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 by
p(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 following cost technologies: C1(q1) = 4q1 and C2(q2) = 2q2^2, where q1 and q2 are 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 found in (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 q1 dffier and why?)