There is a common pool resourc
There is a common pool resource of size 1000. Two firms use theresource in two periods. In the first period, the firmssimultaneously and independently decide how much of the resource touse. Let x1 and x2 denote the corresponding amounts of the resourcethe firms use in the first period. In the second period, theremaining resource is shared equally between the firms, i.e., eachof them gets [1000-(x1+x2)]/2. Each firm receives utility √ fromusing x units of the resource.
(a) Write down each firm’s utility as a function of x1 andx2.
(b) Find each firm’s best response to the other firm’s action inthe 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 asustainable manner that maximizes their total profit. Find thissocially optimal use level in the first period and the resultingprofits
Answer:
A common pool resource is a resource that benefits a group ofpeople, but which provides diminished benefits to everyone if eachindividual pursues his or her own self-interest. The value of acommon pool resource can be reduced through overuse because thesupply of the resource is not unlimited, and using more than can bereplenished can result in scarcity. Overuse of a common poolresource can lead to the tragedy of the commons problem.
Understanding Common Pool Resource (CPR)
Common pool resources (CPR) such as forests, underground waterbasins, grasslands, and fisheries are often managed by acombination of government action and market mechanisms. Sometimes aresource is small enough to be collectively managed by interestedparties in an honor system; in other cases, valuable resources mustbe placed under a local government agency altogether. A key goal ofCPR management is allowing a certain amount of the resource to beused during a given period while leaving the principal, so tospeak, intact. CPR usage is governed by agreements that specify thephysical boundaries of the resource, parties involved, allocations,time limitations, authority for dispute resolution, enforcementmeans, etc.
A common resource (or the “commons”) is any scarce resource,such as water or pasture, that provides users with tangiblebenefits but which nobody in particular owns or has exclusive claimto. A major concern with common resources is overuse, especiallywhen there are poor social-management systems in place to protectthe core resource. A common resource may also go by the termopen-access resource.
Common resources are those that no one individual ororganization 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 leadsto the destruction of the resource in the long term, to thedisadvantage of everyone.
The tragedy of the commons is an economic problem in which everyindividual has an incentive to consume a resource at the expense ofevery other individual with no way to exclude anyone fromconsuming. It results in over-consumption, under-investment, andultimately depletion of the resource. As the demand for theresource overwhelms the supply, every individual who consumes anadditional unit directly harms others who can no longer enjoy thebenefits. Generally, the resource of interest is easily availableto all individuals; the tragedy of the commons occurs whenindividuals neglect the well-being of society in the pursuit ofpersonal gain.
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