Model of Consumer Behavior

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Model of Consumer Behavior

• Lecture 3

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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)

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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
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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.

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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
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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.

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One Change at a Time

• Original Budget Constraint
• What if?
• M increases
• M decreases
• PF increases
• PF decreases
• PC increases
• PC decreases

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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

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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

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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
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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
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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
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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
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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
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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
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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
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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

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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
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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
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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
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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
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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

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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?