Please answer the following 5 questions

Consider a perfectly competitive market for oil, where oil is being extracted and sold to consumers. There are two time periods, t = 1, 2. The demand and supply equations: 0 Supply: marginal extraction cost = $10/barrel in each period. 0 Demand: marginal private benefit = $40 qt, where qt is the number of barrels produced in period t. Reserves are 20 barrels, meaning that no more than 20 barrels can extracted overall across the two periods. The discount rate is 50%. 1.1 How much oil is extracted in each period? What are the equilibrium prices? What are the scarcity rents? 1.2 Draw a diagram showing marginal net benefits and quantities for the two periods. In the diagram, firstperiod production increases from left to right, and secondperiod production increases from right to left. Suppose the marginal external damages of producing oil are $10 per barrel. Suppose that before production occurs in period 1, the government announces it will tax production at $10 per barrel in period 2, but there will not be any tax in period 1. 1.3 How does the production tax affect prices and quantities in periods 1 and 2? 1.4 Draw a diagram similar to the one in 1.2 showing marginal net benefits and quantities, where marginal net benefits are net of the production tax. Suppose that instead of announcing the tax prior to the beginning of period 1, the government waits until after period 1 to announce that in period 2, production will be taxes at $10 per barrel. 1.5 How much oil is produced in period 2, and what is the price