The question is attached below, thank you for your help!

Consider an economy where persons live for two periods only. Their utility function over consumption in periods 1 and 2 is given by U = 2 log C₁) + 2 log (C₂), where C₁ and C₂ are period 1 and period 2 consumption. They have labor income of $100 in period 1 and labor income of $50 in period 2. They can save as much of their income in period 1 as they like in back accounts, which earn interest of 5 percent per period. They have no bequest motive, so they spend all their income before the end of period 2.

a. What is each individual's lifetime budget constraint? If they choose consumption in each period so as to maximize their lifetime utility subject to their lifetime budget constraint, what is the optimal consumption in each period? How much do the consumers save in the first period?

b. Suppose that the government introduces a social security system that will take $10 from each person in period 1, put it in a bank account, and transfer it back to them withinterest in period 2. What is the new lifetime budget constraint? What is the effect of this social security system on private savings? How does the system affect total savings in this society?