Final answer:
Piano concertos of the Romantic era were written for different purposes. Beethoven wrote them for his own performance, while others were commissioned by wealthy patrons.
Step-by-step explanation:
In the Romantic era, piano concertos were written for various reasons. Beethoven, for example, wrote them for his own performance, showcasing his virtuosity as both a composer and a pianist. However, many piano concertos of the time were commissioned by wealthy patrons who wanted to support and promote the work of talented composers. These patrons would commission concertos and provide financial support for their composition and performance.