[Sequential Hotelling Model] (5 points each, 30 points total)Two independent ice cream vendors own stands at either end of a 1-mile long beach. Every day there are 1000 beach-goers who come to the beach and distribute themselves uniformly along the water.Every beach-goer wants exactly one ice cream during the day and values the ice cream from both stands at $100.All of the beach-goers would rather be sunbathing or in the water, so they have a disutility to walking on the beach of $2 per mile.Early's Ice Cream, the firm at location 0, is an early riser and always posts its price first. Cali Creamery, at location 1, is more laid back and posts her price just before the beach opens (the beach requires all prices to be posted by the time the beach opens).Both firms have a marginal cost of $ 4 per ice cream.

Questions:

1, What is the demand for Early's Ice Cream and Cali Creamery, given their prices p0 and p1?

2, What is Cali Creamery's best response function when Early's posts a price of p0?

3, What is the subgame perfect Nash equilibrium for this market?

4, What is the equilibrium outcome for this market?

5, Early's owner feels that his hard work is not paying o, he hires you as a business consultant. He's annoyed that Cali is always undercutting his price and is considering waiting to post so that Cali will not learn his price before naming her own. He wants you to predict how waiting to post his price will aect his prots. What will Early's prots be under this new regime?

6, What advice do you give Early's owner?