In an industry there are three firms, R1,R2andR3, producing differentiated products. They all have constant marginal costs c1=c2=c3=s=8 In addition the government imposes a per unit sales tax F. The demand functions of their respective products are:

• D1(p1,p2,p3)=402p1+p2+p3
• D2(p1,p2,p3)=40+p12p2+p3
• D3(p1,p2,p3)=40+p1+p22p3

1)Set up the profit functions of the three firms. (5)

2)The three firms are in a two stage price setting competition. In the first stage firm R1 sets its price p1 first. In the second stage, firms R2 and R3 once they observe the price set by R1, set simultaneously their respective prices p2 and p3.

Compute the equilibrium prices and profits in this two stage game, as a function of the sales tax F.