 Solution

At a fixed surface warming, a smaller lapse rate makes the upper troposphere warmer than in an unchanged-lapse profile. Its emission to space therefore increases, giving a negative feedback. Water vapor has the opposite effect under the given coefficients. The net restoring coefficient is ${\lambda }_P-2+0.5\simeq 2.24$ W m${}^{-2}$ K${}^{-1}$, so $\boxed{\Delta T\simeq 1.65\mathrm{K}}$. This calculation uses the same $S_0$ and linearized Planck model as the preceding part.