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Suppose that there is a common resource of size y in a two period society. Each of two citizens, one and two, can withdraw a nonnegative amount c1 or c2 for consumption in period one, provided that c1+c2 <=y . In the event that they attempt to consume in excess of what is available, the total amount will be divided equally between them, i.e., each citizen gets to consume y/2. When total consumption in period one is less than y , the leftover amount,y-c1-c2 , forms the resource base for consumption in period two. In period two, each citizen gets to consume (y-c1-c2)/2 .
Suppose that citizen has the utility function,
Ui (c1,c2)= ln(ci) + ln [(y-c1-c2)/2]
, for i=1,2.
Find the Nash equilibrium pattern of resource use in this game of individual competition and compare it to the pattern of resource use that would be socially optimal.
P.S: i know how to solve the Nash quilibrium for individual, but i don't know how to come up with the social optimization.
Thank you

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