Interesting conundrum Vera, you may have a point. Elsewhere Quinn & Dr. Alan Thornhill go into something which seems to be related called the 'demographic trap' - see the first 10-or-so mins in this vid:
Basically, instead of the scenario you describe of the food being levelled off suddenly, they describe the effects of a drop in the death rate (because of improved health & sanitation etc). The result is similar, with lots of new mouths to feed and only the same resources to go around. In the 3rd world scenario that's the point where they start importing food to maintain the population increase until cultural changes eventually lower the birth rate to a replacement level with the low death rate (mainly people find they don't need so many children to help with all the farmwork).
Possibly mice are a bad example, as I think they're geared to big fluctuations in population size in response to the sudden availability of lots of food, hence the large litters and the ability to give birth multiple times in one year. They're also a major prey species so any big population increase is quickly matched by increased predation from carnivorous birds, mammals & reptiles, leading to a balancing increase in death rate. The world isn't as simple as Quinn's cage, as FiniteEarther suggests (and as I think DQ would recognise)! Would a halt in the year-on-year increase of global food production cause as much trouble for a human population as for a mouse population? Seems doubtful to me somehow, though there could be issues if people were gearing up for a big growth that then failed to materialise.
Fwiw the global pop growth rate has slowed from an approx 2% yearly increase in the 60s to more like 1% in the present day (wiki). So a 0% rate would, I guess, be less of a shock now than it would have been then. Several European countries seem to be coping with a negative growth rate at the moment, but you've got to factor in all their food exports which basically outsource this growth to 3rd world countries. The UK had negative growth during the 70s of around 0.07% annually, due mainly to net migration out of the country because of the economic woes of the time, and I think Russia also had a pretty major decline after the collapse of the Soviet Union, so yes it probably won't be a painless process, associated with all the other aspects of social collapse. Quinn thinks it would be better if made as a conscious global policy decision to arrest food production at a certain level and then start to gradually roll it back. Personally I think there's as much chance of that happening as yeast cells refusing to eat available sugar, even as the waste build-up threatens to kill them. Sorry if that's a downer!