2. Competitive equilibrium in the Edgeworth economy (45 points total) You are the benevolent 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 $p_x$ is the dollar price of a pizza, and $p_y$ 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.
