Increasing costs and recycling

Suppose that a particular good can be produced from either raw materials or scrap. The marginal cost of raw production depends on the total amount extracted to date and is given by the equation: MEC = QT, where QT is the total amount produced to date. Producing the good by recycling scrap has a marginal cost of $180. The good is to be produced for 4 periods, each of which has a willingness to pay given by: Pi = 200 – Qi, where Pi and Qi are the price and quantity of the good in period i. The interest rate is zero.

1. Find the market equilibrium production and use of this good. Solve for the price, quantity, marginal extraction cost and royalty in each period. How much is produced from raw materials? How much by recycling? Discuss.
2. Now suppose that each unit of raw production creates an externality of $75. What is the efficient amount of raw production? What is the efficient amount of recycling? Discuss how your results from this section compare to those from part (1).