Assume that a consumer is alive for two periods, work and retirement, and earns income y and y' respectively. The consumer can borrow or lend at the real interest rate of r. Given this information, answer the following questions:

A.) Write down the consumers lifetime budget constraint and also depict it graphically

B.) Assume that population grows at rate n over time, i.e. Nt = (1 + n)Nt1. The government introduces a Pay-As-You-Go (PAYG) social security program that collects taxes t from workers and pays benefits b to retirees. Derive the budget-balancing tax for this program.

C.) Using algebra, derive the effect of this program on the consumers lifetime budget constraint.

D.) When does PAYG Social Security increase or decrease lifetime wealth in this scenario?