1. An small amethyst mine has reserves of 34 tonnes of ore. It receives a price of $201 per tonne of extracted ore, has costs of C(q) = 400 + 492 (where q is the quantity of ore extracted in tonnes per year), and faces discrete-time interest rates of 10%. (a) What is the optimal extraction path for the firm ? (b) What is the effect of a 20% profits tax on the extraction path? (c) What is the effect of a $500 per year operating license fee on the extraction path? (d) What would be the effect on extraction of not having any signifi- cant stock constraint (i.e, enough stock for hundreds of years) (Hint: This is the situation faced by most firms that are not dependent on resources)