(0) Q1. An economy has two consumers, A and B, and two goods, x1 and x2. The data of the economy, utility functions and initial endowments, are given below: A: U A(x A 1 , xA 2 ) = x A 2 , (w A 1 , wA 2 ) = (1, 0) B: U B(x B 1 , xB 2 ) = x B 1 x B 2 , (w B 1 , wB 2 ) = (0, 1) Q1.1 For this economy, define i) an allocation, and ii) a Pareto efficient allocation. Find all Pareto efficient allocations for this economy. Q1.2 For this question, consider a different set of initial endowments from the earlier one: we suppose A is endowed with one unit of time and B is endowed with one unit of good 1. A firm that is owned by B produces good 2 with the production function y2 = 3z A, where z A is the amount of labor A sells to the firm. Time does not enter A's utility function and so A is willing to sell the entire unit of time to the firm. For this economy, define a "competitive equilibrium", and find it. Explain if the resulting competitive equilibrium allocation is Pareto efficient. Q1.3 Suppose you would like to increase B's utility to U B 0 that is greater than the utility B gets in Q1.2. Explain as precisely as you can how you can accomplish this objective without causing any inefficiency. Q1.4 Let's return to the original economy of Q1.1 (that is, there is no time, no firm, no production). Suppose instead that B's utility function is given by U B (x B 1 , xB 2 ) = x B 1 x B 2 x A 1 That is, A's consumption of good 1 reduces B's utility. Find the competitive equilibrium of this economy. Is the equilibrium allocation Pareto efficient? Explain. Q1.5 Continuing with economy of Q1.4. Suppose there is a market where A must buy from B the right to consume good one. Find the competitive equilibrium of this economy. Is the outcome Pareto efficient? Explain. can you please help with the solution