$($Moral Hazard Cost$)(30$ points$)$

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 budget constraint that these mothers face before the introduction of

the welfare benefit and health insurance, after having the welfare benefits but no health

insurance, and after having both welfare program and insurance benefits.

b$.$ Draw a representative indifference curve for each mother. Discuss how the

welfare program changes the behavior of these three individuals.

c$.$ To save money, the government decides to cut back on provision insurance. It

dictates that to receive free health care for their children, single mothers will henceforth

$3$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.

Describe the welfare lock issue here.

d$.$ The government decides to remove the welfare lock by providing free low

quality public health care $($H$0=$$$2,000)$ for everyone. If the individuals want to

consumer health care more than H$0,$ they have to turn to private health care.

Illustrate how Polly, Molly, and Dolly would change their choice between health care

and other consumptions after the reform. You can draw health care on the horizontal

axis and other consumptions on vertical axis.

e$.(5$ points$)$ People complain on the low quality of the public health care. They

argue that they would be much better off if public hospitals have higher quality. What

do you think of this suggestion?

f$.(5$ points$)$ People also complain about the fact that they lose all H$0$ if they want

health care slightly better than H$0.$ The government then changes the system again,

to a voucher system, in which all kids get a free voucher with a value of H$0$ for health

care. Kids can use the public health care, or use the voucher as cash to pay the cost

for private health care. Draw the budget constraint under the voucher program. What

is the effect of the program on people$$s expenditures on health care?