In California, a welfare recipient can earn $225 per month without having her benefits reduced. Beyond $225, benefits are reduced by 50 cents for every dollar of earnings. Consider Elizabeth, a resident of California, who can earn $10 per hour. If she does not work at all, she is eligible for welfare benefits of $645.

a. If she works 10 hours, how much are her earnings, how much is her welfare benefit, and how much is her income?

If Elizabeth works 10 hours per week, her earnings are $100, the benefit is $645, and the total income is $745.

b. After Elizabeth works a certain number of hours, she does not receive any benefit at all. What is that number of hours?

645 - .5(x-225) = 0

645 = .5(x-225)

1290 = X - 225

1515 = X

Elizabeth will have no welfare benefit after working 1515 hours.

c. Use your answer to parts a and b to plot her budget constraint.