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?