Question

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 r > 10%
and still borrow at the same rate. Draw the new budget constraint.
Label all points clearly.

Answer #1

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.)

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...

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will earn $200 in period 1 and $220 in period 2. She can borrow or
save at an interest rate of 10% and the price of the consumption
good is $1 in each period.
a. If Sierra decides to keep her savings at cash, solve for her
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A consumer’s consumption-utility function for a two-period
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market rate of interest is 8%. Calculate the optimal values for c1
and c2 that maximize the consumer’s utility

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}

Tom has preferences over consumption and leisure of the
following form: U = ln(c1)+ 2 ln(l)+βln(c2), where ct denotes the
stream of consumption in period t and l, hours of leisure. He can
choose to work only when he is young. If he works an hour, he can
earn 10 dollars (he can work up to 100 hours). He can also use
savings to smooth consumption over time, and if he saves, he will
earn an interest rate of 10%...

Joan is endowed with $200 in year one and $200 in year two. She
can borrow and lend at an interest rate of 5% p.a. Joan has a
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Joan’s marginal rate of inter-temporal substitution and budget
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Consider a consumer with preferences over current and future
consumption given by U (c1, c2) = c1c2 where c1 denotes the amount
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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...

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 =
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1. Find...

Anthony has an income of $10,000 this year, and he expects an
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Consumption goods cost $1 per unit this year and there is no
inﬂation.
a. What is the present value of his endowment?
b. What is the future value of his endowment?
c. Write an equation to represent his budget set. Graph his
budget set? Label it well.
d. If his utility...

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