Infinite future periods

Suppose a natural resource can be produced from either raw ore or recycled scrap. The marginal cost of production from ore is given by MEC=Qt/10 where Qt is the total amount of ore extracted to date. The marginal cost of production from scrap is given by MRC=20. Consider allocating the resource over the indefinite future (that is, over an infinite number of future periods), where each period has a demand curve given by P=60-Q/2. You may assume the interest rate is zero and that there is always plenty of scrap.

1. Find the efficient allocation of the resource. Calculate the efficient prices, MECs, royalties and quantities for all periods. In what period does recycling begin? Explain why you can solve this problem for an infinite number of periods.
2. Now suppose that production from ore creates an externality of $10 per unit but no externality is associated with recycling. Would this change the efficient allocation of the resource? If so, describe what would change as precisely as you can. Calculate numerical results, if appropriate.