1. Given the demand function for a non-renewable resource, Qt = 100 - Qt (Q is in tons, P is in $/ton). Assume that the marginal cost of extraction is constant at c = 10, the interest rate, r is 10% and the fixed available reserve is R = 153 tons. (a) Derive the dynamically efficient price and extraction profiles assuming that exactly 1 unit is sold in period T (b) During how many periods does extraction take place?