Earnings plus Money
W0
M
c
T
P
P
A
0
R0
Topic 7 Econ 203:
The choice between consumption
and leisure revisited:
The Slutsky formulation
Reading: Varian Chapter 9
pages 166-171 and 174-175
Earnings plus Money
U1
W1
M
c T
P
P
But the reward for
work also rises
W0
M
c
T
P
P
A
0
RA
Earnings plus Money
U0
W1
M
c T
P
P
U1
U2
W0
M
T
P
P
D
B
A
C
0
RC
RA
RB RD
Now we have a substitution effect from A to B,
causing the number of hours of leisure to fall
from RA to RB
Next we have an income effect from B to C,
causing the number of hours of leisure to fall
from RB to RC
Finally we have an ENDOWMENT effect from C
to D,
causing the number of hours of leisure to rise
from RC to RD
• Remember that we usually assume that leisure is a
normal good. The rise in the price of leisure
causes us to buy less of it (from RA to RB).
•
• A rise in the price of any good makes us poorer,
and since ‘real income’ is lower (ignoring the
endowment effect) we buy less leisure (the fall
from RB to RC ).
•
• But now if we take account of the endowment
effect our total income has risen, since for every
hour of work we actually do, our pay has
increased, and so we will consume more leisure
(the move from RC to RD).
•
Terminology:
•
•
•
•
•
•
•
•
I is Income
M is Money or unearned income
W is the nominal wage rate, (w real wage)
P is the price level
T is the total number of hours in the day
R is the number of hours of leisure taken
L is the hours od work done.
c is our actual or real consumption of goods
The Endowment Slutsky Effect
Our consumption of Leisure depends on its price R
and our overall level of Wealth. We are endowed
with M amount of Money and T units of Time. So
our Wealth (I) is:
I = M +WT = Pc+WR
or
c = (T-R)W/P +M/P
which in real terms
implies that
c = (T-R)w +m,
where w is the real wage rate and m is real money
balances
The Endowment Slutsky Effect
So R depends on w and I which is also a function of
w.
That is R[W, I(W)]
So
_
 R[W , I (W )]  R[W , I ]  R   I 




W
W
 I  W 
But if we differentiate I=M +WT with respect to W
we get T
_
 R[W , I (W )]  R[W , I ]  R


T
W
W
I
What about the first term on the RHS?
It is the change in R when Income cannot change
-that is, it’s the usual Slutsky effect
_
 R[W , I ]  R
R

R
W
W
I
S
The Endowment Slutsky Effect
 R[W , I (W )]

W
R

T
I
The Endowment Slutsky Effect
 R[W , I (W )]  R
R
R

R
T
W
W
I
I
S
or in other words, the overall effect is:
the substitution effect (from RA to RB),
minus the usual income effect (from RB to RC)
plus the endowment effect (from RC to RD).
The Endowment Slutsky Effect
 R[W , I (W )]  R
R

 (T  R)
W
W
I
S