1. In this problem we will solve for the general equilibrium for an endowment economy with two agents, A and B and two goods X, and X2. The utility function of A is given by, UA(21, 12) = In z1 + 2 In 12 and the utility function for agent B is B( 21, 12) - 2 lar1 + In 12 The initial endowment is given by, (15,0) for consumer A and (0, 30) for consumer B. (a) (5 points) Find the demand functions for agent A (b) (5 points) Find the demand functions for agent B (c) (10 points) Find the equilibrium in the exchange economy. (Hint: You need to write down the price ratio and an allocation) (d) (10 points) Show the equilibrium in an Edgeworth box and clearly label all relevant objects. () (5 points) Show that both the consumers are better off under the equilibrium than under no trade. Note: the no trade condition is often referred as outarky In economics f) (10 points) Write down the conditions for Pareto optimal allocation for this economny