Let your wealth at time t = 0 (representing today) be w = 1. You can invest your wealth at a net return of r = 0.05 per year. You are considering two alternatives:

a. First, you can invest your wealth at time 0, and then every year until retirement at time T = 10, roll over your entire investment. That is, you don't consume anything from time 0 to time T 1, but at your retirement at time T you consume all the wealth you have accumulated. We call this the decision "to always save."

b. Second, you can invest your wealth at time 0, and then ever year until retirement at time T = 10, consume the proceeds from your investment and reinvest the capital. That is, you consume rw from time 0 to time T 1 and then at time T you also consume w. We call this the decision "to never save."

Assume that utility from consumption c before retirement is u (c) = c, while utility from consumption c at retirement is u (c) = 2c. This assumption simplistically captures the idea that marginal utility at retirement is higher, because there are no other sources of income (hence you are poorer). Assume also that your discount function is hyperbolic, with hyperbolic discounting constant is = 0.25.

Which of the two alternative consumption streams would you choose?