Endowment and demand
Changing the endowment
Changing prices
Buying and selling:
endowment economy
Intermediate Micro
Lecture 8
Chapters 9 and 10 of Varian
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Labor supply
Consumers as buyers and sellers
I
Develop a better model of income/wealth, m
I
How to understand effects of price change
I
Stick with a 2-good model
Borrowing/saving
Endowment and demand
Changing the endowment
Endowment
I
Where does m come
from?
I
Endowment: Amount
of each good
consumer starts with
(ω1 , ω2 )
I
Income is value of
endowment
I
m = p1 ω1 + p2 ω2
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Demand with endowments
1. Sell off endowment
2. Choose consumption
to maximize utility
maxx1 ,x2 u(x1 , x2 )
s.t.p1 ω1 + p2 ω2 = p1 x1 + p2 x2
Example:
u(x1 , x2 ) = x10.4 x20.7
(ω1 , ω2 ) = (10, 90)
(p1 , p2 ) = (2, 1)
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Demand with endowments
I
Gross demand:
(x1∗ , x2∗ )
I
Net demand:
(x1∗ − ω1 , x2∗ − ω2 )
I
Net demander of
good 1: Consumer for
whom x1∗ − ω1 > 0
I
Net supplier of good
1: Consumer for
whom x1∗ − ω1 < 0
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Change to endowment
Which endowment is
better?
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Change to endowment
1. Sell off endowment
2. Choose consumption
to maximize utility
I
More endowment is
better
I
More generally: New
endowment better if
p1 ∆ω1 + p2 ∆ω2 > 0
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Setup
Next few slides:
I
Net demander of
good 2
I
Net supplier of
good 1
I
Do price changes
make consumer
better off or
worse?
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
↓ p2
Suppose p2 ↓
I
Budget line
steeper
I
Can purchase
more x2 for same
sale of x1
I
Always made
better off
I
Will remain a net
demander of good
2
I
Same effect for
↑ p1
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Small ↓ p1
Suppose p1 ↓ a little,
ie: not enough to make
consumer net
demander of good 1
I
Budget line flatter
I
Can afford less x2
for same sale of x1
I
Always made
worse off (if still
net supplier of
good 1)
I
Same effect for
small ↑ p2
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Labor supply
Large ↓ p1
Suppose p1 ↓ a lot, ie:
enough to make
consumer net
demander of good 1
I
Not possible with
all preferences
I
Budget line flatter
I
May be worse off,
may be better off
I
Same effect for
large ↑ p1
Better off
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Labor supply
Large ↓ p1
Suppose p1 ↓ a lot, ie:
enough to make
consumer net
demander of good 1
I
Not possible with
all preferences
I
Budget line flatter
I
May be worse off,
may be better off
I
Same effect for
large ↑ p1
Worse off
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Labor supply
Borrowing/saving
Typical price offer curve with endowment
I
Goes through
endowment
I
Tangent to IC at
every point
I
Slope at endowment
= − pp12 where
(x1∗ , x2∗ ) = (ω1 , ω2 )
Endowment and demand
Changing the endowment
Changing prices
Labor supply
Borrowing/saving
Typical demand curve with endowment
I
Given p2 , p1notrade
leads consumer to
choose endowment
Endowment and demand
Changing the endowment
Slutsky equation
Effect of ↓ p1
I Book splits
income effect into
I
I
I
Endowment
income effect
(dashed line)
Ordinary
income effect
Don’t worry about
this distinction
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Labor supply
Labor supply
We can now develop a model of labor supply
Does labor supply increase or decrease when wages increase?
I
The returns to work are higher - work more
I
What if you were paid $100k/hour?
