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Economics

Two firms, i = 1,2, produce the same good. Each firm i's cost of producing quantity q_{i} is given by C_{i}(q_{i}) = q{_{i}}^{2} . The market demand is given by P_{d}(Q) = a-Q for all Q = q_{1} + q_{2}\leq a (with P_{d}(Q) = 0 for Q> a).

(a) Assume that the two firms choose their quantities simultaneously. Find the Nash equilibrium.

(b) Assume that the two firms choose their quantities sequentially. Find the subgame perfect equilibrium.

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