Sophia and Theo are two Homo economicus engaged in exchange over sour snakes (x) and peanut...

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Sophia and Theo are two Homo economicus engaged in exchange over sour snakes (x) and peanut butter cups (y) - it's close to Halloween after all. Their utility functions are given by the following: Sophiau = (x7).(y") (1) Theou" = (x").(yT) (2) Sophia has an initial endowment of 5 peanut butter cups(y?) and 13 sour snakes (x2). Theo has an initial endowment of 10 peanut butter aups (y) and 7 sour snakes (x). a. Whatis Sophia's marginal rate of substitution of peanut butter cups for sour snakes (mrs*)? (6 marks) b. Whatis Theo's marginal rate of substitution of peanut butter cups for sour snakes (mrs")? (6 marks) Using their marginal rates of substitution: С. i. Find the equation for the Pareto-efficient curve. ii. What is Sophia's utility at her endowment, (x, y)? iii. What is Theo's utility at her endowment, (x,y!)? iv. Is the allocation at their endowments Pareto-efficient? Explain. (10 marks) d. i. Graph the Edgeworth Box depicting the exchange between Sophia and Theo. ii. Show their initial allocations, their participation constraints, the Pareto-efficient curve, the Pareto-improving lens, and each player's most preferred allocation that they can feasibly achieve. iii. Briefly explain your graph. (10 marks) Sophia and Theo are two Homo economicus engaged in exchange over sour snakes (x) and peanut butter cups (y) - it's close to Halloween after all. Their utility functions are given by the following: Sophiau = (x7).(y") (1) Theou" = (x").(yT) (2) Sophia has an initial endowment of 5 peanut butter cups(y?) and 13 sour snakes (x2). Theo has an initial endowment of 10 peanut butter aups (y) and 7 sour snakes (x). a. Whatis Sophia's marginal rate of substitution of peanut butter cups for sour snakes (mrs*)? (6 marks) b. Whatis Theo's marginal rate of substitution of peanut butter cups for sour snakes (mrs")? (6 marks) Using their marginal rates of substitution: С. i. Find the equation for the Pareto-efficient curve. ii. What is Sophia's utility at her endowment, (x, y)? iii. What is Theo's utility at her endowment, (x,y!)? iv. Is the allocation at their endowments Pareto-efficient? Explain. (10 marks) d. i. Graph the Edgeworth Box depicting the exchange between Sophia and Theo. ii. Show their initial allocations, their participation constraints, the Pareto-efficient curve, the Pareto-improving lens, and each player's most preferred allocation that they can feasibly achieve. iii. Briefly explain your graph. (10 marks)

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