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Consider a welfare program in which individuals who do not earn
any income receive $100 in benefits but benefits decrease with
earned income: for each dollar earned 50 cents of benefits are
withdrawn and this is so for any earnings above $0.

(a) Assume that an individual can earn $10 per hour and has no
other income. Sketch her budget constraint with and without the
program in effect.

(b) For an individual earning $100 dollars before the
introduction of the welfare plan explain how hours of work and
total income are affected by the introduction of such a welfare
plan. Use the diagram to (i) illustrate the income and substitution
effects of the welfare program and (ii) show how a fixed subsidy
could lead that individual to the same level of utility at lower
cost.

(c) For an individual earning $200 dollars before the
introduction of the welfare plan explain how hours of work and
total income are affected by the introduction of such a welfare
plan. Use the diagram to show how a fixed subsidy of the same
magnitude as the decreasing subsidy the individual receives within
the welfare program would have allowed the individual to reach a
higher level of utility.