This paper examines the dynamical properties of a one-sector cash-indvance constraint model with constant returns to scale. Its aim is to overcome some of the difficulties encountered by earlier models in establishing the empirical relevance of indeterminacy and sunspots. It is first established that, in opposition to available results, indeterminacy occurs for values of the intertemporal elasticity of substitution in consumption consistent with the bulk of empirical estimates. It is then shown that sunspot shocks generate procyclical movements in consumption. Lastly, allowing both beliefs and technological disturbances, the model is found to perform as well as real sunspot models with increasing returns to scale in matching the business cycle.