Question: The market for widgets consists of two firms that produce identical products. Competition in the market is such that each of the firms independently produces a quantity of output, and these quantities are then sold in the market at a price that is determined by the total amount produced by the two firms. Firm 2 is known to have a cost advantage over Firm 1. A recent study found that the (inverse) market demand curve faced by the two firms is

and the costs are \({{C}_{1}}\left( {{Q}_{1}} \right)=3{{Q}_{1}}\) and \(C\left( {{Q}_{2}} \right)=2{{Q}_{2}}\).

1. Determine the marginal revenue for each firm.
2. Determine the reaction function for each firm.
3. How much output will each firm produce in equilibrium?
4. What are the equilibrium profits for each firm?

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