A mass of 100 beach-goers are uniformly distributed along a kilometre long beach. All consumers value a bag of popcorn at $4. Two popcorn stands are located at either end of the beach (i.e., at 0 and 1). They can produce popcorn at a marginal cost of $1. The two firms compete by simultaneously setting prices.

1. Assumethatbeach-goerscanmovearoundthebeachwithoutincurringanytravelcosts.If the firm at 1 sets a price of 2, what is the best response of the firm at 0? Explain your answer. [3]
2. Again, assume beach-goers can costless move around the beach, what is a Nash equilib- rium strategy profile? Show that your answer is a Nash Equilibrium. [3]

3. For the rest of this question, assume that beach-goers dislike walking. Walking costs for the consumers to the popcorn stands are $1 per kilometre (there and back, i.e., a consumer 0.5 kilometre from a store faces a cost of 50 cents for his trip). For a consumer at location x (between 0 and 1), what is the utility of going to each popcorn stand? [3]

1. Write firm 0's demand as a function of(p0,p1).[3]
2. With costly travel, is your answer to part 2 still a Nash Equilibrium? If so, explain why. If not, show why not. [3]