explain in details please

3. Consider an industry with two firms that produce a homogeneous product. a. The prices charged by the two firms are highly correlated over time. An economist points to this fact as proof that the two firms are colluding. Do you agree? Why? b. Suppose you observe marginal costs (or a good proxy for). How could you test if the firms are colluding? c. If the firms are colluding, how could you test if the collusion follows a pattern predicted by any particular theory? (you can choose any reasonable theory of collusion you like) Your tests can rely on existing work, but be clear about what data you are using, specifically how you plan to use the data, precisely what you are testing, and what are the alternative hypotheses. d. Now assume that you do not observe marginal costs. Without any additional assumptions can you empirically identify the degree of market power in this industry? Explain. (Hint: it may help to demonstrate the identification problem using a graph or using linear demand and cost functions and the associated profit maximization condition.) e. List two possible sets of assumptions that would allow you to identify the degree of market power. Explain. f. Now suppose you are trying to estimate the demand system for a differentiated products industry. What are the difficulties of estimating the own- and cross-price demand elasticities? g. Briefly describe/outline methods available to solve two of the problems you named in (f). h. This is a general IO question. Analyze this "email strategy" for lowering gasoline prices: "For the rest of this year, DON'T purchase ANY gasoline from the two biggest companies (which now are one), EXXON and MOBIL. If they are not selling any gas. they will be inclined to reduce their prices. If they reduce their prices, the other companies will have to follow suit. But to have an impact, we need to reach literally millions of Exxon and Mobil gas buyers. It's really simple to do! Now, don't wimp out at this point.."2. There is a large number / 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 N = 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 6 ) then A"' = ad - be ad - bc C ad -bc ad - bc1.. 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 k 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 DF 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