The inverse market demand for coffee in cafes and restaurants (hereafter 'coffee outside') is given by = 10 , where is measured in dollars; and in hundreds of millions of cups. The marginal cost of producing one standard-size cup of coffee is given by: = 1 + 0.5. a. Derive the price and the quantity of cups of coffee consumed in equilibrium, and illustrate your answer on a graph!

The use of disposable cups is damaging to the environment. Coffee consumed outside, 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 = 0.5

b. Derive the marginal social cost . What would be the socially optimal level of consumption of coffee outside? Illustrate your answer on the graph that you drew in part (a).

c. What is the deadweight loss caused by the over-consumption of coffee in restaurants and cafes? d. If the government wants to achieve the socially optimal level of coffee consumption by

imposing a per-unit tax of $ on producers, what will this tax be (what is )?

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; the change in external costs; and the change in Net Social Benefits (the sum of all the above changes).