Chapter Nine

1
Chapter Nine

• Buying and Selling

2
Buying and Selling

• In this chapter, allow for consumers to not only
  buy goods but they can sell them as well.
• What determines whether a person is a buyer or
  seller of certain goods?
• How do price changes affect consumption and sales
  decisions?

3
Buying and Selling

• Additional consideration
• When people/firms may sell goods, then price
  changes may affect income or wealth as well.
• The new aspect of the models that we now look at
  is that wealth/income is affected by changes in
  market prices.

4
Buying and Selling

• Three applications of buying and selling models
• Endowment Economies where consumers are endowed
  with a given amount of two goods which they can
  consume or sell.
• Labor Supply where consumers are endowed with an
  initial monetary endowment and time that can be
  used for leisure or for working.
• Intertemporal Choice where consumers are endowed
  with money in two periods and decide whether to
  save or borrow to finance their consumption.
  (Chapter 10)

5
Endowments

• The amount of goods with which a consumer starts
  is his endowment.
• A consumers endowment will be denoted by the
  vector (omega).

6
Endowments

• For Ex.states that the consumer is endowed with
  (starts off with)10 units of good 1 and 2 units
  of good 2.

7
Endowments

• The consumer has the option of just consuming his
  endowment or trading off some of one commodity in
  exchange for more of the other commodity.

8
Net and Gross Demands

• Gross Demands are how much of both commodities a
  consumer actually consumes denoted
• Net Demands are the gross demands minus the
  initial endowments denoted

9
Net and Gross Demands

• Net Demands
• If the net demand for a good is positive, the
  consumer is a net consumer of that good because
  the amount consumed is greater than the
  endowment.
• If the net demand is negative, the consumer is a
  net supplier, because the amount consumed is less
  than the endowment.

10
Net and Gross Demands

• The consumers consumption choice/gross demand
  will depend on preferences and the budget
  constraint.
• Deriving optimal demands/choices will work the
  same way that they did before.
• We just find the consumption bundle where the
  consumer gets on the highest indifference curve
  possible.
• The only modification in this analysis is how to
  correctly construct the budget constraint.

11
Endowment Economy Budget Constraints

• Budget constraints always take the same general
  form
• Total Expenditures Total Income
• p1x1p2x2 Total Income
• What determines total income?
• In endowment economies, income or wealth is
  determined by the market value of your endowment.

12
Endowment Economy Budget Constraints

• E.g.states that the consumer is endowed with 10
  units of good 1 and 2 units of good 2.
• What is the endowments value when p12 and
  p23?
• The endowments value 2(10)3(2)26
• The consumer can afford any consumption bundle
  that does not cost more than 26.

13
Endowment Economy Budget Constraints

• So, given p1 and p2, the budget constraint for a
  consumer with an endowment is

14
Endowment Economy Budget Constraints

• The constraintis
• That is, the sum of the values of a consumers
  net demands is zero.
• Notice the individual cannot be a net consumer
  of both goods.

15
Endowment Economy Budget Constraints

• An individual will be a net consumer of one good
  and a net supplier of the other.

16
Endowment Economy Budget Constraints

• How do we draw the budget constraint?
• We take the endowments as given.
• What is the most of good 1 that the consumer
  could consume?

17
Endowment Economy Budget Constraints

• What is the most of good 1 that the consumer
  could consume?
• If the consumer were to not consume any of good 2
  (x20), then the budget constraint will imply

18
Endowment Economy Budget Constraints

• What is the most of good 2 that the consumer
  could consume?
• If the consumer were to not consume any of good 1
  (x10), then the budget constraint will imply

19
Endowment Economy Budget Constraints

• What is the slope of the budget constraint?

Vertical intercept
slope
20
Endowment Economy Budget Constraints

• Also note that the endowment must always be on
  the budget constraint.
• In this case the consumer does not trade at all,
  but would only consume his endowment.

21
Endowment Economy Budget Constraints
x2
Slope -p1/p2
w2
w1
x1
22
Endowment Economy Budget Constraints
x2
w2
Budget set
w1
x1
23
Example 9.1

• Jack has been endowed with 10 units of good 1 and
  2 units of good 2.
• The price of good 1 is 2 and the price of good 2
  is 3.
• What is the equation for his budget constraint?
• Draw his budget constraint and mark the endowment
  point on your graph.

24
Endowment Economies Gross Demands

• A consumers consumption choice will depend on
  both the budget constraint as well as
  preferences.
• The same general principles apply
• The optimal demands will be where the consumer is
  able to get on the highest indifference curve
  possible, given the budget constraint.

