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 = 670 Q/40,

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 $190 per cubic metre.

Big Industries and ConCorp estimate that the proposed merger would reduce their

marginal cost to $145 per cubic metre, while the merged firm is expected to face fixed

costs of $600,000 per day

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.