1. (40 points) Fully funded pensions Consider a highly stylized economy with overlap- ping generations. We assume that the life-cycle has two time periods: youth-denoted by subscript y and old age-denoted by subscript o. Therefore, in each period the economy is populated by a young and an old generation. In each time period t, population sizes are Ny, and Ne, for the young and old generation, respectively. Hence, the size of the total population is: N = Nor + Net- The young generation grows at the fixed growth rate n, so that: Not = (1 + )Ny,-1. A typical individual makes inter-temporal decisions spanning the two periods of life. We assume that only young work while old are retired. The young generation is endowed with one unit of time which they supply inelastically to work in return for the wage rate my. Consumption in the old age is financed by individual savings s, and public pensions. Individual savings earn the interest rate r, in the private market. The pension system in place is fully-funded and taxes the young generation a lump sum tax 7. Contributions earn the public interest rate "; and proceeds are returned to the same generation when retired in the form of pensions p, where pat1 = (1+7;). Individuals discount the future at rate 8, while preferences are given by the lifetime utility function: U(Gus, Catti) = In(cut) + Bla(cast1). A. (10pt) Briefly outline the main differences between a fully-funded and a pay-as-you- go pension system. B. (10pt) Given the description of this economy, solve for the optimal allocations of a typical individual: Cyr, Co,t-1, 8- C. (10pt) Show how savings and the equilibrium level of the capital stock are impacted! by a fully-funded pension system if public and private savings earn the same rate of return ({} = 76). D. (10pt) Show how savings and the equilibrium level of the capital stock are impacted by a fully-funded pension system if the public rate of return is lower than the private one, i.c. no