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 firms—Aggregate Inc., Big Industries and ConCorp—are 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 Industrie
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 firms—Aggregate Inc., Big Industries and ConCorp—are 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
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.
Apply to the market in the absence of a merger.
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.
Number of firms in the industry = 3
Demand function : P = 670 - Q/40
Q = q1 + q2 + q3
Fixed Cost = 400,000
Marginal cost = 190 per cubic metre
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