This lecture is in two parts. The first part is concerned with an extension of the classical Merton portfolio optimization problem. In this extension, the model parameters may depend on some economic factor which varies randomly as an ergodic Markov diffusion process. Tradeoffs between long term growth of expected utility of wealth and of consumption are considered. The second topic is concerned with models of economic units, which have productive capital and may also incur debt. The economic unit could be a national economy, a sector of an economy or a business enterprise. Optimal debt-to-wealth ratios are found in some particular cases.