Rising extraction costs and recycling

Suppose that a particular resource can be produced from either raw ore or by recycling. The marginal cost of production from raw ore is given by MEC = Qt where Qt is the total amount of ore extracted to date. The marginal cost of producing it from scrap is given by MRC = $120. In addition, producing the resource from raw ore causes an externality of $80 per unit but there is no externality associated with recycling.Consider allocating the resource over four periods where each period has a demand curve given by Pi = 200 – Qi. You may assume the interest rate is zero and that there is always plenty of scrap.

1. Find the total market production of the resource (that is, the total over all the periods).
   
2. How much of this is produced from raw ore? How much by recycling? Is this efficient? Discuss why or why not in detail and illustrate your answer with an appropriate graph.