The inverse market demand for bottled water is given by P = 2 0.1Q, where P is measured in dollars; and Q in millions of bottles. The marginal cost of producing one water bottle is given by: MC = 0.2 + 0.08Q. a. Derive the price and the quantity of water bottles consumed in equilibrium, and illustrate your answer on a graph! The use of plastic bottles is damaging to the environment. Bottled water, therefore, entails external costs to society, that are not accounted for by the above (private) marginal cost curve. The marginal external costs are given by MEC = 0.1 + 0.16Q b. Derive the marginal social cost MSC. What would be the socially optimal level of bottled water consumption? Illustrate your answer on the graph that you drew in part (a). c. What is the deadweight loss caused by the over-consumption of bottled water? d. If the government wants to achieve the socially optimal level of bottled water consumption by imposing a per-unit tax of $t on producers, what will this tax be (what is t)? e. On a new graph, illustrate the gains and losses that would result from introducing the per-unit tax that you found in (d): show on the graph and calculate the change in consumer surplus; the change in producer surplus; the change in tax revenues; and the change in external costs. The change in Net Social Benefits (the sum of all the above changes).