3. Consider a model in which individuals live only two periods. Individuala maximize the following utility function If : 4111(01) + 3111(02), where Cl is the consumption in period 1 and 02 is the consumption in period 2. In each period there are N young individuals and N old individuals. An individual receives an income of $300 in period 1 and no income in period 2. The market interest rate is 5 percent, and the person can borrow or lend money at this rate. (a) Use a diagram of indifference curves and an int-ertemporal budget constraint to illustrate the individual's optimal consumption in each period, if there is no public pension system. Make sure you label the axes and provide the numerical value of the slope of the budget- constraint. [2 marks] (1)) Write down the individual's lifetime budget constraint and solve to nd Cl, C2 and S, which is personal savings. [2 marks] (c) Now assume that. the government introduces a public pension program. The government takes $105 from each individual in period 1 and gives it directly to individuals in period 2 (as usual, we assume that. individuals cannot borrow against the public pension). i. What is the terminology for this public pension program? [1 mark] ii. How much does an individual privately save now? [Note: you can round to 2 digits] [2 marks] iii. How does an individual's utility with the public pension system compare to an indi vidual's utility without the public pension system?[1 mark] iv. Explain the intuition behind your ndings in iii. [1 mark]