ECON8034 - Social Security and Welfare Programs - Economics Assignment Help

Assignment Task

1. Consider an economy that is composed of identical individuals who live for two periods. These individuals have preferences over consumption in periods 1 and 2 given by . U ? C1C2

They receive an income of 100 in period 1 and an income of 50 in period 2. They can save as much of their income as they like in bank accounts, earning an interest rate r of 10% per period. They do not leave bequests so they spend all their money before the end of period 2. Individuals choose consumption in each period by maximizing their lifetime utility subject to their lifetime budget constraint, which relates the net present value of consumption to the net present value of income.

(a) What is the individual’s optimal consumption in each period? How much saving does he do in the first period? Provide a diagram.

(b) The government decides to set up a social security system. This system will take $10 from each individual in period 1, and transfer this money back with 10% interest in period 2. How does the system affect the amount of private savings? Show this situation in the diagram carefully labelling all relevant points.
(c) Assume now that the social security has a lower implicit rate of return (5%) than the private return (10%). How would the introduction of the social security system affect the budget constraint? Provide the amounts for consumption in periods 1 and 2, private savings and total savings for this individual. Show this new allocation in the diagram.

2. 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receive $100 in benefits but benefits decrease with earned income: for each dollar earned 50 cents of benefits are withdrawn and this is so for any earnings above $0.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. Carefully label the axes, intercepts and kink points.

(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.

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