Cournot Duopoly with Tariff

Inverse Demand Function

p(z)=a-bz=a-b(x+y)

Foreign firms

π*=x(p(z)-t)-C*(x)=x(a-b(x+y)-t)-cx

FOC ⇒ Reaction Function of Foreign Firms

x=r*(y,t)=(a-c-t)/(2b)-(1/2)y

Home firms

π=y(p(z)-t)-C(y)=y(a-b(x+y)-t)-cx

FOC ⇒ Reaction Function of Home Firms

y=r(x)=(a-c)/(2b)-(1/2)y

Nash Equilibrium

x=(a-c-2t)/(3b)

y=(a-c+t)/(3b)

t↑⇒ x↓, y↑ (C→D)