Question

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 goods that are given to the army. The consumer pays a lump sump tax T equal to 0.35. Suppose that the consumer’s preferences are described by the the utility function.

U(C, l) = C ^1/3 + L ^1/3

1. Write down and graph the consumer’s budget constraint.

2. Define and compute the MRS as a function of C and l.

3. Is it optimal for the consumer to supply Ns = 0.8 units of labour?

4. Find the consumer’s optimal choice of consumption and leisure. Illustrate with a graph.

Answer #1

1. Consider the representative consumer’s problem as follows.
The representative consumer maximizes utility by choosing the
amount of consumption good C and the amount of leisure l . The
consumer has h units of time available for leisure l and for
working Ns , that is, h = l+Ns . Government imposes a proportional
tax on the consumer’s wage income. The consumer’s after-tax wage
income is then (1−t )w(h −l ), where 0 < t < 1 is the tax...

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...

Consider a consumer who has preferences over consumption
(x) and leisure (L) represented
by u(L, x) = 10 ln L + 5 ln
x. The consumer has 24 hours in the day (T = 24)
to divide
between work and leisure. The consumer can choose however many
hours they want to
work. For each hour of work they are paid a wage given by
w = 10. Consumption (x) costs
1 per unit.
(a) Initially suppose that the consumer has...

In the labor-leisure model, the representative consumer receives
satisfaction from consumption of goods (C) and from the consumption
of Leisure (L). Let C be the composite good with price $1 and L
determines the number of hours of leisure this person consumes.
Therefore U = f(C,L) for this consumer. This consumer’s consumption
is constrained by time and income. Let her non-labor income, V, be
$1200 per week, let the hourly wage rate be $8 and h be the number
of...

Suppose that the consumer’s preferences are given by
U(c,l)=2c ^(1/2) +2l ^(1/2)
where c is the level of consumption and l is leisure. The
consumer has to allocate 50 hours between leisure and labour. The
real wage rate is 10 per hour and the real non-wage income is 160.
Assume that there is no
government. Note that (∂c ^(1/2)) / (∂c) = (1/2) c^(-1/2)
(a) Write the budget constraint of the household. (b) Solve for
the tangency condition using the...

Suppose Tom has a utility function U=C*L
C= consumption L= hours of leisure
Tom has 100 hours to divide between work and leisure per
week
wage is $20/hr
1. Write down budget constraint in terms of consumption and
hours of work
2.Tom make decisions on hours of work, leisure and consumption
to max. utility. Explain why we can collapse this problem to one in
which he chooses hours of leisure only
3. Find optimal hours of work and total consumption...

Consider the following labour-leisure choice model. U(C,L) =
C^(2/3)L^(1/3)
C = wN + π – T
H= N+ L Where
C: consumption
L: leisure
N: hours worked
H = 50 : total hours
w = 4 : hourly wage
π = 20 : non-labor income T = 10 : lump-sum tax
Suppose the hourly wage changes to w = 5. Perform a decomposition
and calculate the substitution, income and total effect for each C,
L, N

NEED DETAIL PLZ
Leo thinks leisure (R) and consuming goods (C) are perfect
complements. Goods cost $1 per unit. Leo wants to consume 5 units
of goods per hour of leisure. Leo can work as much as he wants to
at the wage rate of $15 an hour. He has no other source of income.
One day has 24 hours.
a. What is his utility function and budget constraint?
b. How many hours a day will Leo choose to spend...

Santi derives utility from the hours of leisure (l) and from the
amount of goods (c) he consumes. In order to maximize utility, he
needs to allocate the 24 hours in the day between leisure hours (l)
and work hours (h). Santi has a Cobb-Douglas utility function, u(c,
l) = c 2/3 l 1/3 . Assume that all hours not spent working are
leisure hours, i.e, h + l = 24. The price of a good is equal to 1...

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...

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