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Economies of Crime: In an illegal market with three gangs, two gangs form a coalition (doubleton) to compete against the third gang {singleton}. The...
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ECONOMICS 350, mathematical economics 1, unconstrained optimization problem:

d. Economies of Crime: In an illegal market with three gangs, two gangs form a coalition
(doubleton) to compete against the third gang {singleton}. The singleton (S) and doubleton {D}
therefore engage in Com-not competition by choosing quantities as}: and q” . The market demand
for die illegal goods is p = ﬂ- ﬂag + on] , the probability of each group getting arrested is in
proportion {I to the quantity of illegal goods+ and the prison sentence if they are arrested is s .
Each group has proﬁt consisting of revenue minus cost, where the cost is the expected punishment, resulting in profit functions is =[ﬁ -y(q3 + qﬂ}]qs ﬁtting and
ID =[ﬁ- ﬁgs + qr, ﬂqﬂ -2m~q0. Use the FDIC’s {one S undone for D) to find the optimal quantiﬁes.

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