A vegetarian meal takes much less resources to grow as compared to a non-vegetarian meal. Has any research been done to quantify this effect? e.g. If a non-vegetarian person goes vegetarian, how many more people can be fed from the saved resources?
This depends on several factors.
This answer uses Cowspiracy as a source, which in turn uses several reputable sources as source. I will state the sources of these sources in small under the quotes.
If we look to the available land, a non-vegetarian uses approximately six times as much land as a vegetarian and 18 times as much as a vegan. Robbins, John. Diet for a New America, StillPoint Publishing, 1987, p. 352
So if everyone goes vegetarian, we can feed almost six times as much people, if everyone goes vegan, almost 18 times as much. Note that land is actually a limiting factor for food production. In fact, it is the main reason that forests are cut is making more land for food (mainly meat and food for animals) production ("Animal agriculture is responsible for up to 91% of Amazon destruction").
Note: The actual figures are a bit lower since there are already some people vegetarian or vegan, but, unfortunately, that is not enough to make a really significant difference in these 6 and 18.
Some other factors:
Each day, a person who eats a vegan diet saves 1,100 gallons of water, 45 pounds of grain, 30 sq ft of forested land, 20 lbs CO2 equivalent, and one animal’s life.
–“Water Footprint Assessment.” University of Twente, the Netherlands.
“Measuring the daily destruction of the world’s rainforests.” Scientific American, 2009.
“Dietary greenhouse gas emissions of meat-eaters, fish-eaters, vegetarians and vegans in the UK.” Climactic change, 2014.
“Meat eater’s guide to climate change and health.” The Environmental Working Group.
Oppenlander, Richard A. Less Meat, and Taking Baby Steps Won’t Work. Minneapolis, MN : Langdon Street, 2013. Print.
According to fatsecret, 1.3 lbs of flour (this is approximately 1.3 lbs of grain) can feed a person for a day, so 45 pounds of grain can feed 45/1.3 = 34 persons a day. When looking to water, the difference is even greater. 10 gallons of water would be more than enough for a person to drink from and have some personal hygiene (people in wealthy countries use more, but this is what should be more than enough to live), so that would be 110 extra people that would have access to enough water to lvie from. (Note that this is vegan instead of vegetarian. A vegan livestyle saves even more than a vegetarian, so for a vegetarian it will be a bit less.)
Other shocking quotes form this source:
We are currently growing enough food to feed 10 billion people. [...]
– Common Dreams, "We Already Grow Enough Food for 10 Billion People… and Still Can’t End Hunger".
Worldwide, at least 50% of grain is fed to livestock.
– FAO, "Livestock - a driving force for food security and sustainable development".
Some of these facts and calculations need to be taken with a grain of salt, since (for example) the fact that 1,100 gallons of water are saved, does not mean that 110 people in poor countries have access to 10 gallons of water each. But it would be theoretically possible.
Yes, this concept is called "carrying capacity" and it has been studied. One person going vegetarian frees up enough resources to feed one extra vegetarian. In other words, it takes about twice as much resources to feed a person following an omnivorous diet as a vegetarian one.
Consider this 2016 study about Carrying capacity of U.S. agricultural land: Ten diet scenarios published in Elementa that compares the current baseline diet (BAS) against vegan, vegetarian, and omnivorous diets with varying amounts of meat. There are two particularly interesting conclusions.
All diet patterns require approximately the same amount of cultivated cropland, but total land usage is much higher for omnivorous diets.
The study also considered what would happen if all land was used to the maximum extent possible. Unsurprisingly, the study showed that lacto-vegetarian diets could feed the largest number of people with ovo-vegetarian and vegan diets close behind.