How high is the production bonus of a great engineer in Civ5?
To quote the manual:
Special Ability: Hurry Production
You can expend a Great Engineer to create a sudden burst of production in a city. The production is immediately applied to whatever is presently being built in the city – unit, building or Wonder. This will usually be enough production to immediately finish all but the most massive Wonders, and it will drastically shorten their production time.
I had a great engineer during modern times, and using it to help produce the Statue of Liberty (1200 prod needed) yielded 750 production. Letting it help along for a Stock Exchange immediately finished this building (650 prod cost).
I assume that the amount of prod. generated is somehow game-stage related? Are there any known specific rules?
The amount of production of a great engineer on normal speed is calculated using the formula
300 + 30 * city population
So in a city with a population of 1 the engineer only results in 330 production, in a size 15 it results in 750 production.
For quick speed the formula is:
200 + 20 * city population
For epic speed it is:
450 + 45 * city population
and for marathon it is:
900 + 90 * city population
The amount of hammers does not seem to be influenced by era, map size or difficulty level.
Conclusion: If you want to hurry late game wonders, build it in a city with a large population.