Question

Wage rate is $10 per hour for a consumer, and he is choosing earning of $10 per hour and taking leisure of 1 hour together.

a. Derive the mathematical equation and draw the corresponding graph for daily income-leisure constraint.

b. Draw the corresponding indifference curve between earning and leisure.

c. How many hours will this consumer work and how much will this consumer earn?

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%...

Assume the gross wage of w=$10 per hour and gross non-wage
income YN = $5000 per year. Assume a maximum of 6,000 hours of
leisure per year (T= 6000 per year ), so that full income for the
worker is $65,000.
Draw the budget constraint under each of the following taxes and
transfer schemes.
1. A welfare program that pays $8,000 per year if the person
does not work and reduces the welfare benefit dollar for dollar
with earnings (100%...

Suppose you have 24
hours per day that you can allocate between leisure and
working.
(i)
Draw the budget constraint between
“leisure hours” on the horizontal axis and “wage income” on the
vertical when the wage rate is $40 per hour. Mark an optimum point
A that is meaningful. Draw a new budget constraint when the wage
rate falls to $30 per hour. Show a new optimum point B.
(ii)
On your indifference curve diagram,
decompose the effect of the...

A maximizing worker is paid a wage of 10 dollars per hour and a
non-labour salary of 160 dollars per day. She has preferences for
leisure and food defined by u(z, f) = z1/2f1/2. How many hours will
she work?

Ira’s only source of income is from working. He can work as many
hours per day as he wishes (up to a maximum of 24 hours) at a fixed
wage rate of $10 / hour.
b. Suppose, that the government introduces a tax rate of 50
cents in the dollar. Suppose that leisure is a normal good that tax
ends up reducing Ira’s hours worked. Show in your diagram the
effect of the tax on Ira’s budget constraint and possible...

With an initial wage rate of $15 per hour, Thomas works 35 hours
per week and leisures the remaining 75 hours. When his wage
increases to $20 per hour he works 45 per week and when the wage
increases to $25 heworks 40 hours per week. What is Thomas’ labor
supply elasticity as his wage increases from $15 to $20 and then
from $20 to $25? What does this value tell you about the shape of
his labor supply curve...

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...

Sarah has the following utility function and has a market wage
of $10 per hour, and can work upto 2000 hours per year.
U = 100* lnC + 175* lnL ; Where C is the consumption and L is
the leisure
A) Determine the utility maximizing levels of C and L for Sarah.
Also, determine the corresponding maximum level of utility of
Sarah.
Now assume that she is subject to a TANF program that features a
benefit guarantee of $5000...

3. Suppose Jack’s wage rate is $20 and that he can produce $10
per hour of household “goods”. Suppose Jill’s wage rate is $30 and
that she can produce $15 per hour of household “goods”. Who should
specialize in the market sector? Suppose now, Jack’s wage goes up
to $25 per hour. How does this affect the answer?

Suppose that you have a job with a wage of $25 per hour. The job
is extremely flexible: you
can choose to work any number of hours from 0 to 2,000 per year.
The income tax system
is as follows.
•Income up to $10000: no tax.
•Income from $10000 to $30000: 20% tax rate.
•Income from $30000 up: 30% tax rate.
(a) Draw a graph in leisure hours/consumption space, showing
your opportunity set with
and without the tax system. Label...

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