Consider the following duopoly with differentiated goods where x1and x2denote the amounts of the goods 1 and 2 respectively, with prices p1 and p2. The demand functions are:

x1=1-2p1+ p2

x2= 1-2p2+ p1

And the corresponding unitary production costs are c1= 0 and c2= 0.5

Determine the solution under perfect competition between the two firms. Report prices, quantities and profits.