When analyzing the impact of an increase in risk aversion, most literature has treated the demand for market insurance and self-insurance (the expenditure on loss reduction) separately. This paper examines the comparative statics of an increased risk aversion on market insurance and self-insurance simultaneously. We find that, although a more risk averse individual would demands more market insurance and self insurance separately, he/she would maintain the same expenditure on self insurance but demand more market insurance when both market insurance and self insurance are available. Moreover, this result holds no matter his/her self-insurance behavior is observable by the insurer.