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The profit function is given by: $$ \pi = PQ(P) - C(Q(P), \mu) - tQ(P) $$ Assume demand is linear, s $$ p = \alpha - \beta Q \to Q = b(\alpha - P), $$ where $b = 1/\beta$. So: $$ Q_P = -b, $$ where I use subscripts to denote the partial derivatives. The first order condition for profit maximisation gives: $$ \begin{align*} &Q + P Q_P - C_Q Q_P - t ...


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