2.14) Consider the Diamond model with logarithmic utility and Cobb-Douglas production. Describe how each of the following affects \(k_{t+1}\) as a function of \(k_t\):
\(f(x) = k^\alpha\)
\(k_{t+1} = \frac{1}{(1+n)(1+g)}s[f(k)-kf'(k)]\)
\(s(r)= \frac{(1+r)^{\frac{1-\theta}{\theta}}}{(1+\rho)^{\frac{1}{\theta}}+(1+r)^{\frac{(1-\theta)}{\theta}}}\)
With log utility, \(\theta = 1\) so we have:
   \(s(r) = \frac{1}{2+\rho}\)