Question: Two local ready- mix cement manufacturers, Here and There, have combined demand given by Q = 10 – P, where Q=Q₁+Q₂. Their total costs are given by \[T{{C}_{\text{1}}}=\text{5}+{{Q}^{\text{2}}}_{\text{1}}\] and TC₂ = 5 + Q²₂.

(a) If they engage in price competition, what is the equilibrium price? What is the output of each firm?

(b) If they successfully collude, what is the equilibrium price? What is the output of each firm?

(c) If managers at these two firms set their own output levels to maximize profit, assuming that managers at the other firm hold constant their output, what is the equilibrium price? What is the output of each firm? How much profit do managers at each firm earn?