Problem four

Two firms in a homogeneous$-$product duopoly market $($firm $1$ and firm $2)$ have the following cost and demand functions: $T{C}_1=4q_1$;$T{C}_2=4q_2$ and $Q=40-P$;$Q=q_1+q_2.$

a$)$ Derive the reaction function$/$best$-$response function for each firm.

b$)$ Compute the outputs, price and profit for each firm under Cournot equilibrium.

c$)$ Compute the outputs, price and profit for each firm under Stackelberg equilibrium