Theory of the Consumer and Market Demand

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Theory of the Consumerand Market Demand
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Consumer Theory

• How rational individuals make consumption
  decisions given a limited budget
• remember that consumers make choices to maximize
  utility
• utility is a function of (i.e., depends on) all
  the things the person consumes
• in mathematical form

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• furthermore utility is positively related to each
  X but at a decreasing rate. Why?
• because of the Law of Decreasing Marginal Utility
• marginal utility is the additional utility from
  consuming an additional unit of the good
• as we consume more of a good, the additional
  utility we get from consuming more falls
• in mathematical form

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• Dont worry about this if you dont know calculus!

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• an individuals total utility (U) is a function
  of the quantities of all the goods and services
  he or she consumes
• we can simplify this relationship in a way that
  is particularly useful for graphing in two
  dimensions by letting utility be a function of a
  composite of all the goods and services consumed,
  which we can call wealth

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Total Utility
Total Utility
Utility
1
MU
1
Wealth ()
0
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• Note that marginal utility is the slope of the
  total utility curve
• becomes flatter (smaller in value) as consumption
  increases
• Alternatively, we can graph the utility from the
  consumption of one good, holding all other
  factors constant, like the consumption of other
  goods, tastes, etc.
• note importance of ceteris paribus assumption

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Total Utility from Consumption of Apples
Total Utility
Utility
MU
One apple
MU
One apple
Apples
0
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Indifference Analysis

• Utility curves cannot really be measured and they
  dont tell us anything about choices between
  goods and services
• Consider two goods, say beer and pizza. Holding
  a persons consumption of all other goods
  constant, an indifference curve shows all
  combinations of the two goods that gives this
  person the same utility
• indifference analysis not limited to two goods,
  but for more than two we need calculus and cannot
  visualize what is happening graphically

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• For a given level of utility, there exists a
  UNIQUE indifference curve
• every combination of beer and pizza that lies on
  this indifference curve gives the individual the
  same utility
• note that we dont know how much utility is
  associated with an indifference curve and we
  dont need to know
• Utility cannot be measured, but indifference
  curves can be observed -- thus very useful!

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• A particular combination of beer and pizza will
  give the individual a certain (but unmeasurable)
  level of utility and therefore will lie on an
  indifference curve
• A second combination of beer and pizza will be
  associated with one of three possibilities
• it will be preferred to the first and will thus
  lie on a higher indifference curve, although we
  dont know how much higher
• the first combination will be preferred and so
  the second will lie on a lower indifference curve
• the person will be indifferent between the two
  combinations so the two will lie on the same curve

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Graphing Indifference Curves
Beer
Characteristics of indifference curves --
negative slope -- cannot cross -- convex to
origin because of law of diminishing
marginal utility -- infinitely dense as long
as goods infinitely divisible -- utility rises
as distance from origin rises
U3
U2
U1
0
Pizza
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Make sure slope EVERWHERE negative!
Dont let them cross!
They can be as close as you can make them --
but dont let them touch!
This ones upside down!
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Indifference Analysis ContinuedMarginal Rate of
Substitution

• MRS is the trade-off of one good for another so
  as to maintain the same level of utility
• That is, rate at which one good traded off for
  the other along an indifference curve
• Note that this trade-off rate is a change along
  the vertical axis divided by the resulting change
  along the horizontal axis

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• That is, its rise over run -- MRS is the slope
  of the indifference curve
• Note that the slope changes as we move along an
  indifference curve

Beer
Big rise
Same rise
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Pizza
Small run
Big run
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• Rise over run works fine for straight lines, but
  its too inaccurate for curvy lines
• For indifference curves we need to work with
  tangents
• the slope of a curve at a point on the curve is
  equal to the slope of the tangent at that point
• For a given point on an indifference curve, the
  MRS is the slope of the tangent to that point

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Marginal Rate of Substitution
Beer
MRSX gt MRSY
X
Y
U1
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Pizza
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The Budget Constraint

• Indifference curves say nothing about what an
  individual CAN consume given his or her limited
  resources (budget)
• The budget constraint shows all POSSIBLE
  combinations the person can consume given his or
  her budget

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Graphing the Budget Constraint
Beer
Budget constraint I PBQB PPQP Where I
is income for the period PB and QB are price and
quantity of beer consumed PP and QP are price and
quantity of pizza consumed Rearrange (why?) to
get QB I/PB - (PP/PB) QP
Vertical intercept
Slope
Illustration Say I is 100 and beer is 2. If
he spends all his income on beer, then QP is
zero and QB is fifty beers.
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Pizza
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Budget Constraint and Price and Income Changes

• A change in the price of one good causes the
  budget constraint to swivel
• e.g., if price of beer goes up the vertical
  intercept goes down while the horizontal
  intercept stays the same
• A change in the persons income causes a parallel
  shift
• income rises, curve shifts out
• income falls, curve shifts in

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Graphing Price Changes
Beer
Old budget constraint
New budget constraint after prices of beer rises
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Pizza
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Graphing Income Changes
Beer
New budget constraint after income increases
Old budget constraint before income increases
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Pizza
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Consumer Equilibrium

• Indifference curves represent the utilities
  associated with different combinations of goods
• Budget constraints represent what the consumer
  can buy with a given income or budget
• Putting the two together allows us to show how of
  each good the consumer actually will buy

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Say our consumer is enjoying the
combination represented by point A. Can he do
better? He can trade off beer for more pizza,
moving along his budget constraint. As he does
so, he moves to higher and higher indifference
curves until he reaches point X on curve U2.
Note that U2 is the indifference curve tangent
to the budget constraint. Any further and his
utility starts to fall. Point X represents the
utility maximizing combination of beer and pizza
for this consumer. What is MRS at point X?
Beer
A
X
U3
U2
B
U1
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Pizza
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Characteristics of the Equilibrium

• The slope of the budget constraint is -PP/PB
  (i.e., the negative of the price ratio)
• The slope of an indifference curve at a point is
  the MRS
• At equilibrium, the consumer is at the point on
  an indifference curve that is tangent to the
  budget constraint
• At that point, therefore, MRS equals the negative
  of the price ratio
• because slopes are equal at point of tangency

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Deriving Demand

• This model of consumer equilibrium allows us to
  derive the demand curve
• All we have to do is find equilibrium at
  different prices and then plot the resulting
  price-quantity combinations to get the
  individuals demand
• Add all individuals demands horizontally to get
  market demand

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As the price of pizza falls, the budget
constraint swivels out and more pizza is consumed.
Pp
Beer
Individuals demand curve
A
P1
B
P2
A
B
C
C
P3
U3
U2
U1
0
0
Q3
Q1
Q3
Q1
Q2
Q2
Pizza
Pizza
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P
Market demand is the horizontal sum of the
individual demands
P1
P2
P3
DABC
DC
DA
DB
Pizza
0