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Private costs are the costs borne by the firm directly involved in the production process. These costs include labor, materials, taxation, and any other expenses that are internal to the company. In a market without environmental regulations, the supply curve will be affected by the firm's private costs as these costs directly influence production decisions and contribute to determining the firm's supply schedule. External costs, also known as externalities, are the costs incurred by third parties, not directly involved in the production process. Examples of external costs include environmental pollution, noise pollution, and congestion, amongst others. These costs are not borne by the firm but have an impact on society as a whole. In a market without any environmental regulations, these external costs are not taken into account when determining the firm's supply schedule.

Since the supply curve is based on the private costs of production, in a market without environmental regulations, the supply curve for a firm will account for private costs only. External costs, considering that they are not internalized into the decision-making process by the firm, will not impact the supply curve in this case. Therefore, the firm's supply curve in a market without environmental regulations will account only for private costs and not external costs, as these costs are not borne by the firm and hence do not directly influence the firm's production decisions.

In conclusion, in a market without environmental regulations, the supply curve for a firm will only account for private costs since these are the costs directly associated with production and influence the firm's supply schedule. External costs, although they have an impact on society, are not accounted for in the supply curve in this case as they do not interfere in the firm's production decisions.