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2. Consider an exchange economy with two consumer Alice and Ben {denoted by A and B} and two goods coffee and mill: {c and m]. The two consumers have an initial endowment: W4; 2} we; 4] and their preferences are described by the following utility's functions: U'tlir m] Mink\" } ., ._ . , 2 U\"{c.m] = 2s\" + 31:1" a] Draw the preferences of the consumers in an Edgeworth box and display the initial endowment. Construct the set of Pareto efficient allocations {PEA} and the core of the contract more [for simplicity. you can assume 1at91=pc= 1]. h] Find the Wequilihrium allocation {WEA}? c} Explain carefully the implication of the Second Theorem of Welfare Economics for the role of the market and the social planner in a welfarist society. Illustrate your answer with an example