Two factories dump industrial waste into a stream. They can reduce their waste (abate), but it is costly. The Marginal Cost of Abatement (MCA) for factory 1 is 10 + 2A1, and for factory 2 is 5 + A2, where Ai is the amount of pollutants that have been abated. The municipal government has opted for a Cap and Trade policy. The cap effectively requires the firms to reduce total pollution by 30 units. Permits are issued to Firms 1 and 2 such that Firm 1 will have to abate by 10 units and Firm 2 will have to abate by 20 units. 

a) If trade of permits is not allowed, what will be the costs of abatement to each firm? 

b) If trade of permits is allowed, what will be the abatement and marginal cost levels for each firm? 

c) What will the total cost of abatement be after trade of the permits? 

d) If we assume that all permits are bought/sold at the marginal cost you found in part b), what will be the net abatement costs for each firm?