#OK to post homework
#George Spahn, 2-13-2022, Assignment 6

#3

TagedyOfTheCommons := proc(v,G,c,n)
local d1:

	d1 := diff(v,G):
	fsolve(v+1./n*G*d1-c=0,G):

end:

# seq(TagedyOfTheCommons(sqrt(1-G),G,0.5,n),n=1..10);
# 0.4108027069, 0.5240408206, 0.5790991062, 0.6120715420, 0.6341606640, 0.6500444109, 0.6620396765, 0.6714307918, 0.6789893673, 0.6852079369


#seq(TagedyOfTheCommons((1-G)^(1/4),G,0.5,n),n=1..10);
# 0.5980909164, 0.7159713145, 0.7695811633, 0.8009276122, 0.8217454810, 0.8366883478, 0.8479928247, 0.8568756419, 0.8640589838, 0.8700002405

#seq(TagedyOfTheCommons((1-G)^(3/4),G,0.5,n),n=1..10);
# 0.3111336476, 0.4083516515, 0.4565628023, 0.4855049838, 0.5048474518, 0.5187020389, 0.5291205868, 0.5372433987, 0.5437555690, 0.5490938253

# As the number of farmers get larger, the total number of goats increases
# getting farther and farther away from the social optimum