Pre-mixed concrete is an important input for the construction industry. Concrete cannot be stored or transported over long distances as it begins to set after only a few hours. For this reason, only the three local firmsAggregate Inc., Big Industries and ConCorpare in a position to compete in the market. Moreover, the capital and regulatory requirements for constructing a new concrete plant are substantial, creating an effective barrier to entry. Pre-mixed concrete is regarded as a homogeneous good by the construction industry. Inverse demand in the market has been estimated to be,

P= 600Q 50,

where P represents the price of a cubic metre of concrete in dollars, and Q is the total number of cubic metres of concrete supplied into the market on a given day. At present the three firms appear have identical production costs, with each firm facing fixed costs of $400,000 per day and a marginal cost of $180 per cubic metre. Big Industries and ConCorp estimate that the proposed merger would reduce their marginal cost to $120 per cubic metre, while the merged firm is expected to face fixed costs of $1,000,000 per day.

(market in the absence of a merger)

1)Using the information provided in the scenario, derive a profit function for a typical firm in the industry. Use QA to denote the quantity produced by this firm, and X to denote the combined production of the remaining two firms.

2)Derive the best-response function for the typical firm.