THE ECONOMICS OF ADDING AND SUBDIVIDING INDEPENDENT RISKS - SOME COMPARATIVE STATICS RESULTS

In this paper we address the problem of determining whether adding ind ependent risks or subdividing them is a good substitute for insurance. Despite the fact that accepting more i.i.d. risks increases total ris k, it is shown that some risk-averse decision makers can rationally re duce their demand for insurance by doing so. Similarly, a better diver sified portfolio of i.i.d. risky assets can rationally be more insured , even if diversification is a risk-reduction scheme. We derive condit ions sufficient to obtain unambiguous comparative statics results. Ass uming that absolute risk aversion is decreasing and that the fourth de rivative of the utility function is positive, we show that diversifica tion is an exceptionally good substitute for insurance. Under the same conditions, adding independent risks to wealth reduces the demand for insurance on each unit.