Question

There is a common pool resource of size 1000. Two firms use the resource in two periods. In the first period, the firms simultaneously and independently decide how much of the resource to use. Let x1 and x2 denote the corresponding amounts of the resource the firms use in the first period. In the second period, the remaining resource is shared equally between the firms, i.e., each of them gets [1000-(x1+x2)]/2. Each firm receives utility √ from using x units of the resource.

(a) Write down each firm's utility as a function of x1 and x2.

(b) Find each firm’s best response to the other firm’s action in the first period.

(c) Find the symmetric Nash equilibrium.

(d) Find each firm’s equilibrium utility.

(e) Suppose the two firms agree to use the resource in a sustainable manner that maximizes their total profit. Find this socially optimal use level in the first period and the resulting profits

Answer 1

A common pool resource is a resource that benefits a group of people, but which provides diminished benefits to everyone if each individual pursues his or her own self-interest. The value of a common pool resource can be reduced through overuse because the supply of the resource is not unlimited, and using more than can be replenished can result in scarcity. Overuse of a common pool resource can lead to the tragedy of the commons problem.

Understanding Common Pool Resource (CPR)

Common pool resources (CPR) such as forests, underground water basins, grasslands, and fisheries are often managed by a combination of government action and market mechanisms. Sometimes a resource is small enough to be collectively managed by interested parties in an honor system; in other cases, valuable resources must be placed under a local government agency altogether. A key goal of CPR management is allowing a certain amount of the resource to be used during a given period while leaving the principal, so to speak, intact. CPR usage is governed by agreements that specify the physical boundaries of the resource, parties involved, allocations, time limitations, authority for dispute resolution, enforcement means, etc.

A common resource (or the "commons") is any scarce resource, such as water or pasture, that provides users with tangible benefits but which nobody in particular owns or has exclusive claim to. A major concern with common resources is overuse, especially when there are poor social-management systems in place to protect the core resource. A common resource may also go by the term open-access resource.

Common resources are those that no one individual or organization can lay claim to. These may include public spaces (such as parks or nature preserves), certain natural resources (such as fish in the sea), and so on.

Overuse of common resources often leads to economic problems, such as the tragedy of the commons, where user self-interest leads to the destruction of the resource in the long term, to the disadvantage of everyone.

The tragedy of the commons is an economic problem in which every individual has an incentive to consume a resource at the expense of every other individual with no way to exclude anyone from consuming. It results in over-consumption, under-investment, and ultimately depletion of the resource. As the demand for the resource overwhelms the supply, every individual who consumes an additional unit directly harms others who can no longer enjoy the benefits. Generally, the resource of interest is easily available to all individuals; the tragedy of the commons occurs when individuals neglect the well-being of society in the pursuit of personal gain.