25
Example 9.2

• Mario consumes and grows two goods eggplants (E)
  and tomatoes (T), each measured in pounds.
• Each week his garden yields 10 pounds of tomatoes
  and 30 pounds of eggplants.
• Marios preferences are given by the utility
  function U(T,E) min (T,E)
• The market price of both vegetables is 5 per
  pound.
• What is his budget constraint?
• What is his optimal consumption bundle?
• Is Mario a net seller or consumer of tomatoes.
• Draw.

26
Endowment Economies Changes in Endowments and
Prices.

• We now look at how changes in endowments and or
  prices may affect the budget constraints and
  choices.
• We first focus on the changes on the budget
  constraint.

27
How does the Budget Constraint Change when the
Endowment Changes?

• Suppose that the consumers endowment increased
  in such a way that the market value of his
  endowment increased (holding prices constant)

28
How does the Budget Constraint Change when the
Endowment Changes?
x2
When the endowment increases, such that its
market value goes up, this is just like an
increase in income/wealth.
w2

w2
w1
w1

x1
29
How does the Budget Constraint Change when Prices
Change?

• Suppose that the price of good 1 decreases.
• Then we know that the budget constraint will
  become flatter since the slope is p1/p2.

30
How does the Budget Constraint Change when Prices
Change?

• However, this will also affect the value of the
  endowment, so the intercepts will change.
• The maximum amount of good 1 that the consumer
  can buy will increase when p1 goes down. Recall
  if x20

31
How does the Budget Constraint Change when Prices
Change?

• The maximum amount of good 2 that the consumer
  can buy will decrease when p1 goes down. Recall
  if x10

32
How does the Budget Constraint Change when Prices
Change?

• The new budget constraint must still go through
  the endowment
• Therefore, the new budget constraint, will swivel
  around the endowment, becoming flatter.

33
How does the Budget Constraint Change when p1
Decreases?
p1ltp1
x2
w2
w1
x1
34
How does the Budget Constraint Change when p1
Decreases?
The endowment point is always on the budget
constraint.
x2
So price changes pivot theconstraint about the
endowment point.
w2
w1
x1
35
Example 9.3

• Jack has been endowed with 10 units of good 1 and
  2 units of good 2.
• The price of good 1 was 2 and the price of good
  2 was 3.
• Suddenly, the price of good 1 goes to 1. Draw
  the new and old budget constraints marking the
  endowment point.

36
Buyers or Sellers? Revealed Preference

• We can sometimes use the concept of revealed
  preference to see how price changes affect a
  consumers choice to be a buyer or seller.
• Assume monotonicity and strict convexity of
  preferences.

37
Example 9.4 Buyers or Sellers?
Suppose the consumer starts off being a net
supplier of good 1 and a net consumer of good 2.
x2
Original consumption choice
x2
w2
x1
w1
x1
38
Example 9.4 Buyers or Sellers?
The price of good 1 drops.
x2
In this case, will the consumer remain a net
supplier of good 1?
x2
If the consumer does remain a supplier of good 1,
will she be worse off?
w2
x1
w1
x1
39
Example 9.4 Buyers or Sellers?
The price of good 1 drops.
x2
Will the consumer remain a net supplier of good
1?
x2
Revealed preference will not tell us anything
about what the consumer will consume, because
the old bundle is no longer
affordable.
w2
x1
w1
x1
40
Example 9.4 Buyers or Sellers?
The price of good 1 drops.
x2
The consumer may be a net buyer or seller of
good 1. Good 1 has become cheaper, so this makes
her want to substitute good 1 for good 2 in
consumption. On the other hand, her wealth
has decreased making her
consume less of both goods.

x2
w2
x1
w1
x1
41
Example 9.4 Buyers or Sellers?
The price of good 1 drops.
x2
If the consumer does remain a supplier of good 1,
will she be worse off? If she remains a net
seller of good 1, she must be on a lower
indifference curve.
Intuitively, this is because the
value of her sales of x1 have
gone down.
x2
w2
x1
w1
x1
42
Example 9.5 Buyers or Sellers?
Suppose the individual starts off being a net
supplier of good 2 and a net consumer of good 1.
x2
w2
Original consumption choice
x2
x1
w1
x1
43
Example 9.5 Buyers or Sellers?
The price of good 1 drops. Will she remain a net
buyer of good 1? Is she worse off or better off?
x2
w2
x2
x1
w1
x1
44
Example 9.5 Buyers or Sellers?
Will she remain a net buyer of good 1? In this
case revealed preference tells us that she will
for sure remain a net buyer.
x2
w2
x2
x1
w1
x1
45
Example 9.5 Buyers or Sellers?
Is she worse off or better off? Since here old
consumption bundle is still affordable, but she
does not choose it, she must be better off.

x2
w2
x2
x1
w1
x1
46
Slutskys Equation Revisited

• Slutsky Before changes to demands caused by a
  price change (holding income and prices of other
  goods constant) are the sum of
• a pure substitution effect, and
• an income effect.
• However now, price changes affect the actual
  amount of wealth/income. We have an additional
  affect.
• How does this modify Slutskys equation?

