<p>I am interesting in proving that the elasticity of substitution between leisure in two periods is equal to one for the following utility function:
<span class="math-container">$$U = \ln(c_1)+b\ln(1−l_1)+e^{−\rho}[\ln(c_2)+b\ln(1−l_2)]$$</span>
where <span class="math-container">$\rho$</span> is the discount factor. How would I go about doing this?</p>

CC BY-SA 4.0
2024-04-27T19:36:01.707Z
What is the utility function? This depends critically upon that.
Brennan
CC BY-SA 4.0
2024-04-27T21:14:34.947Z
U=ln(c1)+bln(1−l1)+e−ρ[ln(c2)+bln(1−l2)],
where
 ρ
 is a discount rate
Rana Barakat
CC BY-SA 4.0
2024-04-27T21:16:39.763Z
please note that e to the power negative raw is the discount factor
Rana Barakat
<elasticity-of-substitution>
Intertemporal elasticity of substitution for leisure with log utility
Rana Barakat
# Intertemporal elasticity of substitution for leisure with log utility

(Asked by: username_0 on 2024-04-27)

I am interesting in proving that the elasticity of substitution between leisure in two periods is equal to one for the following utility function:
$$U = \ln(c\_1)+b\ln(1−l\_1)+e^{−\rho}[\ln(c\_2)+b\ln(1−l\_2)]$$
where $\rho$ is the discount factor. How would I go about doing this?

**Tags:** elasticity-of-substitution
> **Comments:**
> **username_1**: What is the utility function? This depends critically upon that.  
> **username_0**: U=ln(c1)+bln(1−l1)+e−ρ[ln(c2)+bln(1−l2)], where  ρ  is a discount rate  
> **username_0**: please note that e to the power negative raw is the discount factor  

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## 0 answers

