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:

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.