Question

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 hours this consumer allocates to the labor market. Let 500 hours be the total time available to this consumer per week.

a. Identify the equation of the budget constraint faced by this consumer given the above information and represent this constraint graphically.

b. Now assume that the hourly wage rate reduces to $5. Identify the new budget constraint’s equation and show the change graphically. Given this change in the wage rate, what effects will impact the consumer choice?

Answer #1

Given U = f(C,L)

a) V = $1200

h = no. of hours that a person is willing to work

T = 500

Person's budget constraint:

C = wh + V

that is the dollar value of expenditure on goods is equal to the sum of the labor earnings and non-labor earnings. Now a person can either work or take leisure, therefore T = h + L where L is the total amount of leisure. Therefore the above equation will be:

C = w(T - L) + V

C = (wT + V) - wL

So the slope of is negative (-w).

C = (8*500 + 1200) - 8L

C = 5200 - 8L

b. C = (wT + V) - wL

C = (5*500 + 1200) -5L

C = 3700 - 5L

Consumer will demand less.

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...

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) = c2/3l1/3. Assume that all hours not spent working are
leisure hours, i.e, h + l = 24. The price of a good is equal to 1
and the price of leisure...

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...

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 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...

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 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...

Answer the following questions and be sure to explain
your answers.
1.) Consider a labor-leisure tradeoff problem
where 24 hours must be divided between labor and leisure. You can
assume that for simplicity and assume that labor is paid a wage .
When plotting the time constraint and indifference curves, be sure
to put leisure on the x-axis and consumption on the
y-axis.
a.) Draw the time constraint and give its
equation in slope-intercept form.
b.) Suppose now that the...

Each day, Luke must decide his leisure hours, L, and his
consumption, C. His utility function is given by the following
equation
?(?, ?) = (? − 30)(? − 12).
Luke receives $50 welfare payment per day. Show all the steps,
with the definition of every new notation used in the steps.
a) Suppose that Luke’s hourly wage is $5. Find Luke’s daily
budget constraint equation and graph it. (5 pts.)
b) If Luke’s wage is $5 per hour worked,...

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...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 3 minutes ago

asked 24 minutes ago

asked 29 minutes ago

asked 38 minutes ago

asked 43 minutes ago

asked 47 minutes ago

asked 47 minutes ago

asked 48 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago