Consumer Theory

1
Consumer Theory
2
What is Consumer Theory?

• Study of how people use their limited means to
  make purposeful choices.
• Assumes that consumers understand their choices
  (possibilities) and the prices (opportunity
  costs) associated with each choice.
• Assumes that consumers consider the alternatives
  and choose the one they like best.

3
Consumer Theory - Why?

• Two important reasons
• to understand the foundations of market demand
  (bake the demand curve from scratch)
• to address several interesting consumer theory
  issues that are best understood using this model
  rather than the aggregate demand model

4
Two Components of Consumer Demand

• Opportunities
• What can the consumer afford?
• What are the consumption possibilities?
• Summarized by the budget constraint
• Preferences
• What does the consumer like?
• How much does a consumer like a good?
• Summarized by the utility function

5
What is a Budget Constraint?

• A budget constraint shows the consumers purchase
  opportunities as every combination of two goods
  that can be bought at given prices using a given
  amount of income.
• The budget constraint measures the combinations
  of purchases that a person can afford to make
  with a given amount of monetary income.

6
Lis Demand for Wheat and Rice

• Illustration of consumer theory
• Lis demand for wheat and rice depends upon the
  prices for these goods, her income, and her
  preferences.
• Suppose we look first at her budget constraint
• Wheat costs 4/lb.
• Rice costs 2/lb.
• Li has 40 of income.

7
Lis Budget Constraint

• The mathematical expression for Lis budget
  constraint is I PW W PR R R I/PR - (PW
  / PR)W
• I like to refer to the slope of the budget line
  as the ERSEconomic Rate of Substitution
• In this case it is PW / PR
• For Li PW4 PR2 I40 ERS2

8
Graph of Lis Budget Constraint

• The graph to the right shows a picture of Lis
  budget constraint.

• Each blue diamond is a point from the table.

• The slope is equal to -2, as shown on the last
  slide.

9
Budget Line gymnastics

• An increase in income only.
• An increase in the price of wheat only.
• A decrease in the price of rice only.
• Income doubles as do the prices of wheat and
  rice.
• Note Changes in the price of wheat relative to
  the price of rice will change the ERS.

10
Preferences

• Let R at least as good as
• B0 R B1 means B0 is at least as good as B1
• Let IN indifferent to
• B0 R B1 and B1 R B0 implies B0 IN B1
• Let P strictly preferred to
• B0 R B1 and not B1 R B0 implies B0 P B1

11
Preferences

• Basic assumptions about an individuals
  preferences (R) over bundles (B)
• more is better If B0 has more in it than B1
  then B0 R B1
• transitivity If B0 R B1 and B1 R B2 then B0 R
  B2
• average bundles are at least as good as extreme
  bundles If B0 IN B1 and B2 is an average of
  B0 and B1, then B2 R B0 and B1

12
Utility and Preferences

• Utility is the way economists represent
  preferences.
• Among two bundles, the one with the higher
  utility is the preferred bundle.
• If two bundles have the same utility, we say that
  the consumer is indifferent.

13
Indifference Curves

• Preferences that satisfy the conditions I have
  noted above can be represented by indifference
  curves.
• The set of all indifference curves that describe
  an individuals preferences are referred to as an
  indifference curve map.
• An indifference curve connects all of the bundles
  that a consumer likes equally.
• We will assume only two goods when using
  indifference curve analysis.

14
Indifference Curve Map - Properties

• An indifference curve should not slope up.
• Indifference curves can not cross one another.
• Better bundles are to the northeast.
• Indifference curves will not be bowed out.

15
Lis Preferences in Indifference Curves

• An indifference curve connects all the bundles
  that have the same utility.

• Higher indifference curves indicate more utility
  (IC2 is preferred to IC1).
• Lower indifference curves indicate less utility
  (IC1 is preferred to IC0).
• The indifference curve map is FULL of
  indifference curves.

16
The Marginal Rate of Substitution

• The Marginal Rate of Substitution(MRS) tells us
  how much of one good Li would willingly trade for
  an incremental unit of the other good and remain
  indifferent.
• The MRSslope of the indifference curve at a
  bundle.
• Common to assume the MRS declines as we move down
  an indifference curve.

17
How Much Wheat and Rice

• Lis optimal amount of wheat and rice to consume
  is the amount that maximizes Lis utility subject
  to her budget constraint.
• In the graph...
• Get to the highest indifference curve possible
• Stay on the budget constraint (b/c more is better)

18
How to Find Lis Best Combination

• The black bundle is best.
• The pink bundle is not the best. Li has spent
  all her income but is not on the highest
  indifference curve possible.
• Bundles n/e of IC0 are better and some are
  affordable.
• At (W, R) she is doing the best she can subject
  to her budget constraint.

