Please solve this problem numerically using EXCEL except where indicated. Consider an ore mine that is estimated to contain about 102,000 tons of ore suitable for extraction. Estimated market demand for the ore is specified as Q=666,667-67P, where Qis quantity of ore in tons and P is the price of ore in dollars per ton. Total costs of extraction are TC = 8,0000+.010, and the discount rate is 8.5%. A full set of property rights over the ore gives the rights holder the exclusive ability to extract in perpetuity. a. Set up the monopolist's optimization problem analytically, derive the first-order conditions for the problem, and interpret these conditions. Comment on the realism of the assumed cost function. b. Numerically solve the problem using EXCEL, and determine the following: optimal extraction and price profile, the time path of the stock, total discounted profits to the monopolist, and the overall net social benefit to society of production. (HINT:, the optimal time horizon is between 5 and 10 years). c. Does a Hotelling-type rule hold for your solution? Why or why not? d. Qualitatively describe the price and extraction path for the monopolist. e. Now solve the same problem for a social planner, and compare and contrast the price and extraction profile between the socially optimal path and the monopolist's path. Is it still true that the monopolist restricts output? f. If we took into account a constant negative externality due to CO2 combustion and placed a carbon tax per unit extracted, how would the optimal extraction path for the social planner change? Comment on how this policy would ultimately impact total carbon emissions from this deposit.