2. There is a common pool resource of size 1000. Two firms use the resource in...

2. 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.

Expert Solution

Rahul Sunny answered 1 year ago

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