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 12 ). Consumers face transportation costs of $1.00x from traveling to a coffee shop x miles away. The prices of coffee at Blue Donkey and Kaldi's are pB and pK , respectively, and the marginal cost of coffee is zero. 1. Writedownanequationthatdeterminesthelocationofthemarginalconsumerwhoisindifferentbetween buying coffee from Blue Donkey or Kaldi's. 2. Deriveeachshop'sbestresponsefunctionandsolveforNashequilibriumpricesandmarketshares. 3. Now assume that transportation costs increase to $2.00x for traveling to a coffee shop x miles away. Solve for the new equilibrium prices and explain how and why your answer differs from 1.2