Consider an individual aged 64 who is eligible to collect full social security (public pension) benefits of $6,000 for a year. They have no other income but can work at a weekly wage rate of $600 for a maximum of 52 weeks. Receipt of benefits from the social security program is retirement tested. Specifically, the individual can earn up to $9,000 in annual wage income without a reduction in benefits; however, after $9,000 of earnings, benefits are reduced by 50% for every dollar earned, until the benefits are exhausted. a) Carefully draw and label the budget constraint for this individual. b) Suppose previously there was a retirement test, and then the test is eliminated, i.e., the individual now is allowed to keep all benefits, irrespective of their labour earnings. How would this affect the individual’s labour supply?
Consider an individual aged 64 who is eligible to collect full social security (public pension) benefits of $6,000 for a year. They have no other income but can work at a weekly wage rate of $600 for a maximum of 52 weeks. Receipt of benefits from the social security program is retirement tested. Specifically, the individual can earn up to $9,000 in annual wage income without a reduction in benefits; however, after $9,000 of earnings, benefits are reduced by 50% for every dollar earned, until the benefits are exhausted. a) Carefully draw and label the budget constraint for this individual. b) Suppose previously there was a retirement test, and then the test is eliminated, i.e., the individual now is allowed to keep all benefits, irrespective of their labour earnings. How would this affect the individual’s labour supply?
Chapter17: Capital And Time
Section: Chapter Questions
Problem 17.2P
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Question
Consider an individual aged 64 who is eligible to collect full social security
(public pension) benefits of $6,000 for a year. They have no other income but can work at a
weekly wage rate of $600 for a maximum of 52 weeks. Receipt of benefits from the social
security program is retirement tested. Specifically, the individual can earn up to $9,000 in
annual wage income without a reduction in benefits; however, after $9,000 of earnings,
benefits are reduced by 50% for every dollar earned, until the benefits are exhausted.
a) Carefully draw and label the budget constraint for this individual.
b) Suppose previously there was a retirement test, and then the test is eliminated, i.e.,
the individual now is allowed to keep all benefits, irrespective of their labour
earnings. How would this affect the individual’s labour supply?
Question Two David is a 70-year-old accountant. After serving his accounting firm for 45
years, David decides to retire soon. David has great passion for vintage cars and wants to
work at a local vintage car rental company after he retires. David already knows some
information related to his retirement life:
➢ David does not have a non-labour income.
➢ David is eligible to collect $B of pension payment each month.
➢ If David works at the vintage car rental company after retirement, the payroll tax rate
is to be ?; the retirement test, i.e., the reduced pension because the recipient works
and continues to earn income, is to be ?; the wage rate is to be ?.
➢ David’s total time is ? and leisure hours are ?.
Use the above information to answer the following questions:
(public pension) benefits of $6,000 for a year. They have no other income but can work at a
weekly wage rate of $600 for a maximum of 52 weeks. Receipt of benefits from the social
security program is retirement tested. Specifically, the individual can earn up to $9,000 in
annual wage income without a reduction in benefits; however, after $9,000 of earnings,
benefits are reduced by 50% for every dollar earned, until the benefits are exhausted.
a) Carefully draw and label the budget constraint for this individual.
b) Suppose previously there was a retirement test, and then the test is eliminated, i.e.,
the individual now is allowed to keep all benefits, irrespective of their labour
earnings. How would this affect the individual’s labour supply?
Question Two David is a 70-year-old accountant. After serving his accounting firm for 45
years, David decides to retire soon. David has great passion for vintage cars and wants to
work at a local vintage car rental company after he retires. David already knows some
information related to his retirement life:
➢ David does not have a non-labour income.
➢ David is eligible to collect $B of pension payment each month.
➢ If David works at the vintage car rental company after retirement, the payroll tax rate
is to be ?; the retirement test, i.e., the reduced pension because the recipient works
and continues to earn income, is to be ?; the wage rate is to be ?.
➢ David’s total time is ? and leisure hours are ?.
Use the above information to answer the following questions:
2
a) Write an equation to describe David’s budget constraint, ??, after he retires and works
at the vintage car rental place.
b) What is David’s budget constraint if the payroll tax is zero?
c) Keep the assumption in Part b). Suppose the retirement test is zero in the low-income
range and 50% in the medium-income range. Write down two equations to specify
David’s budget constraints in the low- and medium-income ranges, and then plot his
entire budget constraints.
d) Let David’s earnings at the vintage car rental place be ?, where ? =?(?−?).
Rewrite David’s budget constraint as ?=?+(1−?)?, since the payroll tax rate is
zero. Solve for the breakeven level of earnings, ??, where David no longer receives
any pension income.
a) Write an equation to describe David’s budget constraint, ??, after he retires and works
at the vintage car rental place.
b) What is David’s budget constraint if the payroll tax is zero?
c) Keep the assumption in Part b). Suppose the retirement test is zero in the low-income
range and 50% in the medium-income range. Write down two equations to specify
David’s budget constraints in the low- and medium-income ranges, and then plot his
entire budget constraints.
d) Let David’s earnings at the vintage car rental place be ?, where ? =?(?−?).
Rewrite David’s budget constraint as ?=?+(1−?)?, since the payroll tax rate is
zero. Solve for the breakeven level of earnings, ??, where David no longer receives
any pension income.
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