Consider the Following Inter-Temporal Choice Problem, Where $s^{\prime}$ Is the State Today And

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Consider the following inter-temporal choice problem, where $s^{\prime}$ is the state today and $s$ is the state tomorrow. $\max _{c_{1}} u\left(c_{1}, s^{\prime}\right)+\delta\left[(1-\alpha) u\left(w-c_{1}, s\right)+\alpha u\left(w-c_{1}, s^{\prime}\right)\right.$ . This problem reduces to the rational model of inter-temporal choice when $\alpha=1$ .