With log utility, the solution to the neoclassical consumption model is given implicitly by the two equations on page 446, the Euler equation and the intertemporal budget constraint:

There, we solved these two equations for c_today and c_future in the special case where β = 1. This exercise considers the case where β differs from 1.

(a) Solve these two equations for c_today and c_future when β ± 1.

(b) Verify that the solution matches what we obtained in the text when β = 1.

(c) When β today higher or lower than when β = 1? Why?

Cfuture Ctoday B(1 + R) Cfuture = X. 1 + R C1oday