Milton Friedman and Maximizing Profits

Unbounded
81

What do you think about this, below?

The question is which of these options maximizes both x and y. We’re trying to think about maximizing two (or more) different things.

  1. x=5,y=5
  2. x=4,y=10
  3. x=11,y=1

One way to view it is there are multiple specific things you could try to maximize. I’ll list some of them with the correct answer for each in parentheses after.

x (3)
y (2)
minimum(x,y) (1)
maximum(x,y) (3)
x+y (2)
x*y (2)
2x+y (3)
x+2y (2)
x^2+y^2 (3)
sqrt(x)+sqrt(y) (2)
y-x (2)
x+10y (2)

FYI, the minimum function returns the lowest number from all its inputs. The maximum function returns the highest number from all its inputs.

Option 1 won once, 2 won seven times and 3 won four times. So 2 won the most times, and it won more times than the other options combined. But that might not mean much: you could make a different list and get a different option to win the most times.

For each expression on my list, there is a clear, well-defined answer about which of the three options maximizes it. You can just use math. (We didn’t run into a tie here, but in general ties are possible. Multiple options can tie for the maximum. That’s fine. Due to ties, sometimes maximization has more than one correct answer. Ties are a tangential issue from what we’re talking about.)

Does maximizing x and y (or more generally, maximizing two or more things) have a clear, well-defined answer? If so, is it one of the expressions on the list or some other expression/formula you could write down? If so, which expression and why?

82

Is this an error? From what I understand it seems like the answer should be option 3. It looks like you maybe put the lowest value input (1) as the answer and not the option with the lowest value (3).

If so, option 1 won 0 times. And so none of those equations could represent what my intuition said when I said option 1 maximised x and y.

For it to have a clear answer, it’d need a corresponding expression like the ones in your list. (correct?) Do I think any on that list mean: both x and y? The two obvious candidates for that are:

x + y
x * y

in binary logic multiplication was like AND but I think that only worked with binary logic.

I’m not sure about x + y. Something doesn’t seem right about it.

If you knew how to convert x into y, you might be able to maximise them both? You’d be converting the problem into a problem of maximising one thing.

(None of the other candidates on that list seem like plausible options.)

I don’t know. I think I’m stuck.

83

Evaluate these:

min(5,5)

min(4,10)

min(11,1)

84

min(5, 5) = 5

min(4,10) = 4

min(11, 1) = 1

85

yes. so which one wins?

86

Oh so option 1 gives the maximum value of the minimum function. I was thinking of the minimum function taking all the inputs from all three options, and telling you which option contained the minimum input.

87

Option 1 wins.

88

Yes. We’re still maximizing.

89

Of course, okay.

90

That is one way to give a clear answer. I’m not ruling out there being any other ways but I don’t have one to suggest.

Why x+y is a bad answer is one of the main topics of Multi-Factor Decision Making Math. The essay also applies to x*y some.

My answer is that maximizing 2+ (qualitatively) different things is undefined or impossible in general.

If you have an answer that individually maximizes every single one of the things, then that works. But in general that isn’t available.

Notable previous comments:

The implicit premise here is that you can only maximize a single value, not pairs, which is correct.

But there is no standard, default or common sense way to convert pairs to single quantities in general. This is the problem of combining different dimensions, like length and time, or width and temperature, which can only be done contextually or in special cases (and often only approximately), not universally or generically.

This is correct. You can just say none of the options maximize every individual factor, so none are the combined maximum. That’s a simple way to think of it.

Relating this back to the article and your comments, when Friedman says to maximize profit, it doesn’t mean to maximize profit and customer satisfaction and supplier retention and employee productivity. If you want all four of those things, you make them all goals or high priorities or something; that isn’t maximization.

Friedman means to maximize profit only. Maximizing means just maximizing one thing. He means don’t maximize customer satisfaction.

While you can’t maximize two things, you can maximize one thing while obeying any number of constraints. Any option that violates even one constraint is simply rejected, and the highest scoring option that follows every constraint is the maximum. Friedman says to follow the law while maximizing profit, so that’s constrained maximization.

Make sense? @Eternity too. If so, the next thing to consider may be revisiting Multi-Factor Decision Making Math to evaluate what you didn’t understand previously, and if/why you thought you did understand that, and post mortem what’s going on there. Then continue with the Friedman article.