Due: Nov. 25 in Class: QUESTION-1: [10 marks each part = 40]
Consider the simple overlapping generation model. Assume no population growth, n = 0. The representative consumer faces the income flows yt = 50, yt+1 = 0. Assume consumer’s utility is given by u(ct, ct+1)=lnct+lnct+1. The interest rate is r = 0.05.
a) Suppose the government oversees a PAYG SS system (pay-as-you-go social security system). It taxes each young in the amount of b=20 and redistributes the proceeds equally among the old immediately. Set up the problem of the representative consumer in this economy. Find his/her optimal consumption bundle. How much does the consumer save privately? What is the utility level the consumer enjoys?
Hints:
) Next consider the same hypothetical economy but with fully funded Social Security program in place. The government taxes each young in the amount of b = 20 and invests the proceeds at the rate of r, the gross return is paid out to the same person when he is old. Set up the problem of the representative consumer in this economy. Find his/her optimal consumption bundle. How much does the consumer save privately? What is the utility level the consumer enjoys?
c) Illustrate the lifetime budget constraints and the optimal consumption bundle for both of the systems in the same diagram. Indicate each point, including the points of intercepts of the budget constraints and the endowment points (these are consumption bundles co
esponding to private savings
o
owing)
d) Under which system are consumers better off? If the worse of the two systems is in place, explain the government may go about reforming the system.