Chapter%20Nine

1
Chapter Nine

• Buying and Selling

2
Buying and Selling

• Trade involves exchange -- when something is
  bought something else must be sold.
• What will be bought? What will be sold?
• Who will be a buyer? Who will be a seller?

3
Buying and Selling

• And how are incomes generated?
• How does the value of income depend upon
  commodity prices?
• How can we put all this together to explain
  better how price changes affect demands?

4
Endowments

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

5
Endowments

• E.g.states that the consumer is endowed with 10
  units of good 1 and 2 units of good 2.

6
Endowments

• 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?
• For which consumption bundles may it be exchanged?

7
Endowments

• p12 and p23 so the value of the endowment
  is
• Q For which consumption bundles may the
  endowment be exchanged?

8
Budget Constraints Revisited

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

9
Budget Constraints Revisited
x2
w2
w1
x1
10
Budget Constraints Revisited
x2
w2
Budget set
w1
x1
11
Budget Constraints Revisited
x2
w2
w1
x1
12
Budget Constraints Revisited
x2
w2
Budget set
w1
x1
13
Budget Constraints Revisited
The endowment point is always on the budget
constraint.
x2
w2
w1
x1
14
Budget Constraints Revisited
The endowment point is always on the budget
constraint.
x2
So price changes pivot theconstraint about the
endowment point.
w2
w1
x1
15
Budget Constraints Revisited

• The constraintis
• That is, the sum of the values of a consumers
  net demands is zero.

16
Net Demands

• Suppose and
  p12, p23. Then the constraint is
• If the consumer demands (x1,x2) (7,4), then 3
  good 1 units exchange for 2 good 2 units. Net
  demands are x1- w1 7-10 -3 andx2- w2 4
  - 2 2.

17
Net Demands
p12, p23, x1-w1 -3 and x2-w2 2 so
The purchase of 2 extra good 2 units at 3 each
is funded by giving up 3 good 1 units at 2
each.
18
Example 1

• Chris has the utility function U(a b) ab, his
  endowment is (?a, ?b) (100, 200).
• Prices are pa 1 oraz pb 2.
• Find his gross and net demand for good A and B.

19
Net Demands
x2
At prices (p1,p2) the consumersells units of
good 1 to acquiremore units of good 2.
x2
w2
x1
w1
x1
20
Net Demands
x2
At prices (p1,p2) the consumersells units of
good 2 to acquiremore of good 1.
w2
x2
w1
x1
x1
21
Net Demands
x2
At prices (p1,p2) the consumerconsumes her
endowment netdemands are all zero.
x2w2
x1w1
x1
22
Net Demands
x2
Price-offer curve contains all theutility-maximiz
ing gross demands for which the endowment can be
exchanged.
w2
w1
x1
23
Net Demands
x2
Price-offer curve
Sell good 1, buy good 2
w2
w1
x1
24
Net Demands
x2
Price-offer curve
Buy good 1, sell good 2
w2
w1
x1
25
Labor Supply

• A worker is endowed with m of nonlabor income
  and R hours of time which can be used for labor
  or leisure. w (R,m).
• Consumption goods price is pc.
• w is the wage rate.

¾
¾
26
Labor Supply

• The workers budget constraint iswhere C, R
  denote gross demands for the consumption good and
  for leisure. That is

¾
¾


endowment value
expenditure
27
Labor Supply
¾
rearranges to
¾
28
Labor Supply
()
C
endowment
m
¾
R
R
29
Labor Supply
¾
C
endowment
m
¾
R
R
30
Labor Supply
¾
C
¾
endowment
m
¾
R
R
31
Labor Supply
¾
C
¾
slope , the real wage rate
endowment
m
¾
R
R
32
Labor Supply
¾
C
¾
C
endowment
m
¾
R
R
R
leisuredemanded
laborsupplied
33
Real wage labor suply relation
34
Slutskys Equation Revisited

• Slutsky changes to demands caused by a price
  change are the sum of
• a pure substitution effect, and
• an income effect.
• This assumed that income y did not change as
  prices changed. But does change with price.
  How does this modify Slutskys equation?

35
Slutskys Equation Revisited

• A change in p1 or p2 changes
  so there will bean additional
  income effect, called the endowment income
  effect.
• Slutskys decomposition will thus have three
  components
• a pure substitution effect
• an (ordinary) income effect, and
• an endowment income effect.

36
Slutskys Equation Revisited
x2
Initial prices are (p1,p2).
x2
w2
w1
x1
x1
37
Slutskys Equation Revisited
x2
Initial prices are (p1,p2).Final prices are
(p1,p2).
x2
w2
x2
w1
x1
x1
x1
38
Slutskys Equation Revisited
x2
Initial prices are (p1,p2).Final prices are
(p1,p2).
How is the change in demandfrom (x1,x2) to
(x1,x2) explained?
x2
w2
x2
w1
x1
x1
x1
39
Slutskys Equation Revisited
x2
Initial prices are (p1,p2).
x2
w2
w1
x1
x1
40
Slutskys Equation Revisited
x2
Initial prices are (p1,p2).Final prices are
(p1,p2).
x2
w2
x2
w1
x1
x1
x1
41
Slutskys Equation Revisited
Þ
x2
Pure substitution effect
w2
w1
x1
42
Slutskys Equation Revisited
Þ
x2
Pure substitution effect
w2
w1
x1
43
Slutskys Equation Revisited
Þ
x2
Pure substitution effect
Þ
Ordinary income effect
w2
w1
x1
44
Slutskys Equation Revisited
Þ
x2
Pure substitution effect
Þ
Ordinary income effect
w2
w1
x1
45
Slutskys Equation Revisited
Þ
x2
Pure substitution effect
Þ
Ordinary income effect
Þ
Endowment income effect
w2
w1
x1
46
Slutskys Equation Revisited
Þ
x2
Pure substitution effect
Þ
Ordinary income effect
Þ
Endowment income effect
w2
w1
x1
47
Example 2
The demand function for milk is X110
m/10p1 Endowment w 40 L P0 3 zl/l Price
falls to P1 2 zl/l Find pure substitution
effect, ordinary income effect, endowment
income effect.
48
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
49
Slutsky equation - revisited
50
Slutsky equation - revisited
51
Slutsky equation - revisited
52
Labour market