Suppose a market featuring two goods that differ in quality. Good 1 is of quality 51 and good 2 is of quality 52, with 32 > 81. There is a mass of n = 1 consumers, of different types, identified by a taste parameter 6 ~ LIN/b]. Consumer's utility function is given by 11(9) 952 7 p if it buys one unit of good with quality 5 0 otherwise In What follows, assume $1 = 1 and 52 = 2. In other words, firms cannot choose their quality, this is given and does not change. Firms cost functions are given by: Ci(qi) : Cquf for 1' : 1, 2 where qt is the output of firm 1'. We will also conjecture that parameter values are such that there is full coverage. a) (5 points) Find the taste parameter (3 that identifies a consumer who is indifferent between buying a unit of good 1 or a unit of good 2. b) (5 points) Derive an expression for the demand functions of each good (ie., the demand functions that each firm is facing separately). c) (5 points) Set up each firm's problem. Find the firms' reaction functions and solve for the equilibrium prices d) (5 points) Assume now that c : O, a : 1.2 and b : 3 Find the prices, quantities and profits for each firm. What are the market shares for each firm? Verify that the market is indeed fully covered (HintThz'nk on the condition that needs to he met so that the market is fully covered)