Hello tutors please help

2. There is a large number N of consumers, with identical preferences but different incomes. Incomes are uniformly distributed in the interval [0,1]. There are two possible quality levels for the good: H (high) and L (low). Each consumer buys at most one unit of at most one good. A consumer with income te[0,1] has the following utility function: if she does not buy the good U(k ) [t - p] if she buys one unit of a good of quality k e (L, H ) at price P. Use the following notation: x = U(H) and y = U(L) and assume that x =10, y = 2 and / = 1,200. There are two firms, A and B. For both firms the cost of producing a low quality good is zero. For firm A the unit cost of producing a high quality good is constant and equal to 0.3. For firm B the unit cost of producing high quality is constant and equal to 0.4. Find all the (pure-strategy) subgame-perfect equilibria of the following two games. GAME 1 The two firms play the following two-stage game. In stage 1 they simultaneously decide whether to produce high quality or low quality. In stage 2, after having observed the stage 1 choices of both firms, they simultaneously choose prices (Bertrand competition). Assume that if the two firms have both chosen high quality then the Bertrand-Nash equilibrium (BNE) is given by both prices equal to the higher of the two costs with firm A serving the whole market. GAME 2 The two firms play the following two-stage game. In stage 1 they simultaneously decide whether to produce high quality or low quality. In stage 2, after having observed the stage 1 choices of both firms, they simultaneously choose output levels (Cournot competition). Recall that if A - ( a b ) then A-' = ad -be add - be C ad -be ad -be1.. Consider the following multi-stage game. In the first stage an incumbent monopolist decides whether to be passive or committed. Commitment costs $C and is irreversible. In stage two Nature (i.e. a random mechanism) selects the opportunity cost of entry kek (that is, the profit that the potential entrant could make in the best alternative investment) according to the cumulative distribution function F [thus, for every number x, F(x) is the probability that the opportunity cost of entry & is less than or equal to x]. In stage three the potential entrant observes the opportunity cost of entry which Nature selected and decides whether to enter or not. If she doesn't enter, the incumbent remains the only firm in the market. Monopoly profits are given by $M. If entry occurs, a duopoly game between the two firms follows. Let D, and D be the incumbent's and entrant's profits, respectively, at the Nash equilibrium of the duopoly game following entry with a passive incumbent, and H, and H be their respective profits at the Nash equilibrium of the duopoly game following entry with a committed incumbent (H, includes the commitment cost C). (a) Assume that K = [a, b] (the closed interval between a and b, 0