The paper investigates the importance of domestic and foreign liquidity constraints and variablity of various sources of household income for the properties of the consumption function in the Czech economy, with the consequences for monetary policy and the exchange rate. For this purpose, the paper develops a model of consumption and investment. in an open economy under diffusion uncertainty with soft liquidity constraints. The model is solved by means of the stochastic maximum principle including the adjoint equation for the co-state process. One of the equations of the model, which describes the equilibrium exchange rate, is then used to estimate the precautionary saving and currency substitution effects in the Czech economy of the period 1993-1997. We find that either liquidity constraint factor for precationary saving or the currency substitution are significant in aggregate. Precautionary saving as a reaetion on income uncertainty, is, Oll the other hand, prominent. Considerable are also deviations from simple uncovered parity relations caused by the transaetion technology in the forex market.