First Welfare Theorem 1. Write down the social planner's problem and its two optimality conditions in the Real Business Cycle model with G > 0. 2. Describe the planner's Pareto optimal allocation on the consumption-leisure plane. On the same graph, describe a competitive equilibrium when the government nances G imposing lump sum tax T. Compare the Pareto optimal allocation and a competitive equilibrium. Interpret what you observe. 3. The government nances G using a labor income tax T; instead of the lump sum tax. Describe a new competitive equilibrium on the consumption-leisure plane. Do you observe the same relationship between the Pareto optimal allocation and a new competitive equilibrium as above? Explain the implication of the new observation