Consider two consecutive years, labelled 0 and 1. You are currently at the start of year 0. The following information is available. There is a single fixed stock of a non-renewable resource; the magnitude of this stock at the start of year 0 is 224 (million tonnes). The inverse resource demand functions for this resource in each of the years are

P0 = a-bq0 and P1 = a-bq1

in which a = 107 and b = 1. The constant marginal cost of resource extraction is 5. The social welfare function is discounted utilitarian in form, with a social utility discount rate of 0.1.

(a) Given that the objective is to maximize social welfare over periods 0 and 1, calculate the amounts of resource that should be extracted in each period, subject to the restriction that at least 104 units of the resource should be left (unextracted) for the future at the end of period 1.

(b) What is the resource price in each period?