Polly, Molly, and Dolly are all single mothers. They each can earn $10 per hour working for up to 2,000 hours per year. Their government runs a welfare system that gives income benefits of $5,000 per year for single mothers with no income. The welfare benefits are reduced by $1 for every $2 in earned income. Currently, the government also provides free health care for children of single mothers with less than $25,000 in income. Each mother values this benefit at $2,000 per year. Under this system, Polly works 200 hours per year, Molly works 1,025 hours per year, and Dolly works 1,500 hours, so only Polly receives welfare.
a. Draw the set of hours worked and consumption combinations that these mothers face (carefully labeling the slopes of the budget constraint).
Draw a representative indifference curve for each mother.
b. In an effort to save money, the government decides to cut back on providing insurance. It dictates that to receive free health care for their children, single mothers will henceforth have to be on welfare. On a new set of axes, draw the new budget constraint for the three mothers. Describe what will happen to the number of hours each mother works.