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4. (Homer 2.17) Social security in the Diaruond model. Consider a variation of the Diamond economy that we learned in class in which each individual lives for two periods. The growth rate of technology is g = 0, so technology A is constant over time. Production is CobbDouglas, so production function in intensive form is 3" (let) = k3. Utility is logarithmic, so the utility of an individual born at t is 1 +p U: = 11101,: + 1 11102;...1, p .3" l_. (a) Pay-as-you-go social security. Suppose the government taxes each young indi- vidual an amount T and uses the proceeds to pay benets to old individuals; thus each old person receives (1 + n)T. i. How, if at all, does this change aect equation k,\" = Wk? {2. '50) giving 1.1;\" as a function of Fat? ii. How, if at all, does this change aiTect the halanced-growthpath value of k? (b) Fullyr funded social security. Suppose the government taxes each young person an amount T and uses the proceeds to purchase capital. Individuals born at t therefore receive {1 + n+1)?" when they are old. i. How, if at all, does this change aliect equation lat\" = Wk? (2. 60) giving law] as a function of It}? ii. How, if at all, does this change aect the balanced-growth-path value of k