Question

Suppose that a consumer lives for two periods: working age and retirement age. The consumer works during their working age, and does not work during their retirement age.

a) Write out the consumer’s budget constraint. Draw the budget constraint, with correct labelling.

b) Briefly explain how the following variables are likely to affect how much the consumer will save (ceteris paribus): (i) Discount rate, (ii) interest rate, (iii) uncertainty about retirement age income.

c) Now suppose that there is a third period called “old age,” but only a fraction of consumers make it to old age. Explain how a pension scheme can improve outcomes over a private savings scheme.

Answer 1

In this problem , a person is consuming in two periods. First period (C1) indicates working period when he earned. Second period (C2) is retirement where he consumes the money he saved in period 1 plus interest earned.

1) Intertemporal budget constrain is shon below.

2) i) discount rate= In this case the discount rate l=tell the same story as the interest rae. If the discount rate is high no one will be willing to spend the money in present. If the discount rate is is high more savings will be for future.

ii)interest rate= If the interest rate is high then the consumer will save more , because this will help him earn interst which he can use it in future. reverce will happen if the interest rate is low.

iii) uncertainilty about retirement = In this case the the conumer will save alot more because he is uncertain about the future where he has no idea anout his future income.

3) Pension will help the consumer to not be bothered about the old age. Not many people willmake up o that age so there is no point saving it on its owm. but if pension will be provided then it will be helpful for the consumer in the old age. pension will be like a security from the government which is in short investment +interest.