Question

Suppose preferences for consumption and leisure are: u(c, l) = ln(c) + θ ln(l)

and households solve:

max _{c,l} u(c, l)

s.t. c=w(1−τ)(1−l)+T

Now suppose that in both Europe and the US we have:

θ = 1.54

w=1

but in the US we have:

τ = 0.34

T = 0.102

while in Europe we have:

τ = 0.53

T = 0.124

Compute the amount of leisure and consumption chosen in the US and Europe. Use the parameters given for each country.

Answer #1

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%...

3. Suppose that an individual’s utility function for
consumption, C, and leisure, L, is given by U(C, L) = C 0.5L 0.5
This person is constrained by two equations: (1) an income
constraint that shows how consumption can be financed, C = wH + V,
where H is hours of work and V is nonlabor income; and (2) a total
time constraint (T = 1) L + H = 1 Assume V = 0, then the
expenditure-minimization problem is minimize...

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...

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...

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...

Suppose u=u(C,L)=4/5 ln(C)+1/5 ln(L), where C = consumption
goods, L = the number of days taken for leisure such that L=365-N,
where N = the number of days worked at the nominal daily wage rate
of $W. The government collects tax on wage income at the marginal
rate of t%. The nominal price of consumption goods is $P. Further
assume that the consumer-worker is endowed with $a of cash
gift.
a) Write down the consumer-worker's budget constraint.
b) Write down...

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

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...

Tom faces a labor supply decision. His well-behaved
preferences over the two goods, L (leisure) and C (consumption) can
be represented by u = 4√L + C. He can choose how many hours to work
at the wage rate w per hour and has no non-labor income. The price
per unit of consumption is p, and his total free time is T
hours.
Use the tangency method to find Tom’s demand functions
for leisure and consumption.
In terms of parameters...

Bernice is has the following utility over leisure (l) and
consumption(c): u(l,c) = min{l,c}. We presume that the wage is $9
and that the time allocation is T = 100. The price of consumption
is normalized at $1. She has no other income.
(a) How much will she consume and how much time will she
work?
(b) If the wage rises to $19, how much will she consume and how
much time will she
work?
(c) Is the supply of...

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