Exercise 9' VarsaI pmduct dwamntsatio and product withdrawals A continuum of consumers of mass 1 have unit demand for a product that may be available in a lowquality and a high-quality version. A consumer of type 3 has valuation 1 +Hq p for the version with quality :3 sold at price p; the outside option of not buying in the market gives valuation {1. Type E is uniformly distributed on [11,1]. One or two rms are active in this product marl-Let. Their marginal cost of production is equal to zero and, thus, independent of quality. 1. Consider the market environment in which rm 1 is a monopolist and oers a lowquality version sf, 2 and a highquality version a H = 2. The regulator requires the rms to set its prices such that all consumers buy in the marl-Let. Determine the monopoly solution [the monopolist sets 31;, and pg}. 2. Suppose that the lowquality version s1, is not provided by rm 1, but by rm 2. Firm 1 continues to offer .93. Characterize the duopoly solution of the game in which the two rms simultaneously set prices. 3. Suppose now that rm 1 offers both versions 3L and 31-1 and rm 2 3L. Characterize the duopoly solution of the game in which the rm 1 sets 31}, and Pi: and rm 2 simultaneously sets pi. 4. Suppose that rms have to pay a xed cost If 1': 13'?- for each product they offer. Firm 1 has versions L and H available {it may offer none, either one, or both] and rm '2- has only version L avaialable [it may offer this or no version}. At stage 1, rms decide simultaneously whether to withdraw any of the versions. At stage 2, they incur a xed cost If for any version they offer and simultaneously set prices for each available version. Characterize the subgame-perfect equilibrium of this game