19
How to Find the Best Combination

• Utility is maximized when
• the indifference curve is just tangent to the
  budget line.
• Utility is maximized when
• you are on the budget line and
• the slope of the indifference curve equals the
  slope of the budget line
• Utility is maximized when
• IncomePRR PWW
• MRSERS

20
The bang per buck story

• Let MUW Lis marginal utility of wheat
• it measures the change in utility as we change
  wheat consumption by an incremental unit while
  holding rice constant
• Let MUR Lis marginal utility of rice
• it measures the change in utility as we change
  rice consumption by an incremental unit while
  holding wheat constant
• Common to assume that marginal utilities decline
  as we increase consumption - the law of
  diminishing marginal utility

21
The bang per buck story

• The MRS MUW / MUR
• The ERS PW / PR
• At an optimal bundle MRSERS
• Rewritten we have
• MUW / MUR PW / PR
• MUW/PW MUR/PR
• bang/buck in wheat bang/buck in rice
• Get same optimal bundle either way

22
Handling a change in PW

• Li wants to achieve the highest indifference
  curve that the budget constraints permit.

• The points A, B, and C represents the best that
  Li can do at prices of 4, 2, and 1 for wheat.
• The equation MRSERS is satisfied at each of the
  points.

23
Lis Demand for Wheat

• The table shows the amount of wheat that Li
  demands at each price.

• These are the points of tangency from the
  previous slide.

24
Graph of Lis Demand for Wheat

• When we connect the points from the table in the
  previous slide we get Lis demand for wheat.

• The points A, B, and C correspond to the
  tangencies of the budget constraint and the
  indifference curves.

25
Lis Best Choice Reconsidered

• Consider the choice at PW2/lb.
• The point B is optimal.
• The point A is feasible but inferior to all
  points on the red budget line between E and F.
• The point C is preferred to B but cannot be
  purchased with Lis 40 income at the given
  prices it is above the red budget line.
• The point E is feasible but Li prefers more wheat
  and less rice (B).
• The point F is feasible but Li prefers less wheat
  and more rice (B, again).
• There is no combination that Li prefers to B that
  she is able to buy.

26
Handling a change in PW

• Li wants to achieve the highest indifference
  curve that the budget constraints permit.

• The points A, B, and C represents the best that
  Li can do at prices of 4, 2, and 1 for wheat.
• The equation MRSERS is satisfied at each of the
  points.

27
Lis Demand for Wheat

• The table shows the amount of wheat that Li
  demands at each price.

• These are the points of tangency from the
  previous slide.

28
Graph of Lis Demand for Wheat

• When we connect the points from the table in the
  previous slide we get Lis demand for wheat.

• The points A, B, and C correspond to the
  tangencies of the budget constraint and the
  indifference curves.

29
From IC Map to Lis Demand for Wheat
30
Income and Substitution Effects

• Economists decompose the effect of a change in
  price on the quantity demanded into an income and
  a substitution effect.
• Income effect due to the increase in real income
  associated with a fall in prices (you can buy
  more with the same nominal income) or the loss of
  real income associated with a rise in prices (you
  cannot buy as much as you once did with the same
  nominal income).
• Substitution effect due to the change in the
  relative price of the good, cheaper goods are
  substituted for more expensive ones.

31
Income and Substitution Effects Price Decline,
X normal

• When the price of a good falls, the quantity
  demanded rises for two reasons.
• The income effect real income is higher because
  the same money income buys more at the lower
  prices. For normal goods, then, the income effect
  of a price fall is positive.
• The substitution effect consumers substitute the
  now cheaper good for ones whose price has not
  fallen, real income held constant. This increase
  in demand is called the substitution effect of a
  price decline.

32
Lis Income and Substitution Effects Price
Fall, Rice normal

• Graph shows the income and substitution effects
  of the fall in the price of wheat from 4/lb. (A)
  to 1/lb. (C).
• The movement from point A to point D is the
  substitution effect Li buys less rice and more
  wheat, and would do so even if she had an income
  of only 20 (as the black budget line shows).
• The movement from point D to point C is the
  income effect, the price decline is like giving
  Li an additional 20 of real income.

33
Lis Substitution Effect

• The substitution effect is the amount by which
  Li's wheat consumption increased holding real
  income constant.
• Substitution effect is the difference between
  Li's consumption of wheat at the new and old
  prices holding her real income constant, that is,
  staying on the same indifference curve (compare
  points A and D).

