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【正文】 ,0P a Q a? ? ?Cont’d Firm A’s problem: 22()20220A A A A B A AAABABAAAPq c q a q q q c qda q q cdqa q cqddq? ? ? ? ? ? ??? ? ? ? ?????? ? ?Cont’d By symmetry, firm B’s problem. Figure Illustration: Response Function, Tatonnement Process Exercise: what will happens if there are n identical Cournot peting firms? (Convergence to Competitive Equilibrium) The problem of Commons David Hume (1739): if people respond only to private incentives, public goods will be underprovided and public resources overutilized. Hardin(1968) : The Tragedy of Commons Cont’d There are farmers in a village. They all graze their goat on the village green. Denote the number of goats the farmer owns by , and the total number of goats in the village by Buying and caring each goat cost and value to a farmer of grazing each goat is . nthiig1 ... nG g g? ? ?c()vGCont’d A maximum number of goats : , for but for Also The villagers’ problem is simultaneously choosing how many goats to own (to choose ). m a x : ( ) 0G v G ?m a xGG? ( ) 0vG ? m a xGG?39。( ) 0 , 39。39。( ) 0v G v G??igCont’d His payoff is (1) In NE , for each , must maximize (1), given that other farmers choose 1 1 1( . . . . . . )i i i i n ig v g g g g g c g??? ? ? ? ? ? ?**1( , .. ., )ngg *igi* * * *1 1 1( , .. ., , , )i i ng g g g??Cont’d First order condition (FOC): (2) (where ) Summing up all farmers’ FOC and then dividing by yields
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