You are the Minister and are considering a project providing citizens with a service. It is common knowledge that the demand for this service is given by P = 10 – Q, where P is the price and Q is the amount/level of service used by citizens.

1. Your Deputy Minister claims this service has a constant marginal cost of $8. If you believe her, what would be the optimal amount of service? (that is, what is the quantity of service that maximize total surplus?) What is the total cost of this project (that is, how much should you allow your Deputy Minister to spend on this project) ? Also show in a demand diagram, the optimal quantity, the area corresponding to the total cost of the project, and the area corresponding to the gross value of the project.

For questions 2 and 5, we will look at this project from the point of view of the Deputy Minister, so now imagine you are her. You know the true marginal cost of the project is $1, but you know the Minister does not know it, and you report to him a marginal cost of $8.
2. Assuming the minister orders you to provide the level of service from question 1 and allows you to spend the corresponding budget from question 1, how much “slack” did you create for you? Also show in the diagram you used to answer question 1, the area corresponding to this “slack”.

For questions 3 and 4 assume the service, instead of being provided by the Ministry, is provided by a monopolist. The monopolists knows the true marginal cost of the service, $1. For the demand P = 10 – Q, the marginal revenue of is given by MR = 10 – 2Q.
What level of service would the monopolist provide? How much is the monopolist’s profit, and what is the deadweight loss created by the monopoly? Also show, in a demand diagram, the area corresponding to the monopolist’s profit and the area corresponding to the deadweight loss.

4. Assuming many firms engage in wasteful competition to be appointed as the monopoly provider of this service, what is the deadweight loss caused by rent-seeking behaviour?

5. If the Deputy Minister wishes to maximize her “slack”, what is marginal cost she should report to the Minister?

Note that is this assignment the Minister is not so dumb as the example in the textbook, where is allows the Deputy to choose the level of service. Here the Minister, after hearing Deputy’s report about marginal cost, chooses the level of service.