Question

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*

Answer #1

Suppose the following model of government efficiency. Utility
function over consumption of private goods (C) and public goods (G)
U(C,L) = C^0.5G^0.5
Exogenous Income: Y = 50 Lump-sum tax: T Budget constraint: C +
T = Y PPF: C = Y – G/q Government efficiency: q = 0.8 (This
measures the number of public goods that can be produced from one
unit of private consumption good) We want to maximize the
representative consumer’s utility and balance the government
budget. Find...

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...

A consumer’s consumption-utility function for a two-period
horizon (t = 1, 2) is given by U(c1,c2) = ln(c1)+ln(c2). The
consumer’s income stream is y1 = $1500 and y2 = $1080, and the
market rate of interest is 8%. Calculate the optimal values for c1
and c2 that maximize the consumer’s utility

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...

(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...

Isabella has preferences U = c1c2, receives income of Y1 = 200
today and Y2 = 100
tomorrow. The interest rate for saving or borrowing is r = 0:1.
What levels of
consumption c1 and c2 will Isabella choose?

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...

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...

Question 2: Consumption Decisions
Suppose a person's life is divided into two main blocks, periods 1
and 2. The consumer does not desire
to perfectly smooth consumption over the two periods. In
particular, preferences are such that c2 = 0:5 c1.
Income in the two periods is equal to y1 = 500 and y2 = 1000, and
income taxes are proportional 1 = 50%
and 2 = 50%. The real interest rate is r = 0%.
(a) What is the...

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...

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