Help with question about General Equilibrium?

5. General Equilibrium a) What condition on preferences/utility is required to guarantee existence of a competitive General Equilibrium? b) There are two goods x and y and two economic "agents". Let the initial endowment of x be 20 for Agent A and 80 for Agent B, and the initial endowment of x be 30 for Agent A and 20 for Agent B. Draw the Edgeworth box for where the two economic agents have convex indifference curves. Mark the initial endowment point and draw the budget constraint/price line, as well as the agent's indifference curves at the initial endowment. Shade in the outcomes that will make both agents better off. c) T/F - True or False - a competitive general equilibrium is Pareto efficient - True or False - a competitive general equilibrium outcome gives higher weight in the Social Welfare Function to the agent with more initial wealth - True or False - if preferences are convex then the competitive general equilibrium is guaranteed to be unique