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Assume the preferences of Ann, Bertha. and Chen can be represented by the same utility a 2 function \"(3:1, 3:2} = 3:13". Prices are 111 = 2 and p2 = 2. Ann is initially endowed with monetary income :11 = 120, Bertha is endowed with 50 units of good 1 and 10 units of good 2 (and no money) and Chen has 10 units of good 1 and 50 units of good 2 (no money). Bertha and Chen can buy and sell their endowments at prim p1 and 132. {a} What is the initial demand (Le. gross demand, after computing endowments into income) of Ann, Bertha, and Chen for both goods? (h) Now suppose the price of good 1 increases from 2 to 3. For each of the three consumers, compute the total effect of the price change on good 1, the substitution effect and the income effect, respectively. (c) How can you explain the sign of the income eect for each of the three consumers? Discuss dierences in the total effect between the consumers