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Second Order Derivatives in Becker's Crime and Punishment

You have to apply both chain and product rule for derivatives here. In this case: $$C_p'=\frac{\partial C(pO)}{\partial p}=C_p'(pO)O$$ But note when calculating cross-derivative you take the 2nd order …
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Why is MC = ATC the same point for both the breakeven point and an investor maximizing return?

This is not a general result this is a result that holds only for certain market structures. For example, suppose market is competitive so firms are price takers meaning $p(y)=p$. Then when you set up …
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Long Term Economic Profit for Perfectly Competitive market

This is because we are talking about economic profit not accounting profit. An economic profit takes into account opportunity cost. If you are skilled programmer that can earn $\\\$100000$ per year be …
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Why are cost functions often assumed to be convex in microeconomics?

There are several reasons: Didactic Reasons: Other users seem to have missed it but in your question you specify you are talking about "(introductory) microeconomics" [emphasis mine]. Well the most p …
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