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Model of Consumer Behavior

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Title: Model of Consumer Behavior


1
Model of Consumer Behavior
  • Lecture 3

2
Todays Lecture
  • Budget Constraint (what I can purchase)
  • Preferences (what I would like to purchase)
  • Conditions for maximizing personal well-being
    from consumption allocation choices (pursuing
    ones self-interest)

3
Picturing Consumption Choices
  • Real quantities of the goods are on the axis.
    Not dollar values!
  • In this diagram, I have two goods and the
    individual is making a choice between the two
    goods
  • A point in the picture, represents a consumption
    choice -- a combination of food and clothing.
    This is called a consumption bundle

CA
FA
4
Alternative Graph
  • Still real quantities not dollar values
  • In this diagram, I have two goods and the
    individual is making a choice of how much to
    spend on Food out of their total budget. We will
    normalize the price of All Other Goods to be 1
    -- what every a dollar will buy.
  • All other Goods is often called a Composite
    Good
  • Use this graph set up when analyzing one good and
    you are not worried in particular about other
    goods

All Other Goods
OA
Food
FA
5
Limits on Choice
  • Scarcity enters the model via the total amount of
    money you have to spend on the goods. Typically
    this is your income but it could represent the
    budget you have set for spending on the goods.
  • Let M denote your Money Income -- how many
    dollars you have available to spend on food and
    clothing.
  • Let us assume the current price ( per unit of
    the good) of food and clothing are PF and PC
    respectively. Then the feasible set of
    consumption must satisfy the following
    relationship
  • PF F PC C M
  • Where F and C are the real units of food and
    clothing respectively. The Budget Constraint
    is the above relationship with in place of
    . The budget constraint reflects the
    maximum of combinations of goods (bundles)
    possible to consume.

6
Graphing the Budget Constraint
  • The Budget Constraint
  • PF F PC C M
  • To graph, first rewrite so C is expressed an
    explicit function of food and the other
    parameters (prices and money income)
  • C (M/PC) - (PF/PC) F
  • Maximum C or Y Intercept (F0) M/PC
  • Maximum F or X Intercept (C0) M/PF
  • Slope ?C/?F - PF/PC
  • Budget Constraint and Shaded Area are all
    feasible consumption bundles

Clothing
Food
7
Slopes
  • Economists have a nasty habit of dropping the
    negative sign of slopes when they know it is
    negative. If we dont know the sign then we keep
    track of the sign. This is very annoying but it
    is the custom.
  • Case in point is the slope of the budget
    constraint. Since we know it is negative, we
    will drop the sign and think just the relative
    prices (PF/PC) so when the price of food falls
    relative to the price of clothing then the slope
    of the budget constraint becomes flatter --
    Food has gotten relatively cheaper. The term
    relative is important. For example, what if food
    prices rose by 5 but clothing prices rose by
    10. The price of food is higher but it is
    relatively cheaper compared to clothing.
  • The slope of the budget constraint (PF/PC) is the
    opportunity cost of food in terms of clothing.

8
One Change at a Time
  • Original Budget Constraint
  • What if?
  • M increases
  • M decreases
  • PF increases
  • PF decreases
  • PC increases
  • PC decreases

9
Multiple Changes
  • Original Budget Constraint
  • What if?
  • M increases by 10 and PF and PC both increase by
    20
  • M increases by 10,PF increases by 10 and PC
    increases by 20
  • M increases by 10 and PF and PC both increase by
    10

10
Non Linear Budget Constraints
  • Phone Calling Plans
  • Plan 1 pay 4 per minute
  • Plan 2 Pay 50 for 1,000 Minutes then 2 per
    minute for minutes in excess of 1,000
  • Note Price of all other goods is 1

11
Preference Ordering
  • We will assume that individuals know what they
    like and what they dont like.
  • Operationally we will interpret this assumption
    as the individual will always be able to compare
    consumption bundles and tell us whether they
    prefer one bundle to the other or they are
    indifferent between the two bundles. This can be
    written as
  • x P y
  • y P x
  • x I y
  • Where P denotes Preferred to and I denotes is
    Indifferent to. Note we have assumed there is a
    Utility Function but we will assume that there
    exists a function that can represent this
    preference ordering.

Clothing
x
y
Food
12
Assumptions about the Preference Ordering
  • Completeness for all consumption bundles it
    must be the case that either x P y, or y P x, or
    x I y.
  • Reflexive if x P y then y P x.
  • Transitive if x P y and y P z then x P z
  • More is Preferred to Less if w contains more of
    all goods compared to x then w P x
  • The Set of Preferred Consumption is Convex Let
    Sx all v such that v P x then Sx must be
    convex

Clothing
Food
13
Indifference Curves
  • Consider all the consumption bundles that are
    indifferent to x -- picture them in the figure.
    For example, assume x I y. These bundles form
    what is called Indifference Curve, there is not
    a unique curve but through any bundle there must
    be an indifference curve.
  • The indifference curve divides up all the three
    consumption bundles into three sets
  • all z such that x P z
  • all y such that x I y
  • all v such that v P x
  • We have shown the indifference curve sloping
    downward but could it be upward sloping (through
    v)?
  • No it cant because it would violate the
    assumption of more is preferred to less.

