Q4. (8 points) Competitive equilibrium and the first welfare theorem. a) (1 point) State the first welfare theorem of economics. b) (1 point) Provide the definition of a Pareto Efficient allocation. c) (1 point) Suppose that a crazy mad dictator allocates all resources in an economy. The dictator gives some resources to every individual. Would the resulting allocation likely be a Pareto Efficient allocation? Answer either "YES" or "NO" in big letters and then explain in 1 sentence. d) (1 point) Suppose that a benevolent dictator allocates all resources in an economy. The dictator gives some resources to every individual. Would the resulting allocation likely be a Pareto Efficient allocation? Answer either "YES" or "NO" in big letters and then explain in 1 sentence.e] [2 point] Suppose that initially a market economy and a command economy are equally developed (in that their economies are just as large) and suppose that the market economy grows at rate 2.0% per year and the command economy grows only a little hit slower, at rate 1.0% per year. Approximately how long will it tale: for the market economy to be twice as. wealthy as the command economy? Hint: We have not covered the formulas for calculating this. It may he useful to review the relevant high-school math (or google the relevant formulas) to do this important calculation. f] {2 points) Provide the graphical OH. formal proof of the rst welfare theorem of economies