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3. (22 marks) Consider a two-period overlapping generations model, in which individuals are endowed with goods y, and y2 when young and old respectively. The population, N. is constant over time. Individuals can save through two assets: capital (k), which pays a constant gross marginal product of capital, r > 1; government bonds (b), which pay a gross real rate of return r > 1. The two assets are viewed as perfect substitutes by agents. At time t each young individual pays a lump-sum tax of nut goods, and each old individual pays a lump-sum tax of T2: goods. The government also spends an amount g on goods and services. First and second period consumption are normal goods. At time to the government raises expenditure on infrastructure by an amount Ag, and cuts taxes on the young by an amount A71. (a) (9 marks) If the government does not raise taxes on the old this or next period, what is the effect of this policy on an individual's consumption, savings, and allocation of savings between capital and bonds? Explain. (b) (4 marks) If the production technology is instead f(k), and exhibits a diminishing marginal product given by f'(k), how would the policy of Ag > and An and AT1