(c) (6 points) Solve the social planner's problem for a planner who maximizes the sum of the welfare of household 1 and household 2, deriving the first order con- ditions with respect to (c, l,) for each type of agent. (d) (4 points) Find the socially optimal levels of consumption and leisure, i.e., the levels that solve the social planner's problem. (e) (4 points) Compare the Planner's allocations with the competitive equilibrium allocations. Are they the same, i.c., do the Welfare Theorems hold? Explain your answer. (f) (4 points) Is there any need for government intervention in this economy? What policy would you suggest to the government, if any, to restore social optimality