E. McDevitt
UCLA
Economics 102
SQ #2
GOODS MARKET
1. Assume a two-period model with U = C
1
0.5
C
2
0.5
, r = 0.12, Y
1
= 14
and Y
2
= 11.76.
a. What is the consumer’s budget constraint?
b. Find the consumer’s optimal combination of C
1
and C
2
. Find S
1
.
You may use the “short cut”
method. Show this result on a graph.
c. Continue to assume that Y
1
= 14 and Y
2
= 11.76, but now suppose that
r is 0.05
.
What
happens to C
1
,C
2
. and S
1
? Show result on a new graph. Explain the impact on current
consumption in terms of the substitution and income effects.
d. Let us again assume that r equals 0.12 but now suppose Y
2
decreases to 8.96.
What happens to C
1
,C
2
. and S
1
? What is the intuition behind this outcome?
2. Continue to assume a two-period model and a utility function of U = C
1
a
C
2
1-a
. Consumers have
a certain amount of real income in the current period (Y
1
) and in the future period (Y
2
). In class,
we ignored real wealth (assets) holdings. Let us know bring this into the model.
a. Write out the budget constraint that includes assets. Let A
1
= real wealth (assets) at the
beginning of period 1.
b. Demonstrate that optimal consumption is given by the following equations:
C
1
= a [A
1
+ Y
1
+ Y
2
/(1+r)]
and C
2
=
(1-a)[A
1
(1+r) + Y
1
(1+r) + Y
2
]
c. How does an increase in A
1
affect C
1
and S
1
?
3. Assume a two-period model with U = C
1
.30
C
2
.30
ℓ
1
.20
ℓ
2
.20
where
ℓ
is leisure.
Assume the time endowment is 1 (so time working is
1-
ℓ
). Furthermore assume that r = 0.05 and
w
1
= 10 and w
2
= 12.6.
(Assume that
A
1
= 0, as we did for question 1).
a. Write out the budget constraint with “full income” on the right-hand side.
b. Find the utility-maximizing quantities for
C
1
,C
2
,
ℓ
1
, and
ℓ
2
using the “short cut” method we
talked about in class.
c. Suppose
r falls to 0
.
Find the utility-maximizing quantities for
C
1
,C
2
,
ℓ
1
, and
ℓ
2
. What is the
intuition behind the impact on leisure in the current period?
4. Assume a two-period model.
The utility function is U = C
1
0.5
C
2
0.5
and r = 0%.
Initial values: Y
1
= $12,000, Y
2
= $10,000, G
1
= G
2
= T
1
= T
2
= $1,000.
a. Find MRS. Write out the consumer’s budget constraint and the government budget constraint.
What is consumption for each period? What is the definition of private saving, public saving and
national saving? Find private saving, public saving and national saving in the current period.
b. Now suppose there is a permanent
increase in G to $2,000 (i.e., G
1
and G
2
now equal $2,000).
Current taxes are not
raised, so the current increase in G is financed by borrowing. What does this
permanent increase in government spending, holding current taxes constant, imply about future
taxes?.
. about future after-tax income? Intuitively, how do you think consumers will respond to this
in terms of saving behavior.
Formally solve for C
1
, S
1
, S
g
, S and compare with their values from
part (a).
c. How would your answer to the last part of (b) change if the increase in government spending in