1) 2) Formulate the typical agent's decision problem and characterize the demand for children as a function of w. Denote the level of utility derived, in equilibrium, by the high (low) ability agent by E (g), respectively, With E > g > 0. Suppose the government is seeking to guarantee a minimal level of well-being given by fl, Where g E > 0. Each agent is endowed with a given amount of time (normalized to unity) that can be allocated between labor and leisure (caring of children). The utility of a typical agent is given by: =1 +b U(C,n)=[:=0 C c where c denotes consumption, n denotes the number of children and b>0, the imputed value of leisure. It is further assumed that the time required for nurturing is given by b _ 0 01W + (1 (JOE. The Council of Economic Advisors has 7) proposed to replace the child benets system with a paid parental leave system, in which eligibility for a transfer is conditioned on the duration of parental leave, denoted by d > a. Reformulate the government problem in light of the suggested reform (notice that there are two incentive compatibility constraintsl). Draw the government optimization problem in the durationtransfer plane, where the duration (6}?) is on the horizontal axis and the transfer (T) is on the vertical axis. Show, graphically, that the social optimum is obtained as a solution for a system of two equations (solved for two unknowns). 3) 4) 5) The Council of Economic Advisors has recently proposed to replace the universal transfer system With a child-benets system, that Will selectively grant a transfer to a household with children. Provide a verbal explanation for the rationale underlying the suggested reform. Characterize the dead-weight loss of the child benet system as a function of the transfer level, T. Show that the suggested reform will be cost-saving when {I S LEW + (1 ODE. Is the First-Best allocation attained in this case