1. Utility Maximization Lecture 13
Dr. Jennifer P. Wissink
©2019 Jennifer P. Wissink, all rights reserved.
March 11, 2019

2. Why Bother with Consumer Theory?
The “Market Demand Function & Curve” for a single good aggregates and summarizes all market consumers’ intended purchases.
“Consumer Theory” allows us to build a model from scratch to:
Goal 1: Build the market demand from its core “ingredients.”
Goal 2: Use the consumer theory model to address issues not adequately explained via reference to the summarized and aggregated model.

3. Consumer Theory Goal #1 Build the Market Demand
We are going to study the demand for two goods (beans and carrots) using two different consumers (Maryclaire and Katie).
For each good and each consumer, the theory produces a demand function:
Demand function for beans: Bi = fB(PB, PC, I) i=Maryclaire, Katie
Demand function for carrots: Ci = fC(PB, PC, I) i=Maryclaire, Katie
where PB is the price of beans, PC is the price of carrots, and I is the consumer i’s income.
When we properly aggregate the two consumers’ demand equations we get the market demand equations, one for beans and one for carrots.

4. Two Components of Consumer Demand
Opportunities:
What can the consumer afford?
What are the consumption possibilities?
Summarized by the budget constraint and budget line
Preferences:
What does the consumer like?
How much does a consumer like a good?
How would a consumer willingly trade off one good for another?
Summarized by preferences, indifference curve maps and the utility function
Interesting NPR Piece on “habit formation”!
How You Can Harness The Power Of Habit

5. What is a Budget Set and a Budget Line?
A budget set shows the consumer’s purchase opportunities as every combination of two goods that can be bought at given prices using up a given amount of income.
A budget line is the boundary of the budget set.

6. Maryclaire’s Budget Set & Budget Line
Suppose the following:
Income = $40
Price of Carrots = $2/lb
Price of Beans = $4/lb
MC’s Budget Set:
MC’s Budget Line:
Let the│slope│of the budget line be the Economic Rate of Substitution (ERS)
The ERS = 2 in this example (since we chose to put Beans on the horizontal and Carrots on the vertical).
Note: if you had put Beans on the vertical and Carrots on the horizontal, then the ERS = 1/2

7. i>clicker question
How will Maryclaire’s budget line change if just her income increases?
It will get steeper.
It will shift in parallel to itself.
It will get flatter.
It will shift out parallel to itself.
It will not change. C 20 10 B

8. i>clicker question
How will Maryclaire’s budget line change if just the PC increases?
It will get steeper.
It will shift in parallel to itself.
It will get flatter.
It will shift out parallel to itself.
It will not change. C 20 10 B

9. i>clicker question
How will Maryclaire’s budget line change if just the PB decreases?
It will get steeper.
It will shift in parallel to itself.
It will get flatter.
It will shift out parallel to itself.
It will not change since the prices did not change. C 20 10 B

10. i>clicker question
How will Maryclaire’s budget line change if her income stays the same and both the price of beans and the price of carrots double?
It will get steeper.
It will shift in parallel to itself.
It will get flatter.
It will shift out parallel to itself.
It will not change since the prices did not change. C 20 10 B

11. More Budget Line Gymnastics… Quantity Discounts20 10 B

12. Now Onto The Consumer’s Preferences that is…Maryclaire’s Preferences
How can we model what you like?

13. Preferences Defined
A bundle of goods, G, specifies exact quantities of all the possible goods and services a consumer cares about.
Assume Maryclaire has preferences over all the possible bundles that could be assembled with Beans and Carrots.
How can we define her preferences?
With an “at least as good as” operator.
Let R = “at least as good as”
G0 R G1 means bundle G0 is “at least as good as” bundle G1 .
Now let I = “indifferent to”
G0 I G1 means bundle G0 is “indifferent to” bundle G1 .
And let P = “strictly preferred to”
G0 P G1 means bundle G0 is “strictly preferred to” bundle G1 .

14. Assumptions on the Consumer’s (Maryclaire’s) “at least as good as” Operator
A1: She feels more is at least as good as less (monotonicity)
If Y has more of at least one good than X (and no less of any other good), then Y R X
If Y has more of ALL goods, then let’s agree that we will say Y is actually better than X, so then Y P X
A2: She is rational (transitivity)
If X R Y and Y R Z, then X R Z
A3: She feels that average bundles are at least as good as extreme bundles (convexity)
If X I Y and Z is an “average” of X and Y, then Z R X and Z R Y C B C B

15. From Preferences (at least as good as) to Indifference Curve Maps
An indifference curve connects bundles that a consumer likes equally.
An indifference curve map contains ALL the consumer’s indifference curves.
The indifference curve map for someone with nicely behaved preferences has 5 properties.
(P1) Every bundle lives on some indifference curve.
(P2) Indifference Curves never slope “up”.
(P3) Better bundles are on indifference curves to the “north-east”.
(P4) Indifference Curves never cross each other.
(P5) Indifference Curves never “bow-out”, they either are linear or “bowed-in”.

16. Maryclaire’s Preferences Represented via Indifference Curves
These 3 indifference curves describe a part of Maryclaire’s preferences.
Points on IC2 are preferred to points on IC1.
Points on IC1 are preferred to points on IC0.

17. Maryclaire’s Marginal Rates of Substitution
At any given bundle, the Marginal Rate of Substitution (MRS) tells us how much of one good Maryclaire would willingly trade for an extra unit of the other good and remain indifferent.
Her MRS equals the absolute value of the slope of the indifference curve at a bundle.
Her MRS declines as we move down any indifference curve.