Ask Umbra: Do the costs of LEDs outweigh the benefits?

My little brother, a pretty staunch environmentalist, just graduated from college and spent the last year of his service-learning job working for the college’s electricity crew. He adamantly insists that while LEDs indisputably save a lot of energy in their usage, the components and energy that go into constructing the LED and its circuit board outweigh the savings — just like the construction of a new electric car uses more resources and energy than it would save over driving a used car. I haven’t been able to find too much on this aspect anywhere and was wondering if you might be able to weigh in.