Before revision:  By consuming patiently, these individuals maintain a wealth-to-habit ratio that is greater than the minimum acceptable level  .
After revision:  By consuming patiently, these individuals maintain a wealth-to-habit ratio that is greater than the minimum acceptable level . Additionally, we prove that the optimal consumption path is hump-shaped if the initial wealth-to-habit ratio is either: (1) larger than a high threshold; or (2) below a low threshold and the agent is less risk averse. Thus, we provide a simple explanation for the consumption hump observed by various empirical studies .