Question

Anthony has an income of $10,000 this year, and he expects an income of $5,000 next year. He can borrow and lend money at an interest rate of 10%.

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 function is U(c1, c2)=4ln(c1)+2ln(c2) , how much will he consume in each period?

e. How would his utility change if the interest rate goes up to 15%? Is he better off or worse off? Explain.

f. What about if there is a 10% inflation? Show how his budget constraint and his utility changes with a graph. A simple illustration is fine.

g.Graph his budget constraint and find his optimum bundle if the interest rate to borrow is 15% but return to his savings is 10% with no inflation.

h. Discuss the importance of financial markets and how they can improve our utility.

Answer #1

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
utility function given by U(C1,C2) = -e^-aC1C2 (a) Write down
Joan’s marginal rate of inter-temporal substitution and budget
constraint. (b) Find Joan’s optimal consumption bundle (C1* and
C2*). Is Joan a borrower or a lender? What is the value of her
utility function at the optimal bundle if a= 1/10000? (c) Suppose...

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...

Emil has access to a perfect capital market1 with interest rate
r ∈ (0, 1). He has preferences over bundles (x, y) ∈ R2+ of money
for consumption in period 1 (x) and money for consumption in period
2 (y) that can be represented by the following utility function
u(x, y) = x2 · y
Emil has an endowment of E = (2000, 1200), that is his income in
period 1 is m1 = 2000 and his income in period...

Q4 ) John earns income of 400 units in the first period and 300
units in the second period.
Further suppose that John can borrow money at an interest rate
of 8%.
(a) Draw his budget constraint recalling that c2 = Y1(1 + r) +
Y2 − (1 + r)c1.
(b) Draw John’s budget constraint if he only receives income in
the first period.
(c) Draw John’s budget constraint if he only receives income in
the second period.
(d) Now...

Imagine an individual who lives for two periods. The individual
has a given pattern of endowment income (y1 and
y2) and faces the positive real interest rate, r.
Lifetime utility is given by U(c1, c2)=
ln(c1)+β ln(c2)
Suppose that the individual faces a proportional consumption tax
at the rate Ԏc in each period. (If the individual
consumes X in period i then he must pay XԎc to the
government in taxes period). Derive the individual's budget
constraint and the F.O.C...

(15) Smith receives $100 of income this period and $165 next
period. His utility function is given by
U=Xα Y1-α, where X is
consumption this period and Y is consumption next period.
When the interest rate was 10%, his consumption was
(C1*,
C2*)=(100, 165).
7) Find the value of α.
(8) If the interest rises to 50%, what would be the optimal
consumption bundle?

3. Consider an individual who lives for two periods. His income
in the first period is !Y1 and his
income in the second period is Y2. His consumption in the first
period is !C1 and his consumption
in the second period is C2. He can lend and borrow at zero real
interest (!r = 0 ).
(a) Write his budget constraint (again, assume !r = 0 ).
(b) Assume that the government collects a lump sum tax of !T
units...

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%...

Beta lives for two periods. In period 1, Beta works and earns a
total income of $2, 000. If she consumes $c1 in period 1, then she
deposits her savings of 2, 000 − c1 dollars in a bank account that
gives her an interest rate of 10% per period. (Notice that Beta is
not able to borrow in period 1, so c1 ≤ 2, 000.) In period 2, Beta
leads a retired life and receives $110 in social-security income....

i just uploaded another screenshot as a correction for below
question
【 4 】 Consider an individual who lives
for two periods. The individual has no initial wealth and earns
(exogenous) labor incomes of amounts Y1 and Y2 in
the two periods. The individual can borrow and lend at a fixed
interest rate r. The individual’s lifetime utility
function is given by U = ln C1 +
1 ln C2, where ρ is the rate of time
preference.
Also consider...

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