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Acme and Tartine are identical bakeries and are the only suppliers of baguettes in San Francisco. They have agreed to form a cartel: they jointly

Acme and Tartine are identical bakeries and are the only suppliers of baguettes in San Francisco. They have agreed to form a cartel: they jointly sell Q=16 baguettes and charge p=9. Each bakery shall produce half of the joint quantity. Acme is tempted to cheat on the cartel agreement and increase its own production by 2 units. Acme knows that if they cheat, there is a 50% chance Tartine will catch them and force them to pay a fine of F that is taken out from their profits. If the market demand curve is Q=342P and the marginal cost of producing baguettes is constant and equal to 1 (assume there are no fixed costs), how big does F have to be to make Acme indifferent between cheating and not?

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