Consider an economy with two agents, Bunter and Quelch, and two goods, apples and oranges. If...

 

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Consider an economy with two agents, Bunter and Quelch, and two goods, apples and oranges. If Bunter consumes rg units of apples and yB units of oranges, his utility will be uB(TB, YB) = XB YB- If Quelch consumes ro units of apples and YQ units of oranges, his utility will be uo(xQ, yQ) = min{rQ, yQ}. In this economy, Bunter owns all of the apple trees, and Quelch owns all of the orange trees. Before the two agents engage in trade to reach the Walrasian equilibrium, there is a chance that a blight will descend upon Bunter's apple trees. If there is no blight, Bunter will receive 24 units of apples; if there is a blight, Bunter will be left with only z units of apples, where 0 < z < 24. The blight does not affect orange trees, so Quelch will always receive 16 units of oranges. After the two agents receive their endowment of fruit, they engage in competitive trade. All of the details of this economy and the endowments, including the extent to which a blight has affected Bunter's apple trees, are common knowledge to both Bunter and Quelch at the beginning of trade. 1. Find the Walrasian equilibrium allocation and prices for this economy if there is no blight. Let oranges be the numeraire. 2. Find the Walrasian equilibrium allocation and prices (as a function of z) for this economy if a blight leaves Bunter with z units of apples. Let oranges be the numeraire. 3. At the beginning of time, Bunter hopes that none of his apples will be lost to blight. His reasoning is that "he will always be better off in the Walrasian equilibrium if he participates in trade with more apples, rather than fewer apples". Determine if Bunter is correct that losing no apples is the best-case scenario for him; if he is not correct, also determine what Bunter should hope for instead (in other words, the size of the blight that will make him the best off in the Walrasian equilibrium). Consider an economy with two agents, Bunter and Quelch, and two goods, apples and oranges. If Bunter consumes rg units of apples and yB units of oranges, his utility will be uB(TB, YB) = XB YB- If Quelch consumes ro units of apples and YQ units of oranges, his utility will be uo(xQ, yQ) = min{rQ, yQ}. In this economy, Bunter owns all of the apple trees, and Quelch owns all of the orange trees. Before the two agents engage in trade to reach the Walrasian equilibrium, there is a chance that a blight will descend upon Bunter's apple trees. If there is no blight, Bunter will receive 24 units of apples; if there is a blight, Bunter will be left with only z units of apples, where 0 < z < 24. The blight does not affect orange trees, so Quelch will always receive 16 units of oranges. After the two agents receive their endowment of fruit, they engage in competitive trade. All of the details of this economy and the endowments, including the extent to which a blight has affected Bunter's apple trees, are common knowledge to both Bunter and Quelch at the beginning of trade. 1. Find the Walrasian equilibrium allocation and prices for this economy if there is no blight. Let oranges be the numeraire. 2. Find the Walrasian equilibrium allocation and prices (as a function of z) for this economy if a blight leaves Bunter with z units of apples. Let oranges be the numeraire. 3. At the beginning of time, Bunter hopes that none of his apples will be lost to blight. His reasoning is that "he will always be better off in the Walrasian equilibrium if he participates in trade with more apples, rather than fewer apples". Determine if Bunter is correct that losing no apples is the best-case scenario for him; if he is not correct, also determine what Bunter should hope for instead (in other words, the size of the blight that will make him the best off in the Walrasian equilibrium).