Let us define a left-wing extremist as a voter whose political views lie to the left of the left most candidate, a right-wing extremist as a voter whose political views lie to the right of the rightmost candidate, and a moderate voter as one whose political views lie between the positions of the two candidates. Assume that each extremist contributes to the candidate whose position is closest to his or her own views and that moderate voters make no campaign contributions. The number of dollars that an extremist voter contributes to his or her favorite candidate is proportional to the distance between the two candidates. Specifically, we assume that there is some constant C such that if the left-wing candidate is located at x and the right-wing candidate is located at y, then total campaign contributions received by the left-wing candidate will be $Cx(y - x) and total campaign contributions received by the right- wing candidate will be $C(1-y)(y-x). In equilibrium, what are the two candidates' positions? 2. [This question regards a business practice called limiting pricing" where the incumbent use price as the instrument to deter entry. Although we didn't spend much time on this topic in class, you'll find the issues illustrated here are closely 1 related to "advertising as a signal" (Ch. 13) and of course "entry deterrence" (Ch 15).] Suppose there is only 1 consumer who has a demand of a product up to 1 unit per period. There are 2 periods. Her willingness to pay is $10 per unit. There are two firms, I and E. Firm I is the incumbent and is the only producer in the 1st period. Firm E is the potential entrant with 0 marginal cost but must incur an entry cost of $1 if entering this market. Firm I knows its marginal cost (c) but Firm E does not know for sure: it knows c is either 0 or 5. Without any further information/signal, Firm E believes the probability for either case is 50%. The timing of the game is the following: Firm I sets the price in the 1st period (pi); Firm E makes its entry decision; Were "not enter" chosen, Firm I will remain as a monopoly in the 2nd period and set the price at $10. Were "enter" chosen, the two firms engage in Bertrand competition in the 2nd period. Lastly, assume both firms have a discount factor of 0.8. 2.a (3 points) Show that if Firm E does not update its belief, its optimal choice is entering this market. Next, we investigate if Firm I is low-cost (c = 0), whether it can signal Firm E this information by setting a particular level of pi. 2.b (3 points) Show that pi = 8 will not do the job. (Hint: The question is whether a high-cost incumbent find mimicking this strategy profitable.) 2.c (4 points) How should Firm I set pi to maximize its profit?