There are two firms producing an identical product. Suppose firm 1 is located in the city centre where consumers can easily access it and buy the product. But firm 2 is located outside the city where buyers have to travel and pay a travel cost equal to $t if they choose to buy from it.

Both firms are competing by choosing the prices P1 and P2. A consumer buy from firm 1 if its price is less than firm 2's final price (price plus travel cost), and other way around,if the two final prices are the same the buyer toss a coin and choose from which firm to buy.

a.) Find the best response functions of firm 1 and firm 2 (or P1*(P2) and P2*(P1)).

b) guess what is the nash equilibrium price for this game. Explain why you believe your suggestion is a NE