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.
3.
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.