DSE 2020 Question 12: Consumption and investment

A consumer lives for periods $1$ and $2$ with utility $U=\ln c_1+(1+\rho)^{-1}\ln c_2$, incomes $w_1,w_2$, and lifetime budget constraint $c_1+(1+r)^{-1}c_2=w_1+(1+r)^{-1}w_2$, where $r$ is the interest rate on savings. If $r>\rho$, then