Comment by cpgxiii

That is a somewhat complicated answer. The simplistic answer is that certification criteria require all turbine aircraft (turboprop or jet) to meet minimum climb performance following an engine failure at the worst part of takeoff. Multiengine piston aircraft (almost all of which are grandfathered in under prior rules anyways) are not required to do so. As a proportion of commercial passenger aircraft, multiengine piston aircraft are fortunately fairly rare in terms of passenger-miles flown, but they are still fairly common in certain markets.

However, that answer is hiding a lot of complexity. In a multiengine turboprop, single-engine climb performance is dependent on fathering the propeller of the dead engine(s); if you don't (or can't), you will probably crash.

In all aircraft, different takeoff conditions (ambient temperature, pressure, runway length) will result in different performance (maximum takeoff weight, runway length and takeoff thrust required). In some extreme conditions (e.g. "hot and high" airports like Mexico City or Denver) this can result in a reduction of maximum takeoff weight to ensure that engine-out climb performance is maintained. Generally aircraft used in these airports are designed and/or acquired with these conditions in mind, and thus the aircraft are still profitable to operate with the reduced MTOW.