Consider the Weil [1650] model introduced in Sect. 9.5. By applying Jensen's inequality, prove Proposition 9.15.

Data From Proposition 9.15

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Proposition 9.15 In the context of the above model (see Weil [1650]), it holds that rj and * r* if and only if u'""> 0. This proposition provides an example of the implications of market complete- ness, since in the setting considered above the presence of uninsurable labor risk makes the market incomplete. When u" >0 (the utility function u exhibits prudence, see Sect. 3.3), there is a precautionary saving motive: the presence of uninsurable labor risk increases the demand for both the risk free and the risky