# Isn't Laffer curve a special case of Profit Maximization curve if not the same? [closed]

I have discovered that Profit Maximization and Laffer curves convey similar ideas. Basically, down-side parabola.

Would it be correct to say that Laffer curve is nothing but application of the profit maximization curve by the government? If not, how do they differ?

• "I have discovered that Profit Maximization and Laffer curves convey similar ideas. Basically, down-side parabola." is excellent, if intended as satire. Would you agree that a rainbow also conveys a similar idea? Jul 14 at 18:34
• Kidding aside, it is not quite clear what you are asking. Surely you do not mean a geometric shape, so similar idea in what sense? If the government is trying to maximize tax revenue, then both curves have to do with maximization, but the fact that a tax maximization problem and a profit maximization problem both involve maximization is probably not very surprising. Jul 14 at 18:37
• @Giskard, I would suppose that same geometric shape already says that the nature of both relationships is the same. For instance, even when discussing time complexity of algorithms, we don't really care what is the exact growth function but we rarher say whether this is quadratic, cubic, etc. While I don't intend to connect time complexity with economics, I want to say the fact that both relationshops have the same curve should tell us about their same intrinsic nature. Shouldn't it? Jul 14 at 20:25
• I guess the connection is maximizing a strictly concave function that admits both positive a negative derivatives somewhere without any additional constraints. Jul 14 at 21:27
• @Michael Greinecker, exactly how I am seeing it. Thank you for clarifying more precisely! Jul 14 at 21:32

No, it would not be correct even by a stretch. Just because there is some superficial similarity, or just because plots of profit function and Laffer curve resemble each other that does not mean they are special cases of each other. For example, the cosmic web structure looks like structure of neurons in our brains, that does not mean our brains are special cases of cosmic web.

1. In economics government is traditionally not considered having profit function. Government has its own social welfare function, similarly as individuals have utility function not profit function. We usually talk about profit functions only in context of firms (e.g. see Varian Microeconomic Analysis or MWG Microeconomic Theory). Taxonomy and semantics aside, while there are some parallels between these concepts we often impose different assumptions on properties, shapes or behavior of these functions so they are not really special cases of each other, even if some undergraduate social-welfare/utility/profit maximizations problems might superficially look very similar.
2. Even if we would ignore 1. Laffer curve gives you relationship between tax revenue and tax rate. That is not even superficially related to profit, since profit is by definition revenue minus cost ($$\pi = PQ-C(Q)$$). A more close analogue to Laffer curve, would be the relationship between price and revenue, but even here you have to squint your eyes and force the analogy. Firms do not set prices as shares of your income. Even if they did, firm-customer relationship is fundamentally different from taxpayer-government one. So even though there you could at least find some parallels it would not be possible to defend argument that they are special cases of each other.
• "Firms do not set prices as shares of your income." A markup $(P/MC(Q) - 1)$ analogy would work though! Jul 14 at 19:13
• @Giskard I am not sure about that, market power is not bounded, markup can go to infinity, also how does it relate to shares of personal income?
– 1muflon1
Jul 14 at 19:21
• It does not, it is not the exact same situation, it is just a better analogy than the one you proposed. Jul 14 at 19:26
• More generally I wonder if answering unclear questions based on a guess of what the question is rather than asking for clarification is a good idea. I have seen several instances of this on the site during the last two weeks. Jul 14 at 19:27
• @Giskard well I don't think this is clear cut case, but I see your point
– 1muflon1
Jul 14 at 19:28