Gilroy, CA is the garlic capital of the world. Unfortunately, the stench of garlic permeates all...

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Gilroy, CA is the garlic capital of the world. Unfortunately, the stench of garlic permeates all aspects of life in the city. There are only two residents willing to live within city-limits, Abe and Betty. Abe's income is YA = 460, and Betty's income is YB = 440. A traveling salesman is visiting the town, offering odor conversion units, which conveniently input garlic odor and output clean air. Abe and Betty have the same preference (utility function) over clean air (C) and all private consumption goods (r;): U = 5ln(x;) +ln(C), i {A, B} The total provision of clear air is given as the sum of individual purchases: C = CA + CB. The price of clean air is 2 while the price of all private goods is 1. (c) (10 points) What is the socially optimal level of clean air provision? Gilroy, CA is the garlic capital of the world. Unfortunately, the stench of garlic permeates all aspects of life in the city. There are only two residents willing to live within city-limits, Abe and Betty. Abe's income is YA = 460, and Betty's income is YB = 440. A traveling salesman is visiting the town, offering odor conversion units, which conveniently input garlic odor and output clean air. Abe and Betty have the same preference (utility function) over clean air (C) and all private consumption goods (r;): U = 5ln(x;) +ln(C), i {A, B} The total provision of clear air is given as the sum of individual purchases: C = CA + CB. The price of clean air is 2 while the price of all private goods is 1. (c) (10 points) What is the socially optimal level of clean air provision?