Astravax and Zenevax are price-setting pharmaceutical firms. Each firm has paid 100, 000 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 p1 denote the price of the Astravax vaccine and p2 the price of the Zenevax vaccine. Prices are

set simultaneously by the two firms.

Demand qi for vaccines of firm i is 1000 - pi if pi is strictly lower than the price of the rival firm, is 0 if Pi is strictly higher than the price of the rival firm and is 1/2(1000 pi) 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?

Hello could you please help with these two questions? (detailed answer would be appreciated)