題組內容
V.A father-son pair use the following income streams to finance their living in 2021 and 2022. The father earns $100 in 2021, but plans to retire early and so will only earn $20 in 2022. The son is undergoing a training program and earns only $20 in 2021, but will finish the training and earn $100 in 2022. By consuming $c1$ in 2021 and $c2$ in 2022, the father obtains utility $UF = \min\{c1, c2\}$, and the son obtains $US = \ln c1 + 0.8 \ln c2$. Both $c1$ and $c2$ are continuous.
(c)(7%) Following the previous question, find out all the Pareto optimal pairs, if any, that could be implemented by the financial market (i.e., through private borrowing and saving when both are price-takers), and the corresponding interest rate.