Borrowing/saving
Endowment and demand
Changing the endowment
The model
I
2 things traded
I
I
I
Consumers have of
I
I
I
Time
Consumption
L̄ hours to work/relax
Non-work income of M
Prices are
I
I
Work pays w per hour
Consumption costs p
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Labor supply
I
Workers want (goods)
I
I
I
Relaxation R
Consumption C
Endowments
I
I
R̄ = L̄ (24 hours)
C̄ = M
p
Budget
pC + wR = p C̄ + w R̄
Labor supply
Borrowing/saving
Endowment and demand
Labor supply
Changing the endowment
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Income/substitution effects
Effect of ↑ w
I For low w , L
increases
I
I
I
Substitution
effect
R gets more
expensive
For high w , L may
decrease
I
I
Income effect
Want more R
when you can
afford a lot of
C
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Backward-bending labor supply
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Increasing L
How to increase L
I
Want to limit
income effect
I
Keep substitution
effect
I
Suggestion: only
offer high w for
hours above
threshold L∗
I
Looks like
overtime pay
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Progressive tax and L
How do progressive tax
rates compare?
Lower labor supply
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Labor supply
Allocating consumption across time
A consumer lives 2 periods
I Endowment in each period (ω1 , ω2 )
I
In this case, think of ω as $ income
I
Aggregate consumption good for each period (c1 , c2 )
I
Interest rate r for borrowing and saving
No inflation
I
I
I
$1 today buys 1 consumption good today
$1 tomorrow buys 1 consumption good tomorrow
If consumer doesn’t borrow or save:
c1 = ω1 , c2 = ω2
Borrowing/saving
Endowment and demand
Changing the endowment
Saving
I
Suppose consumer
chooses c1 < ω1
I
Saves ω1 − c1
I
Has
ω2 + (1 + r ) ∗ (ω1 − c1 )
to consume in period
2
I
Prices:(p1 = 1, p2 =
1
1+r )
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Borrowing
I
Suppose consumer
chooses c1 > ω1
I
Borrows c1 − ω1
I
Has
ω2 − (1 + r ) ∗ (c1 − ω1 )
to consume in period
2
I
Can not borrow more
than can be repaid
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Labor supply
Borrowing/saving
Present value
1. Sell off endowment
2. Choose consumption to maximize utility
I
How to value endowment?
I
Present value: The value, in period 1 dollars, of the entire
endowment
Earlier periods are given more weight
ω2
PV = ω1 +
1+r
Consumers always prefer an endowment with a higher PV
I
Endowment and demand
Changing the endowment
Changing prices
Labor supply
Present value - more than 2 periods
How to value endowment (ω1 , ω2 , ..., ωT )?
PV (ω1 , ω2 , ..., ωT ) = ω1 +
T
X
t=2
ωt
(1 + r )t−1
If ωt = ω̄, ∀t and there are infinite periods:
PV (ω̄, ω̄, ...) = ω̄ +
∞
X
t=2
1+r
ω̄
=
ω̄
t−1
(1 + r )
r
This is a good approximation for large T , as well
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Labor supply
Present value - more than 2 periods
Present value of multiple endowments:
PV ((ω1 , ω2 ) + (ψ1 , ψ2 )) = PV (ω1 , ω2 ) + PV (ψ1 , ψ2 )
ω2 + ψ 2
= ω1 + ψ1 +
1+r
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Assessing investment projects
Which investments should be undertaken?
I
Treat them like an endowment
I
(Usually) high up-front cost, ω1 << 0
I
Benefits come later, ω2 > 0, ω3 > 0, ...
I
If PV ≥ 0, project will repay loan for costs
Labor supply
Borrowing/saving
Endowment and demand
Project
Changing the endowment
Changing prices
Labor supply
Borrowing/saving
Endowment and demand
Changing the endowment
Changing prices
Labor supply
Examples
(ω1 , ω2 , ω3 ) = (−1000, 500, 550)
r = 0.05
Should the project be carried out?
(ω1 , ω2 , ω3 , ...) = (−2500, 120, 120, 120, ...)
For what values of r will the bank agree to make the loan?
Borrowing/saving