solve 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 clasticities? 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 are N consumers, with the same income, denoted by E, but different preferences concerning quality. Each consumer is characterized by a different value of a parameter . which is uniformly distributed in the interval [0,1]. A firm produces a product of quality .x. where x belongs to the interval [4,10]. Each consumer buys at most one unit. If a consumer identified by the value re [0. 1] of the parameter does not buy the good. his utility is equal to E, while if he buys one unit of a product of quality x at price p his utility is equal to: E- p +xt. (a) Consider first the case of a single-product monopoly with zero production costs. What quality level x would the monopolist choose? What price would it charge and how many units would it sell? Prove your claims. (b) Continue to assume that production costs are zero. Would a monopolist prefer to offer only one quality or to offer two qualities? That is, would the firm choose to be a single- product firm or a multi-product firm? Give a verbal argument without trying to prove your claim (we'll come back to this in point (g). From now on we continue to assume that the industry is a monopoly and also that the monopolist is offering only one product. However, we relax the assumption of zero production costs and we assume instead that the firm has the following cost function: C(q x) =cq where q is output and c is a positive constant with 0