I'm playing in Endless pace, so values are related to this speed.

So, food, give you a percentage of growth for the next turn :

16 food, gives you 12% of growth for the next turn.

48 food -> 24%

100 food -> 33%

200 food -> 40%

533 food -> 46%

989 food -> 48%

1531 food -> 48%

So, in Endless pace the max growth of population seem to be 48% per turns. 

I find those figures quite frustrating, being at mid range of the max growth rate with 50 food and earning only 2 percent from 500 to 1500 seem really hard and makes big food income really useless.

Now, for the Machu Picchu.

It says : 

This is the growth of the city having the Machu Picchu

And this is what every city gain of it : 

So every city gain a flat amount of food equivalent to half of the growth of the city having the Machu Picchu. 46% -> +23 food

It seem to be a little different of the description.

I think large amounts of food are meant to support large populations rather than grow them.  (also, it is possible the %growth doesn’t only depend on excess food but also on population or total food production). However that is really bad for MP. They REALLY need more formulas.

Uitaneko wrote:

I'm playing in Endless pace, so values are related to this speed.

And this is what every city gain of it : 

So every city gain a flat amount of food equivalent to half of the growth of the city having the Machu Picchu. 46% -> +23 food

It seem to be a little different of the description.

Allow me to correct you here:
It only gives that bonus to one city. At least in my game.

The city that was build (not conquered) after the wonder has been constructed.

IT'S A BUG.

Here is my Steam Thread concerning that

You are right on the fact that this line appear ONLY on cities created after the Machu Picchu is constructed.

But I tried it ! I decreased the growth of the city having the Machu Picchu and the food of all other cites decreased of the right amount :

Going from 26% growth to 16% -> 10% loss, so -5 food, and every cities actually lost 5 food.

So the bug is that it doesn't appear in the details of old cities, but it's actually count in "District"

Great, but it still doesn't consider my output of 1323 or my gains 2604 in the city I specifically tailored around Farming to get Machu Picchu there. 
It's buggy, describing it badly and not promising what it says on the box. I want all the industry production back I farmed so hard to get. *pout* 

To be honest, if the machu picchu would actually do what it says, it would be extreme.

If you add half the surplus (let alone raw production) of food of one city (especially one crafted for food) to all other cities... then all your cities will never have to deal with food ever again to grow to a reasonable size.

Compare that to late-game wonders that just give +10% on everything and the early-game wonder machu picchu still wins by far.

The thing is that the Machu Picchu doesn't exactly do what you think when you read its description, and you need to do a lot of tests to find exactly what it does.

To fix this they need to adapt the description or change how it works.

For the balancing, if it does what it says, giving 50% of the food to all cities seem really huge, even if it's only on the flat exceeding food. But for now, it's pretty useless, in endless speed, it gives at max 24 food to every other cities. 

If you compare this to other wonders, it's really not worth. 

To point out how others are broken, if you combine Angkor Wat (1 Faith = 1 Food) and Saint Basile's Cathedral (1 District (in your entire empire) = 1 Faith) in the same city, you can litterally make thousands of food excees. But, as i saied in the begining, this is quite pointless as 500 excess food and 2000 gives the same growth per turn.

Both pop growth and pop starvation is capped towards 100% on standard speed. This work fine in early game when food numbers is small but it don't give any rewards for really focusing on maintaining huge food surplus, nor is it that punishing for huge cities with massive negative food surplus. Right now the only way to grow huge population is spamming alot of cities no matter how small they are or exploting various mechanics that create population.

This huge city with over 1000 population have a massive negative food surplus, but it will only lose a population per turn and it is close to the end of the game, losing maybe 50 population of 1200 seems like a very small penalty for being able to completely ignore your food income.

I think something need to be changed about the population growth rate such as base it on era, faster growth rate in later eras, maybe based on technology which would fit better with the increased population requirement of military units, or base growth rate upon number of territories attached to the city, cities with more territories would have higher growth rate. This would make huge multi territorial cities stay more competetive in terms of population growth compared to having alot of small cities. Starvation could work the same way.

I think the simplest solution would be to have the growth or starvation rate multiplied by 1+population*0.02.... so at 50 pop you could get lose 2 a turn, 100 pop you could get/lose 3 a turn and so forth.