Page ( (f) What you have demonstrated is an (Example of marl-net unraveling. Explain the intuition for Why it happened. 2. (40 points, Social Security Example) Consider an economy that. is composed of identical indis viduaLs who live for two periods. Individuals maximize: 11mm = 2mm) +21%); (1) where q is consumption in each period 1'. In each period there are N young individuals and N old individuals. Each individual receives an income of $300 in period 1 (their \"youth\") and no income in period 2 (their \"retirement"; Individuals do not Want to leave behind any money. They can save from Period 1 to Period 2 at intermt rate 'r, and the price of consumption in each period is one. (a). Write down the individual's lifetime budget constraint, and solve to nd the optimal personal savings (3'). Now suppose that the Federal government institutes a social security system. The government takes $50 from each agent in Period 1, saws it, and gives it back with interest r in Period 2. Individuals are still able to privately save at intenst rate r. (b). What is the terminology for this social security system? (c). What is the new equilibrium individual savings? (d). What is the e'eet of this social security system on social welfare:] Suppose that some individuals do not care about their retirement very much, and have utility tune tions: 9 1 Uimpatiem : TU 111(E1l + IT) 111(02)- (2) The social security system still forces them to save $50. (e). If the agents can save and borrow at 1', then what will their response he to the \"forced\" saving of $50 by the social security system? (f). Suppose that these impatient agents cannot borrow hemuse credit markets are imperfect. In that case, show that the social security system has actually made them worse off. (g). In the real world, we often observe very low savings rates. Some plmdits have used this fact to justify the existence of social security, arguing that savings rates are too low. Explain how the preference; (2) versus (1) refute this story. 3. (20 Doints. ConsuthionSmoothin: Benets from Insurance) Your utilitv function is ZOOM +