Problem 1: Hotelling model There are two coffee shops - Blue Donkey and Kaldi's - located on Main Street, which is one mile long. One hundred residents are uniformly distributed along Main Street. Each resident buys one cup of coffee per day. Coffee is differentiated only according to the distance of its seller from the resident. Each consumer's willingness to pay for a cup of coffee is $3.00. Blue Donkey is located at the left end of the Main Street {i.e. at 0], while Kaldi's is located in the middle {i.e. at %]. Consumers face transportation costs of $1.00): from traveling to a coffee shop x miles away. The prices of coffee at Blue Donkey and Kaldi's are p3 and pg, respectively, and the marginal cost of coffee is zero. 1. Write down an equation that determines the location of the marginal consumer who is indifferent between buying coffee from Blue Donkey or Kaldi's. 2. Derive each shop's best response function and solve for Nash equilibrium prices and market shares. 3. Now assume that transportation costs increase to $2.00): for traveling to a coffee shop .1: miles away. Solve for the new equilibrium prices and explain how and why your answer differs from 1.2