Optimal Consumption and Savings with Stochastic Income and Recursive Utility

We develop a tractable continuous-time consumption-savings model for a liquidity-constrained agent who faces both permanent and transitory income shocks under incomplete markets. We derive an explicitly-solved consumption function and show that the marginal (certainty equivalent) value of liquidity measures the effects of financial frictions on welfare. We further analytically characterize steady-state target savings and demonstrate that risk aversion and inter-temporal substitution have very different effects on savings and the dispersions of wealth and consumption