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Your eq (2.10) is not more general than (2.9), but corresponds to an alternative specification. A more general version would be: $$ C_i(Q_i)=FC_i+a_{1,i}Q_i+a_{2,i}Q^2_i. $$ This specification allows marginal cost to be constant as in (2.9) if $a_{2,i}=0$ or nonconstant as in (2.10) for $a_{1,i}=0,a_{2,i} \neq 0.$ It is more general because it is compatible ...

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