Question

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 C*, G*, T*

2) Consider the following two-period problem for the representative consumer Y1 = 50 T1 = 5 Y2 = 20 T2 = 10 r = 0.10 C1 = consumption in the first period C2 = consumption in the second period S = saving in the first period U(C1, C2) = min{C1, C2} What is the optimal saving, S*, that maximizes the representative consumer’s lifetime utility?

Answer #1

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

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....

Suppose that the economy is characterized by the consumption
function C=151+ 0.1(Y-T) with exogenous investment I = 10,
government purchases G = 20, and taxes T = 10. Which of the
following is true?
the multiplier is 0.9
the equilibrium consumption/output ratio is C/Y = 0.9
the autonomous spending is 170.
equilibrium output is Y = 200
the government budget is balanced

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....

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?...

Which utility function for the representative consumer best
describes a one-period model in which government spending is not
wasteful?
A.
U(C,L)=ln(C+0.2•G) +ln(L)
B.
There is no such utility function. In the one-period model
government spending is always wasteful.
C.
U(C,L)=ln(C) + 0.5•L

Assume the representative consumer lives in two periods and his
preferences can be described by the utility function U(c,c′)=c1/3
+β(c′)1/3, where c is the current consumption, c′ is next period
consumption, and β = 0.95. Let’s assume that the consumer can
borrow or lend at the interest rate r = 10%. The consumer receives
an income y = 100 in the current period and y′ = 110 in the next
period. The government wants to spend G = 30 in...

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%...

Suppose the representative consumer’s preferences are given by
the utility function,
U(C, l) = aln C + (1- a) ln l
Where C is consumption and l is leisure, with a utility
function that is increasing both the arguments and strictly
quiescence, and twice differentiable.
Question:
The total quantity of time available to the consumer is
h. The consumer earns w real wage from working in
the market, receives endowment π from his/her parents, and pays the
T lump-sum tax...

A representative consumer living in a Country A values consuming
goods (C) and enjoys leisure (l). The consumer has h = 1 units of
time to divide between working and enjoying leisure. For each hour
worked, he receives w = 1.5 units of the consumption good. The
consumer also owns shares in a factory which gives him an
additional π = 0.55 units of income. The government in this economy
taxes the consumer and uses the proceeds to buy consumption...

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