2. Competitive equilibrium in the Edgeworth economy (25 points total) You are the benevo- lent dictator of Sbarroland, an Edgeworth economy of two people-Alessandra and Bruno-and two goods-pizzas (x) and breadsticks (y). The economy has a total of 20 pizzas and a total of 16 breadsticks. The initial endowment is as follows. Alessandra was born owning 4 pizzas, and she was born owning 13 breadsticks. Bruno was born owning the other 16 pizzas and 3 breadsticks. In Edgeworth-style notation, the initial endowment is therefore (4,13,16,3). Unless you use your dictator powers to prevent them from doing so, Alessandra and Bruno will be able to engage whatever mutually-agreeable trades with each other that they like. Alessandra proposes that the two people trade according to a specific pair of prices, where px is the dollar price of a pizza, and py is the dollar price of a breadstick. Given the specific prices that Alessandra has proposed, Bruno calculates that he could afford to turn his initial endowment of 16 pizzas and 3 breadsticks into a final allocation of 14 pizzas and 9 breadsticks. Given that Bruno has done his calculations correctly, what specific numbers might Alessandra have proposed for px and py? (Note: There are multiple possible correct answers.) Explain. 2 The Edgeworth box shown here represents Sbarroland. It is drawn perfectly to scale (each grid square is 1x1). The picture depicts two of Alessandra's indifference curves (labeled A1 and A2) and two of Bruno's indifference curves (labeled B1 and B2). The picture also depicts two perfectly straight dashed lines, which are not indifference curves at all, but rather are provided as tools to help you answer the questions below. The black dots are also provided as helpful tools: Each dot has whole-number coordinates and sits at a location where two or more curves/lines meet. Breadsticks → 82 B1 Pizzas 10 A1 A2 OB Consider the pair of prices that you named in your answer to part 2a above. Could these prices be part of a competitive equilibrium, given what we know about Alessandra and Bruno? Explain. Now consider the allocation z = (14,8,6,8). Could z be the final allocation for a competitive equilibrium? Explain. (d) Does the initial endowment represent a Pareto efficient allocation? Explain. 3 (e) Is z a Pareto efficient allocation? Explain. (f) True or false: The First Fundamental Theorem of Welfare Economics indicates that a government intervention may be needed in order to ensure that Alessandra and Bruno don't end up consuming their precise initial endowments. Explain.