34
Lis Income Effect

• When the price falls from 4/lb. of wheat to
  1/lb. per wheat, Li is able to buy both more
  wheat and more rice.
• The income effect is the difference between what
  she would have bought on the old indifference
  curve at the lower wheat price (point D) and what
  she actually did buy with her nominal income
  (40) at the lower price (point C).
• Li increases her consumption of wheat and rice
  because of the increase in her real income from
  the price decline.

35
General effect of a price fall
PX falls
Substitution Effect X now looks relatively cheaper
Income effect - you feel richer
X normal
X inferior
Quantity demanded increases
Quantity demanded increases
Quantity demanded decreases
Total effect is the substitution effect AND the
income effect working at the same time.
36
From Individual to Market Demand

• Market demand is the sum of all individual
  demands in the economy.
• In the following example there are two consumers
  of wheat Li and Juanita.
• The market demand, then, is the sum of the
  quantities demand by Li and Juanita.

37
Juanitas Demand for Wheat

• Juanitas income is also 40.
• Juanita faces the same price for rice as Li
  2/lb.
• Her preferences are different from Lis.
• Her demand for wheat is derived in the figure at
  the left.

38
Graph of Juanitas Demand for Wheat

• The points A, B and C correspond to Juanitas
  best choices given her income and the three
  prices of wheat illustrated.
• This is her demand curve for wheat.

39
Market Demand

• The market demand (green) is the sum of Lis
  (blue) and Juanitas (red) demand for wheat at
  each price.
• At PW4, Li demands 6 lbs., Juanita demands 5
  lbs. and the market demand is 11 lbs.
• At PW2, Li and Juanita demand 10 lbs. and the
  market demand is 20 lbs.
• At PW1, Li demands 16 lbs., Juanita demands 18
  lbs. and the market demand is 34 lbs.

40
Application Effect of a Tax Transfer Program

• Suppose I have the preferences illustrated at the
  right.
• Question AIf Income 16If Price of food
  1If Price of shelter 1Food ?Shelter
  ?Indifference curve ?

41
Answer A

• Point AIf Income 16If Price of food 1If
  Price of shelter 1 Food 7Shelter
  9Indifference curve I4

42
Effect of a Tax and Transfer Program Addition of
Tax

• Question BIf Income 16If Price of food
  1If Price of shelter 1 and Tax on shelter
  100 Tax-inclusive price of shelter ? Food
  ?Shelter ?Indifference curve ?

43
Answer B

• Point BIf Income 16If Price of food 1If
  Price of shelter 1 and Tax on shelter 100
  Tax-inclusive price of shelter 2Food
  9Shelter 3.5Indifference curve I2

44
Effect of a Tax and Transfer Program Tax
Transfer

• Question CIf Income 16If Price of food
  1If Price of shelter 1 and Tax on shelter
  100 andTransfer payment 8Food ? Shelter
  ? Indifference curve ?

45
Answer C

• Point CIf Income 16If Price of food 1If
  Price of shelter 1 and Tax on shelter 100
  andTransfer payment 8Food 10Shelter
  7Indifference curve I4

46
Tax and Transfer Systems Give Pure Substitution
Effects

• Notice in the example that the consumer ends up
  on the same indifference curve after the tax and
  transfer program as in the initial choice (I4).
• In public finance (the study of tax and transfer
  systems) this result usually occurs when the tax
  and transfer system is combined with a balanced
  budget.
• In our example, tax receipts are 7 per person (
  7 units of shelter x 1 tax), while the transfer
  is 8 per person. This is as close to balanced
  as we can get and still be able to graph the
  consumers choice legibly.
• Knowledge of the substitution effect of the price
  change induced by the shelter tax is sufficient
  to predict the effect of the complete tax and
  transfer system.

47
Food Stamps vs.

• Suppose the following for the Parker family
• u(F, aog) where aogall other goods
• I200
• PF 2/unit
• Paog 1
• Consider three alternative government policies
• no support
• 200 in food stamps
• 200 in cash

48
Food Stamps vs.

• Notes
• the budget line under the food stamp program is
  the thick black segment and the purple segment
• The budget line with cash is the red and purple
  segments
• the Parkers are indifferent between food stamps
  and cash

aog
200
IC1
IC0
BL0
Food
100
200
49
Food Stamps vs.

• Notes
• the budget line under the food stamp program is
  the thick black segment and the purple segment
• The budget line with cash is the red and purple
  segments
• if this is the case then the Parkers prefer cash
  to food stamps

aog
IC
ICFS
IC0
BL0
Food