Question

Consider a consumer with preferences over current and future consumption given by U (c1, c2) = c1c2 where c1 denotes the amount consumed in period 1 and c2 the amount consumed in period 2.

Suppose that period 1 income expressed in units of good 1 is m1 = 20000 and period 2 income expressed in units of good 2 is m2 = 30000. Suppose also that p1 = p2 = 1 and let r denote the interest rate.

1. Find the optimal consumption bundle when r=0.15. Is the consumer a saver or a borrower?

2. Let p1 = p2 = 1 and r = 0:2. Suppose the consumer is asked to choose between two bundles, (c1; c2) = (25; 16) and (c1; c2) = (9; 36): Which one would she choose?

3.Consider again our consumer from above, and suppose that (m1; m2)=(110; 100), p1 = 1, and r = 0: What are the inflation rates that make her be a saver and what are the ones that make her be a borrower?

Answer #1

Consider a consumer with preferences over current and future
consumption given by U (c1, c2) = c1c2 where c1 denotes the amount
consumed in period 1 and c2 the amount consumed in period 2.
Suppose that period 1 income expressed in units of good 1 is m1
= 20000 and period 2 income expressed in units of good 2 is m2 =
30000. Suppose also that p1 = p2 = 1 and let r denote the interest
rate.
1. Find...

utility function over consumption
today (c1) and consumption tomorrow
(c2):
U(c1, c2)
= log(c1) + blog(c2) where
0 < b < 1 and log denotes the
natural logarithm
Let p1 denote
the price of c1 and p2
denote the price of c2. Assume that income is
Y. Derive Marshallian demand functions for
consumption today (c1) and consumption tomorrow
(c2). What happens to c1
and c2 as b approaches 0? {Math hint:
if y = log(x), dy/dx = 1/x}

Suppose that Jessica has the following utility, U = C1^1/2
C2^1/2 and that she earns $400 in the first period and $700 in the
second period. Her budget constraint is given by C1 + C2/1+r = Y1 +
Y2/1+r . The interest rate is 0.25 (i.e., 25%). She wants to
maximize her utility.
(a) What are her optimal values of C1 and C2?
(b) Is Jessica a borrower or a saver in period 1?
(c) Suppose the real interest rate...

Vanessa’s utility function is U(c1,
c2) = c1/21 +
0.83c1/22, where
c1 is her consumption in period 1 and
c2 is her consumption in period 2. In period 2,
her income is 4 times as large as her income in period 1. At what
interest rate will she choose to consume the same amount in period
2 as in period 1? (Choose the closest answer.)

(Intertemporal Choice )Consider a consumer whose preferences
over consumption today and consumption tomorrow are represented by
the utility function U(c1,c2)=lnc1 +?lnc2, where c1 and c2 and
consumption today and tomorrow, respectively, and ? is the
discounting factor. The consumer earns income y1 in the first
period, and y2 in the second period. The interest rate in this
economy is r, and both borrowers and savers face the same interest
rate.
(a) (1 point) Write down the intertemporal budget constraint of...

Consider a two-period economy consisting of people with
identical preferences and identical
endowments. There are two consumption goods, one for each period
(C1 and C2); the goods have
prices P1 and P2, respectively. The endowment of the first period
is the same as the endowment
for the second period.
The preferences are of the form U(C1, C2) = ln(C1) + 0.99 *
ln(C2)
Let the number of people in this economy be 1. Let the endowment of
C1,C2 be 1000,1000...

Consider the following 2-period model U(C1,C2) = min{4C1,5C2} C1
+ S = Y1 – T1 C2 = Y2 – T2 + (1+r)S Where C1 : first period
consumption C2 : second period consumption S : first period saving
Y1 = 20 : first period income T1 = 5 : first period lump-sum tax Y2
= 50 : second period income T2 = 10 : second period lump-sum tax r
= 0.05 : real interest rate Find the optimal saving, S*

Hira has the utility function U(c1; c2) = c11/2 +2c21/2 where
c1 is her consumption in period 1 and c2 is her consumption in
period 2. She will earn 100 units in period 1 and 100 units in
period 2. She can borrow or lend at an interest rate of 10%.
Write an equation that describes Hira’s budget.
What is the MRS for the utility function between c1 and
c2?
Now assume that she can save at the interest rate...

Consider the following consumption decision problem. A consumer
lives for two periods and receives income of y in each period. She
chooses to consume c1 units of a good in period 1 and c2 units of
the good in period 2. The price of the good is one. The consumer
can borrow or invest at rate r. The consumer’s utility function is:
U = ln(c1) + δ ln(c2), where δ > 0.
a. Derive the optimal consumption in each period?...

A consumer likes two goods; good 1 and good 2. the consumer’s
preferences are described the by the cobb-douglass utility
function
U = (c1,c2) =
c1α,c21-α
Where c1 denotes consumption of good 1, c2
denotes consumption of good 2, and parameter α lies between zero
and one; 1>α>0. Let I denote consumer’s income, let
p1 denotes the price of good 1, and p2
denotes the price of good 2. Then the consumer can be viewed as
choosing c1 and c2...

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