We consider a cap-and-trade system that covers two firms. There are two types of emitters. They are called 1 and B, and are modeled by their marginal abatement costs functions; Type A: MAC (e) =100 - e and Type B: MAC,(e) =300 - 3e. For simplicity, it is assumed that o ≤ e S 100 for both types of emitters. In your cap-and-trade system there is one emitter of Type A and one of Type B. Each firm is awarded 7s permits, counting one unit of emissions each. That is, if a firm wishes to emit more (i.e. e>75), it will need to purchase additional allowances from the other firm 

Create a chart that illustrates the two marginal abatement cost functions. Use this chart to explain why any trade between the two would involve 4 selling permits to B. HINT: Have emissions, e, on the first axis (the "x-axis"). 

Illustrate the supply and demand curves and calculate the clearing price. Additional information 

The cap-and-trade system is proving effective, and regulators have decided to include 8 additional firms to the system. Two of these firms are of Type A and the remaining six firms are of Type B. The cap-and-trade thus counts three firms of Type A and seven firms of type B. For simplicity, it is assumed that o S e S 100 for all emitters. Each firm is awarded 7 permits. 

Illustrate the supply and demand curves and calculate the new clearing price.

 
Assume that "Type A" and "Type B" reflect technology choices, and that emitters of Type B can switch type at a cost. If only one firm switches, what are the cost savings for that firm? Will those cost savings also apply to the next emitter that shifts from Tune B to Tune A? 

In 400 words or less, explain how your analysis above can help us understand the relationship between cap-and-trade systems and investments in abatement technologies