An ice cream factory forms the output at C=q^2, where q is the quantity of ice creams formed, in tons. In addition, two units of emissions are formed 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 the $10 per ton.
1. Determine the numbers of tons of ice cream will the factory produce? How much does it pay in emission fees? What are its profits?
2. How much would the firm be willing to pay for such a device when a device is invented that would reduce the firm's emissions to one unit for each town of output (e=q).