### How many tons of ice cream will the factory produce

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An ice cream factory produces output at C=q^2, where q is the quantity of ice creams produced, in tons. in addition, 2 units of emissions are produced for each ton of ice creams (e=2q). pollution damage is \$2 for each unit of emissions, which leads the government to charge \$2 per unit of emissions as a Pigovian fee. the firm's output sells competitively for \$10 per ton.

q1: how many tons of ice cream will the factory produce? how much does it pay in emission fees? what are its profits?
q2: a device is invented that would reduce the firm's emissions to one unit for each town of output (e=q). how much would the firm be willing to pay for such a device?

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