In section 14.2.3, we asserted that a new energy source that generates $100 million per year forever to the economy adds $100 million/rr to life-cycle wealth and, therefore, $100 million per year to permanent income.

Prove this result by using the definition of life-cycle wealth. (The trick is to sum the infinite series in a manner analogous to computing the multiplier in Chapter 13, equations (13.18)–(13.21).)