1.Assume there is a continuum of depositors, uniformly distributed along a circle of length 1, each endowed with one unit of cash.The total mass of deposits is denoted by D.There are n banks (indexed by i=1,...,n) located on the same circle.The banks collect deposits and invest the funds in a riskless technology with a constant rate of a per unit of distance traveled.The transportation cost for a depositor located at distance x_i from bank i is, therefore, x_i.

(a)Assuming free entry by banks and a fixed set up cost of F, derive the number of banks that will enter.40%

(b)Derive the number of banks that minimizes total costs (set-up costs plus transportation costs). 40%

Compare your answers in (a) and (b) and comment.