Use an income-retirement model for the following situation (simply replace "leisure" with "retirement" in our normal income-leisure model):

Moe Mulligan is 65 years old and deciding between retirement (leisure) and work. She is eligible to collect a pension of$10000 a year. She also has the option of working for$800 a week for a maximum of 52 weeks of the year.

Benefits from the pension program are income-tested. Moe can earn up to$8000 in annual wages without a reduction in benefits, but if she earns more than$8000 in labour income her benefits are reduced by 50 cents for every dollar earned until the benefits are exhausted.

Draw and label her budget constraint, and show the optimal decision where Moe keeps a portion of her labour earnings (i.e. she receives a pension greater than 0 but less than $10000).