Mathematics of producer surplus wrong?

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SUMMARY

The discussion centers on the formula for producer surplus, which is defined as Income minus expenses, represented mathematically as P*Q - ∫M(Q)dQ. A key point raised is the inclusion of fixed costs (FC) in the formula, suggesting it should be P*Q - (∫M(Q)dQ + FC) to accurately reflect total costs. The conversation also touches on the nature of marginal costs as derivatives of total costs, emphasizing the importance of considering fixed costs in production calculations. Additionally, the role of demand curves in representing market willingness to purchase is questioned.

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Nikitin
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The formula for producer surplus is:

Income - expenses = P*Q - ∫M(Q)dQ

However, shouldn't it be P*Q - (∫M(Q)dQ + FC), with FC= fixed costs?

I mean, the marginal costs are just the derivative of total costs, and thus integrating them is the same as just integrating the variable costs, ignoring the fixed costs of production.
 
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And concerning demand-curves:

Do they represent the quantity the market is willing to buy?
 

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