Suppose two firms compete by choosing quantities and that neither of them sees the other’s quantity

1. Suppose two firms compete by choosing quantities and that neither of them sees the other’s quantity before having to commit to its own production level. Inverse market demand is given byp(Q) = 100-2Q;where Q is industry quantity. Firm 2 has a cost advantage over Firm 1 in small quantities, but Firm 1 is able to produce at lower marginal cost at larger quantities. This is reected in the followingcost technologies: C1(q1) = 4q1and C2(q2) = 2q2^2, where q1and q2are Firm 1 and Firm 2 quantities,respectively.(a) What are the equilibrium quantities in this market?(b) What is the equilibrium price?(c) Suppose Firm 2 is shut down. What will Firm 1’s new quantity be?(d) What measurable harm has this closure had on consumers?(e) In a surprise move, Firm 2 is allowed to re-open. However, Firm 2 is now strictly following Firm 1, who has already determined how much it will produce this period (i.e., that quantity foundin (c)). What will Firm 2’s quantity be upon re-entry?(f) What is the new equilibrium price?(g) Even though Firm 2 is explicitly choosing quantity after Firm 1, this is not a Stackelberg game. From Firm 1’s perspective, what difference will this make? (E.g., how would q1dffier and why?)