Clothing
Food
14
More On Convexity Assumption
  • Given our downward sloping Indifference Curve, it
    divides up all the three consumption bundles
    into three sets
  • all z such that x P z
  • all y such that x I y
  • all v such that v P x
  • The last set is Sx. Take another bundle in Sx
    such as w then convex implies that a convex
    combination of v and w (see connecting line) will
    be preferred to x (be in the set Sx)

Clothing
Food
15
Violation of Convexity Assumption
  • Draw an indifference curve through bundle x that
    is bowed outward from the origin.
  • Now pick two bundles that are preferred to x (w
    and v) and examine all the convex combinations of
    w and v.
  • Note that some of the convex combinations (such
    as z) are not preferred to x or in other words x
    P z.
  • Convex of preferences implies the indifference
    curves must be bowed inward toward the origin.
    But does this assumption make sense when we think
    of individuals?

Clothing
Food
16
Diminishing MRCS
  • Let us begin with a consumption bundle x and
    another bundle y that is indifferent to x. To
    move from x to y requires the individual to give
    up clothing for a given amount of food. Since the
    x I y, the red distance represents the maximum
    amount of clothing they are willing to trade for
    the black amount of food.
  • The trading rate is denoted as the Marginal Rate
    of Commodity Substitution
  • MRCS ?C/?F
  • Now consider another equal increase in food, note
    the individual is willing to give less clothing
    -- Diminishing MRCS
  • Convexity of Preferences implies Diminishing MRCS

Clothing
Food
17
MRCS Slope of Indifference Curve
  • Instead of discrete changes, economists speak of
    trading rates in terms of marginal changes. In
    other words, we will denote the slope of the
    indifference curve as the MRCS.
  • This assumption means as we get more of a good
    then we would be willing to give less of other
    consumption to get even more of the good.
  • Since we know the slope of the indifference curve
    will always be negative, we will refer to the
    slope in terms of the absolute value of the slope

Clothing
y
Food
18
Utility and Indifference Curves
  • If an individual has a preference ordering that
    is complete, reflexive, transitive, more is
    preferred to less and where preferences sets are
    convex, can we represent their preferences with a
    utility function,
  • U U(F,C)?
  • The answer is yes! Indifference curves represent
    combinations of food and clothing yielding the
    same utility. By the Implicit Function Theorem

19
Reflections of Preferences
X provides no pleasure
X is a nuisance (bad)
X and Y are absolutely identical
I must consume X and Y in fixed proportions
20
Is any feasible consumption my best choice?
  • Let us assume the individual has M dollars of
    income to devote to Food and Clothing. When he
    faces the market prices, their budget constraint
    is shown in the graph.
  • Now let us assume the individual picks a bundle
    on the budget constraint, X
  • Would they choose one above? Not feasible
  • One below? No, more is preferred to less
  • How can we determine whether this choice of X
    makes the individual as best off as possible? Is
    there another feasible bundle that is preferred?

Clothing
Food
21
Can I Improve my well being?
  • The relative prices (PF/PC) reflects how others
    are willing to trade clothing for food, but what
    is my willingness to trade?
  • It is the MRCS at X -- the slope of the
    indifference curve through bundle X.
  • If my willingness to trade clothing for food
    (MRCS) exceeds the rate what others are wiling to
    trade (PF/PC) I can make myself better off by
    buying less clothing and more food.
  • Example
  • (PF/PC) 2 and MRCS 4
  • I would willing to give up to 4 units of clothing
    to get 1 unit of food but I only have to give up
    2 units of clothing

Clothing
Food
22
Next Move
  • I would move along the budget constraint buying
    more food and less clothing -- bundle Y
  • Note my change in consumption doesnt change the
    relative prices (M is assumed to be constant)
  • Now I ask the same question again, what is my
    willingness to trade? Given that I am consuming
    less clothing and more food, my MRCS must fall
  • Example
  • PF/PC 2 and MRCS 3
  • Continue to buy more food and less clothing
  • This process could continue until
  • MRCS PF/PC

Clothing
Food
23
Rules for optimal consumption allocation
  • Equate your willingness to trade to the rate that
    others are willing to trade
  • Equate the Marginal Utility per Dollar spent on
    goods

24
For the Next Lecture
  • Read Chapter 4
  • Consider the following questions
  • If you are given vouchers that can only be spent
    on food, will you spend more food? Will you
    spend more on food using your own money?
  • Assume the price of food rises, will you purchase
    less food? Will your total dollar spending on
    food rise?
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