Observe datas and answer questions/graphs about environmental economics

ECON381/ES312 A02, Page 1 of 5

Assignment 5: Last Name: First Name: Student ID:

1. Recall that in our common pool resource game, groups of n members share a resource where the size, z, is not known. Each group member j ∈ {1...n} requests rj units from the random resource pool. Decisions are made independently and anonymously. If (r1 + r2 + ... + rn < z), each member j is granted his/her request; otherwise, all group members get nothing. For all group sizes the resource level is a random variable drawn from a uniform distribution over support [0, 20n]. Expected profits for individual j are equal to their request size rj times the probability that the resource is allocated P (r1 + r2 + ... + rn < z)

E[Πj] = rjP (r1 + r2 + ... + rn < z) = rj

( 20n− r1 − r2 − ...− rn

20n

) (1)

(a) (5 points) Suppose that rather than sharing the resource, you had exclusive rights: n = 1. Use Figure 1 to draw a graph of how your expected profits vary with your request size. What request size maximizes your expected payoff? What is your expected payoff at the optimal request size?

(b) (5 points) Now suppose that you are sharing the resource with one other person. Furthermore, you happen to know that the other person has requested 40

3 . Draw a graph of how your expected profits

vary with your request size (Figure 2). What request size maximizes your expected payoff? What is your maximum expected payoff?

Please go on to the next page. . .

ECON381/ES312 A02, Page 2 of 5

(c) (4 points) Now suppose that you are sharing the resource with two other people. Furthermore, you happen to know that the other people have requested 60

4 (each). Draw a graph of how your expected

profits vary with your request size (Figure 3). What request size maximizes your expected payoff? What is your maximum expected payoff?

(d) (5 points) Now suppose that you are sharing the resource with three other people. Furthermore, you happen to know that all the other people have requested 80

5 (each). Draw a graph of how your

expected profits vary with your request size (Figure 4). What request size maximizes your expected payoff? What is your maximum expected payoff?

(e) (3 points) How does the request size that maximizes expected profit vary with group size? Hint: How do the improper fraction solutions to the above questions vary with n, the number of people?

Please go on to the next page. . .

ECON381/ES312 A02, Page 3 of 5

(f) (3 points) In the experiment, did request size vary with group size? (use file experiment5.csv)

(g) (3 points) How does the equilibrium expected profit vary with group size? (hint: plug r? for all rj where j ∈ {1..n} into the expected profit function.

(h) (5 points) Did average group size get bigger or smaller as the experiment progressed? Is this consis- tent with the answer to question (g)? (use file experiment5.csv)

(i) (4 points) Did average request get bigger or smaller as the experiment progressed?(use file experi- ment5.csv)

Please go on to the next page. . .

ECON381/ES312 A02, Page 4 of 5

E[Profit]

Request

Figure 1: Expected profit with exclusive rights.

E[Profit]

Request

Figure 2: Expected profit when sharing the resource with one other.

E[Profit]

Request

Figure 3: Expected profit when sharing the resource with two others.

Please go on to the next page. . .

ECON381/ES312 A02, Page 5 of 5

E[Profit]

Request

Figure 4: Expected profit when sharing the resource with three others.

End of assignment