Consider a simple one-period, closed economy model where the representative consumer has utility function u(C, l) and h available hours to divide between work and leisure. The representative firm has technology given by Y = zF(K, N^d ). There is a government that imposes a sales tax τ on each unit of the consumption good sold to the consumer. The revenue of this tax finances the provision of public goods G. Consumer’s budget constraint is then (1 + τ )C = wN^s + π.
1. Define a Competitive Equilibrium for this economy. (Hint: Government Budget Constraint must equalize tax revenues and government expenditures).
2. Find the optimal conditions for the CE, that is, characterize the CE.
3. Write down the Social Planner’s problem associated with this economy.
4. Find the optimality conditions for the Social Planner’s problem, that is, characterize the SPP.
5. Is the Competitive Equilibrium Pareto Efficient? Explain in no more than 5 lines.