Consider a two firm differentiated product environment where firms choose their pricebut not their producttype. The product is differentiated in one dimension: in particular, the good can take on types ranging from zero to one. As we saw in class, consumers derive an inherent utility from consuming one unit of the good( v), paya pricepifor it (whereican be either 1 or 2, depending which firm they are buying from) and incur in alinearadjustment cost (dis-utility) oft=1 when deviating from their favorite type. Consumer types are identifiedwith the parameterwhich is distributeduniformlyin the [0,1] interval. Suppose now a differentiated product environment where there are N firms, located equidistantly one from theother and sharing the same cost function:C(qi) =12qi+110. Consumers in this market are assumed to behave inthe exact same way as before.

a) (3 points) What is the demand function that a firmiis facing in this market? Provide a clear expression

b) (3 points) Set up firmis maximization problem and find the optimal price. Use this to obtain firms profits

c) (4 points) Find the equilibrium number of firms in the market (if you obtain a non-integer number, thenconsider only the integer part of your number to answer this question). Suppose fixed cost drops to181.What is the new number of firms? Provide an explanation to your results.