degree to which your valuation of X depends on your holdings of X

14. The elasticity of substitution measures the curvature of the indifference curve
If the elasticity of substitution is small, then small changes in x and y cause large changes in the MRS
If the elasticity of substitution is large, then large changes in x and y cause small changes in the MRS

15. We often assume that the marginal rate of substitution is dependant only on the ratio of X and Y – i.e. preferences are homogeneous

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

17. First Order Necessary Conditions

19. Demand Curves present the same information in a different format – therefore, all the properties of preferences are present in the demand curve

20. Demand relationships are based off of the theory of consumer choice
Demand relationships are based off of the theory of consumer choice. We can characterize the average consumer by their utility function.
“Utility” is a function of lemonade and hot dogs
Consumers make choices on what to buy that satisfy two criteria:
Their decision on what to buy generates maximum utility
Their decision on what to buy generates is affordable
These decisions can be represented by a demand curve

21. Example: Suppose that you have $10 to spend
Example: Suppose that you have $10 to spend. Hot Dogs cost $4 apiece and glasses of lemonade cost $2 apiece.
# Hot Dogs
MU (Hot Dogs)
# Lemonade
MU (Lemonade) 1 9 4 2 8 3 7
1.5 6 5 .5
This point satisfies both conditions and, hence, is one point of the demand curve

22. The marginal rate of substitution controls the height of the demand curve
Willingness to pay is low $2
$10
Willingness to pay is high

23. Now, suppose that the price of hot dogs rises to $6 (Lemonade still costs $2 and you still have $10 to spend)
# Hot Dogs
MU (Hot Dogs)
# Lemonade
MU (Lemonade) 1 9 4 2 8 3 7
1.5 6 5 .5
You can’t afford what you used to be able to afford – you need to buy less of something! (Income effect)
Your decision at the margin has been affected. You need to buy less hot dogs and more lemonade (Substitution effect)

24. Now, suppose that the price of hot dogs rises to $6 (Lemonade still costs $2 and you still have $10 to spend)
# Hot Dogs
MU (Hot Dogs)
# Lemonade
MU (Lemonade) 1 9 4 2 8 3 7
1.5 6 5 .5
This point satisfies both conditions and, hence, is one point of the demand curve

25. Demand curves slope downwards – this reflects the negative relationship between price and quantity. Elasticity of Demand measures this effect quantitatively
Price
$6.00
$4.00
Quantity 1 2

26. The elasticity of substitution will control the slope of the demand curve

27. Elasticity of Substitution vs. Price Elasticity

28. Perfect Complements vs. Perfect Substitutes
(Almost)

29. Now, suppose that the price of a hot dog is $4, Lemonade costs $2, but you have $20 to spend.
# Hot Dogs
MU (Hot Dogs)
# Lemonade
MU (Lemonade) 1 9 4 2 8 3 7
1.5 6 5 .5
Your decision at the margin is unaffected, but you have some income left over (this is a pure income effect)

30. Now, suppose that the price of a hot dog is $4, Lemonade costs $2, but you have $20 to spend.
# Hot Dogs
MU (Hot Dogs)
# Lemonade
MU (Lemonade) 1 9 4 2 8 3 7
1.5 6 5 .5
This point satisfies both conditions and, hence, is one point of the demand curve

31. For any fixed price, demand (typically) responds positively to increases in income. Income Elasticity measures this effect quantitatively
Price
$4.00
Quantity 2 4

32. Income elasticity measures the response of consumers to changes in income holding prices constant – the homogeneity of preferences will effect this

33. Cross price elasticity refers to the impact on demand of another price changing
Note: These numbers aren’t coming from the previous example!!
Price
$4.00
Quantity 2 6
A positive cross price elasticity refers to a substitute while a negative cross price elasticity refers to a compliment

34. Cross price elasticity measures consumer response to changes in other prices – this is influenced by both homogeneity and elasticity of substitution

35. An Example: Cobb-Douglas Utility

36. An Example: Cobb-Douglas Utility

37. An Example: Cobb-Douglas Utility
With Cobb-Douglas Utility functions, your MRS is directly proportional to your relative consumption of the two goods.

38. An Example: Cobb-Douglas Utility
Cobb-Douglas Utility functions have constant elasticity of substitution

40. Cobb-Douglas demands are independent of other prices!