Question 3 (15 points) The cost of controlling carbon dioxide emissions [C(E)] at a firm goes up rapidly as the amount of emissions (E) increase. Let's assume the relationship is defined by the function below. C(E) 5000+40E+ 2E E0 = where E is measured in tonnes per year and C is measured in dollars per year. a) Determine the Marginal Cost function for controlling carbon dioxide emissions and find the marginal cost at 50 tonnes of emissions: (3 points) b) Determine the Average Cost Function for controlling carbon dioxide emissions and find the tonnes of emissions at minimum average cost. (7 points) c) The government is charging a tax of $270 for every tonne of carbon dioxide emitted. At, 50 tonnes of emissions, is it profitable for the firm to control emissions on its own or pay the carbon tax? (5 points)