Question

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% per period. Suppose also that he
values the future and the present equally, i.e. β = 1. (Remember
the marginal utility of ln(c) is 1/c and marginal utility of
leisure is given by 2/3l).

(a) Draw a standard indifference curve on the consumption
today and leisure set. What is

the slope of the indifference curve?

(b) Draw a standard indifference curve on the consumption
today and consumption tomor- row set. What is the slope of the
indifference curve?

(c) Write down the budget constraint in the first
period.

(d) Write down the budget constraint in the second
period.

(e) Derive the lifetime budget constraint.

(f) Draw the lifetime budget constraint on the consumption
today and leisure set. What is the slope of the budget line?

(g) Draw the lifetime budget constraint on the consumption
today and consumption to- morrow set. What is the slope of the
budget line?

(h) Find Tom’s optimal consumption in each period (c∗1, l∗ and
c∗2) and optimal saving rate?

Answer #1

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 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...

Hira has the utility function U(c1; c2) = c11/2 +2c21/2 where
c1 is her consumption in period 1 and c2 is her consumption in
period 2. She will earn 100 units in period 1 and 100 units in
period 2. She can borrow or lend at an interest rate of 10%.
Write an equation that describes Hira’s budget.
What is the MRS for the utility function between c1 and
c2?
Now assume that she can save at the interest rate...

Let Jane's Utility function be given by: U=100 x ln(C) + 50 x
ln(L) where C is consumption (in dollars) per year and L is hours
of leisure per year. Jane can make $15 per hour and can work up to
2,000 hours per year.
a. set up the maximization problem, showing the budget
constraint.
b. How many hours will Jane want to work per year

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...

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 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 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...

(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...

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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