Suppose the demand function for a mineral (exhaustible resource) is given by pt = 700 - 0.2qt:
Assuming that the marginal cost of extraction is constant and equal to $200 per unit extracted, and the discount rate (r) is 0:05.
(a) State the values of the maximum(choke) price and marginal revenue
(b) State the equation of resource rent at any time t, both under perfect competition and monopoly while explaining the intuitions
(c) State the equations of the optimal price and extraction paths under perfect competition
(d) State the equations of the optimal price and extraction paths under monopoly
(e) Present, graphically, comparisons of optimal price and extraction paths under perfect competition and monopoly
(f) Assuming that the resource depletes in 5 years, determine prices, quantity extracted, and rents in year 2 under both market assumptions and explain the differences