Astravax and Zenevax are price-setting pharmaceutical firms. Each firm has paid 100, ()(0) to develop a vaccine against Covid-19 that cannot be recouped. Each has a production capacity of 300) and faces a marginal cost of production of 100. Both vaccines are equally safe and effective and so are perceived as identical by governments, who purchase vaccines to roll out in their respective countries. Let pi denote the price of the Astravax vaccine and py the price of the Zenevax vaccine. Prices are set simultaneously by the two firms. Demand q; for vaccines of firm : is 1000 - p; if p; is strictly lower than the price of the rival firm, is () if py is strictly higher than the price of the rival firm and is : (1000 - p;) if both firms set the same price, where i = {1, 2}- (a) Find the Nash Equilibrium prices, explaining your reasoning carefully. Are Astravax and Zenevax willing to produce and sell vaccines at these prices? (b) Astravax and Zenevax consider colluding to set prices to maximise industry profits. Find the prices firms would set under such a collusive arrangement, as well as their vaccine sales and profits. Can they sustain collusion? (c) Trials show that antibodies from Covid-19 vaccination fade, and so the population needs to be periodically revaccinated. Astravax and Zenevax therefore interact repeatedly and indefinitely into the future, setting prices simultaneously in every time period t. Astravax and Zenevax have a common discount factor o = 0.1. i) Can Astravax and Zenevax sustain collusion each period as an equilibrium of the infinitely repeated game if cheating is punished as severely as possible forever after? [Hint: cheat- ing is lowering price by an amount c where (), with the rival also doing so] iii) Astravax hires a consultant to review its pricing policy. The consultant suggests adding a number of restrictions to the LPG. Governments can still claim the lower price, but only if they provide sufficient evidence of a price gap, submitted using a special form by a strict deadline. Does this amendment to the LPG harm or benefit governments seeking to buy vaccines? [Refer to the course reading when answering this question]