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Following up a pretty long but very informative discussion with 1muflon1, I want to expand and merge with consumer surplus to have a big picture.

In research of Dasgupta, 2019 about that after antitrust, firms expand their asset growth and fund such asset expansion mainly by equity issuance. So, from my understanding, the normative theory is: anticollusion is good for consumers based on the thought of the policymakers; the positive theory is that due to the logical relation that anticollusion breaks the cartels, the market become more competitive, and consumer gain more consumer surplus, progressing consumers' advantage. And empirical result is we did some empirical result to prove that asset growth increase after laws statistically.

Is it a correct thought?

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Both of these propositions appear to be positive.

The first statement is positive because it states a fact which can be rather easily measured. If anti-collusion is good for consumers it is a true statement, so we can research it. It seems as if the proposition is trying to be normative, yet has not fully succeeded. That's due to its adjective, "good" (beneficial, utility-augmenting), which although a nonquantifiable one, it can be objectively measured.

If the sentence was altered to "anti-collusion is more important to consumers than a universal basic income (random comparison)", it would be a normative proposition, as it would contain a value judgement within it.

It would also be a normative proposition to say that anti-collusion measures "should" or "ought" to be taken.

P.S.: Did you know that the guy who first introduced the dichotomy of positive and normative statements was John Neville Keynes, JM Keynes' dad? Also Milton Friedman, in his 1953 paper "The Methodology of Positive Economics" focused on this dichotomy.

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    $\begingroup$ @Koutsoulis , first time I know about Keynes' story, thanks for sharing the knowledge :D $\endgroup$
    – Louise
    Aug 20 at 15:18
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So, from my understanding, the normative theory is: anticollusion is good for consumers based on the thought of the policymakers; the positive theory is that due to the logical relation that anticollusion breaks the cartels, the market become more competitive, and consumer gain more consumer surplus, progressing consumers' advantage.

As the other +1 answer states both statements appear to be positive. I would change the first sentence "we should have anti-trust laws as they are good for consumers". This change is subtle but the should/ought is important. For example, it is empirical question if anti-trust is good for consumers, but it is moral question if we should actually do what is good for consumers (some industry lobbist could argue screw consumer do whats good for producer). Also, if you are still somewhat unclear about this I recommend reading J. Reiss Philosophy of Economics: A Contemporary Introduction, it is undergraduate text so it is easy to read and covers these issues with more nuance.

And empirical result is we did some empirical result to prove that asset growth increase after laws statistically.

This is also correct, but note empirical results are by definition part of the positive economics, so this is not a separate category. Statement: "asset growth increase after laws statistically" is positive statement, and you came to that conclusion based on some empirical result.

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