# Tag Info

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 ...