47
Slutskys Equation Revisited

• A change in p1 or p2 changes
• There will be an additional income effect, called
  the endowment income effect.

48
Slutskys Equation Revisited

• Slutskys decomposition will thus have three
  components
• a pure substitution effect
• an (ordinary) income effect (change in purchasing
  power)
• An endowment effect (change in value of
  endowment).

49
Slutskys Equation Revisited
Overall change in demand caused by achange in
price is the sum of (i) a pure substitution
effect (ii) an ordinary income effect (iii) an
endowment income effect
50
Example 9.6 Slutskys Equation Revisited

• Example In an endowment economy, can we say for
  sure how the demand for x1 will change if the
  price of good 1 increases even if we assume x1 is
  normal?
• (i) a pure substitution effect
• X1 will decrease
• (ii) an ordinary income effect (purchasing power
  decreases)
• X1 will decrease since normal
• (iii) an endowment income effect
• The value of the endowment increases.
• X1 will increase since normal.
• Overall effect is ambiguous.

51
Example 9.6 Slutskys Equation Revisited

• This implies that we can get a good that looks
  like a Giffen good even when the good is normal.
• This occurs when the endowment effect outweighs
  the substitution and ordinary income effects.
• Example Why might potato farmers increase their
  consumption of potatoes when the price of
  potatoes rises?
• It could be because potatoes are inferior goods
  or they might still be normal but the endowment
  effect increased the value of their wealth so
  much that farmers increased consumption of them.

52
Labor Supply

• We can also use the idea of an endowment to
  analyze a consumers labor supply decision.
• In this application, we assume that individuals
  are given a certain amount of time from which
  they choose to work or to enjoy leisure.
• Leisure is a good, but also consumers need to
  work to buy other consumption goods.
• Therefore, there is tradeoff between leisure and
  consumption of other goods.

53
Labor Supply

• Notation
• T Hours available to spend between work or
  leisure
• R Leisure hours
• L Labor hours
• Time Constraint RLT
• C Expenditures consumption goods
• U(C,R) Consumers get utility from leisure and
  consumption goods.
• PcPrice of Consumption Goods
• m Money income that consumer is endowed with.
• w hourly wage rate.

54
Labor Supply Budget Constraint

• Budget Constraint
• Total Expenditures on Consumption Goods Total
  Income/Wealth
• PCCm wL
• Since LT-R, then
• PCCm w(T-R) or
• PCCwR m wT

55
Labor Supply Budget Constraint

• BC PCCwR m wT
• Notice that the price of leisure is the hourly
  wage (the opportunity cost of not working).
• We now draw the budget constraint with R
  (leisure) on one axis and C (consumption) on the
  other.
• Assume Pc1

56
Labor Supply Budget Constraint
C
If the individual does not work at all (RT)
then the most C that he could buy is m/Pcm/1m.
m
T
R
Pc1 Budget Constraint CwR m wT
57
Labor Supply Budget Constraint
¾
C
If the individual, works the maximum amount of
hours (R0), then he can buy
m
R
T
Pc1 Budget Constraint CwR m wT
58
Labor Supply Budget Constraint
¾
C
¾
slope -w
m
R
T
59
Labor Supply Optimal Demands

• Again, the consumer wants to get on the highest
  indifference curve possible given the budget
  constraint.
• Therefore, we solve for the optimal demands the
  same way we did before.
• Suppose that preferences were Cobb-Douglas.

60
Labor Supply
¾
C
¾
Optimal demands for leisure and C.
C
endowment
m
R
R
T
leisuredemanded
laborsupplied
61
Example 9.7 Labor Supply

• Fred gets utility from consumption goods (C) and
  leisure (R).
• U(R,C)RC
• Fred has 50 of non-wage income per week.
• The most time he has available for work or
  leisure is 50 hours per week.
• If he works he can earn a wage of 5 an hour.
• Assume the PC1.
• Find Freds budget constraint.
• How much does Fred consume of C and R? How much
  does he work?
• Draw.