### Theory of Consumer Choice

```Theory of Consumer Choice
Main Assumption
• Homo-Economus
• The Economic Man
• Assume people are rational and make rational
decisions
• That is, they “maximize” or “minimize”
correctly
Consumer Problem
• Maximize happiness (or utility)
• Constrained by prices in the market and their
budget
• They have some function that describes their
“happiness” or “utility” as an output where
goods they consume are the input
• Similar to a firm producing a good with
various inputs
Budget Constraint
• Limit to two goods for simplicity (easily generalize
to many goods)
• Budget constraint
– Limits the consumption bundles a consumer can
afford
– There is a trade off between consuming one good
(means less of another)
• Slope of the budget constraint
– Rate at which a consumer can give up one good and
– Equals the price ratios of the two goods
– How far out the budget line is reflects income level
Budget Constraint
Quantity of
Good A
10
If spent all money
on good A could
Say Income = \$100
Good B cost \$20
Good A cost \$10
Slope = rise/run = Q of A/Q of B = -10/5 = -2
Slope = -2 = Price B/Price A
So it reflects the trade off b/w A and B
Give up 2 of A for 1 of B
If spent all money
on good B could
5
Quantity of
Good B
Preferences: What You Want
• Tells us what people prefer, what they like
• Can be represented in a curve called an
Indifference Curve
– Shows the consumption bundles that give the
same level of satisfaction/happiness/utility
– All points on the curve have the same utility
– Further out curves are “happier” curves (more is
assumed to be better)
• Slope of the indifference curve
– Rate at which consumers are willing to trade off
b/w two goods and keep same level of utility
– Called Marginal Rate of Substitution
Indifference Curves
Quantity of
Good A
Points A,B,C all have same
happiness/utility level associated
with them b/c they are on the
same Indifference Curve. D and E
have same level also and both are
equally better than A,B or C.
A
D
E
B
MRS
IC2
C
IC1
Quantity of
Good B
Properties of Indifference Curves
• Higher ones are preferred to lower ones
– More is better
• The slope downward
– To stay at the same utility you can’t get more of both,
then you’d be happier
• They never cross
– If they represent happiness/utility levels, then
crossing would imply they had the same happiness
level
• They bow inwardly
– Because of decreasing marginal satisfaction, initial
unit of B is really good, so give up a lot of A, later on
not so much
IC’s Cannot Cross
Quantity of
Good A
Since B is on both IC’s then B makes you
just as happy as A and just as happy as
C. Therefore C must make you just as
happy as A, but this can’t be b/c C has
more of both goods, and more is better.
C
A
B
Quantity of
Good B
Curvature of IC’s
Quantity of
Good A
When you have only a
little of B, its very
valuable and you’ll give a
lot of A up for it in order
to stay just as happy.
MRS is high.
Good A/Good B
Example of diminishing utility
so IC’s bow inward.
Once you have a lot of B its not
as valuable, so you will only
give up a little A for it in order
to stay just as happy. Low MRS.
Good A/Good B
Quantity of
Good B
Extreme IC’s
Perfect Substitutes
Old Dollar Bill
Perfect Compliments
Left Shoe
IC’s are straight lines: MRS
is constant
New Dollar Bill
IC’s are right angled,
more of one gives no
more happiness
without the other
Right Shoe
Optimal Choice
• Given a budget, prices, and a utility function,
what is the best consumption bundle to
choose?
• Budget curve is fixed
• Highest IC that has at least one point on the
budget line
• The point where IC and budget line are
tangent, or just touch.
• Slope of IC equals slope of budget line
• MRS = price ratios
Optimal Consumer Choice
Quantity of
Good A
Utility maximizing point
Can’t afford this utility
level
Can do better than
this level
Quantity of
Good B
Quantity of
Good A
Optimal Consumer Choice II:
Why Tangency
Could afford this point, but could
do better. IC is steeper than
budget curve. So you’re willing to
give up more of A for B than the
market demands. So B is worth
more to you at this point
(relatively) than to the market, so
giving up A and taking more B
makes you better off and you can
still afford it.
So moving here makes you
better off.
Quantity of
Good B
Deriving Demand Curves
• We can use indifference curves to derive our
downward sloping demand curve
• As one price changes (the good whose
demand curve we wish to chart) the intercept
of the budget curve changes
• We find a new optimal point
• Use these points to chart demand curve
– Prices/Quantities demanded
Good
A
Constructing Demand
Curves from IC’s
As price of B falls budget
curve intercept goes out
because could by more if
spent all money on B.
Price of B
P1
Good
B
P2
P3
Quantity B
Applications of IC’s
• Could use to describe purchasing decisions (as
we did here)
• Could use to describe labor/leisure trade off
as wages change (that is labor supply)
• Could use to describe savings rates as interest
rates change
Similarities in Production
• Production decisions have a similar nature to
our consumer choice here
• Instead of indifference curves we call them
Iso-quant curves
– Show trade off b/w two inputs that still produce
the same output
• Instead of budget lines have iso-cost curves
– Show bundles on factor inputs that cost the same
• Leads to the same type of decision
– How do I produce
– Previously we only looked at how much to
produce
```