Neco 2023 Economics Question 38

The market for a homogeneous product is described by the inverse demand function \( P = 100 - Q \), where \( Q = Q_{1}+Q_{2} \) is total output of two firms. Firm 1 has a constant marginal cost of \( MC_{1}=20 \). Firm 2 has a constant marginal cost of \( MC_{2}=30 \).\n(a) Assuming Cournot competition, determine the equilibrium outputs \( Q_{1} \) and \( Q_{2} \), the market price, and each firm's profit.\n(b) The government imposes a per‑unit tax of \( t=2 \) on Firm 2 only, raising its marginal cost to \( 32 \). Re‑calculate the Cournot equilibrium outputs, price and profits.\n(c) Which firm experiences the larger absolute change in profit as a result of the tax?