<p>I'm reading Simon Gilchrist's notes <a href="http://people.bu.edu/sgilchri/teaching/EC%20745%20Fall%202013/Lecture%20Slides/lecture6_recursive_preferences.pdf" rel="nofollow noreferrer">here</a>. I understood everything until and including page 14, where it reads</p>
<p><span class="math-container">$$\frac{W_h^{1-\rho} + W_l^{1-\rho}}{2} \geq \frac{c_h^{1-\rho} + c_l^{1-\rho}}{2} $$</span></p>
<p>and that's supposed to show that the certainty equivalent of lottery A is higher than the CE of lottery B. However, the CE of the two lotteries, according to page 12, are <span class="math-container">$(\frac{1}{2} c_h^{1-\alpha} + \frac{1}{2} c_l^{1-\alpha})^{ 1/(1-\alpha)}$</span> and <span class="math-container">$(\frac{1}{2} W_h^{1-\alpha} + \frac{1}{2} W_l^{1-\alpha})^{ 1/(1-\alpha)}$</span>.</p>
<p>I know that we are supposed to assume <span class="math-container">$\rho &gt; \alpha$</span>, but I'm not sure how that helps.</p>

CC BY-SA 4.0
2021-03-02T17:28:41.183Z
/have you tried the Jensen inequality?
Grada Gukovic
CC BY-SA 4.0
2021-03-03T00:05:06.390Z
@GradaGukovic Can you write out the answer, so I can select it?
user1691278
<uncertainty><recursive-macroeconomics>
Epstein zin and resolution of uncertainty
user1691278
# Epstein zin and resolution of uncertainty

(Asked by: username_0 on 2021-03-01)

I'm reading Simon Gilchrist's notes [here](http://people.bu.edu/sgilchri/teaching/EC%20745%20Fall%202013/Lecture%20Slides/lecture6_recursive_preferences.pdf). I understood everything until and including page 14, where it reads

$$\frac{W\_h^{1-\rho} + W\_l^{1-\rho}}{2} \geq \frac{c\_h^{1-\rho} + c\_l^{1-\rho}}{2} $$

and that's supposed to show that the certainty equivalent of lottery A is higher than the CE of lottery B. However, the CE of the two lotteries, according to page 12, are $(\frac{1}{2} c\_h^{1-\alpha} + \frac{1}{2} c\_l^{1-\alpha})^{ 1/(1-\alpha)}$ and $(\frac{1}{2} W\_h^{1-\alpha} + \frac{1}{2} W\_l^{1-\alpha})^{ 1/(1-\alpha)}$.

I know that we are supposed to assume $\rho > \alpha$, but I'm not sure how that helps.

**Tags:** uncertainty, recursive-macroeconomics

> **Comments:**
> **username_1**: /have you tried the Jensen inequality?  
> **username_0**: @username_1 Can you write out the answer, so I can select it?  

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## 0 answers

