Question

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 the marginal benefit of leisure relative to consumption.

c) Write down the marginal cost of leisure relative to consumption.

d) Based on your answers to parts b and c, write down the consumer-worker's decision rule.

e) Derive the labor supply equation. (Hint: Subsititute the budget constraint into the decision rule in part d, and solve the result for L in terms of P, W, a and t.)

f) Based on your answer to part e, if the government increase the income tax rate t, labor supply {INCREASES, DECREASES, STAYS THE SAME} as the labor supply curve shifts {RIGHTWARD, LEFTWARD, NOWHERE} . Please help! Thank you!

Answer #1

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
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A representative consumer living in a Country A values consuming
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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...

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
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In the labor-leisure model, the representative consumer receives
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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...

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...

Using the budget constraint, PC=W[T-l], where
C is consumption and l is leisure and T is total time,
show that a cultural constraint or government requirement to work 8
hours per day will tend to make total satisfaction in society lower
than it could be if there is no restriction on the number of hours
a worker chooses to work.

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 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
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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...

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