<p>This is a part of Online Appendix to Business Cycle Dynamics under Rational Inattention (Mackowiak and Wiederholt, 2015).</p>
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<p>I don't understand why C_j is supposed to be a denominator. Could anyone give me an explanation? I learned log-linearization but this is non-sense to me. I understand the product of labor and wage part but don't get any sense why C_j appear at numerator in a consumption log-linearizatino term.</p>

CC BY-SA 4.0
2022-09-25T19:12:15.347Z
The approach to log-linearization of utility functions is no different than that for other expressions. And with expressions as tricky as (35) there is no way to just see the solution.  There is no substitute for doing the math. What have you tried?
BrsG
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2022-09-25T19:28:38.860Z
@BrsG Thanks for your comment. I tried to derive (36) from (35) but my equation did not have a C_j as a denominator. I'm aware of the basic concept of log-linearization but don't understand why there C_j is supposed to be.
user14261785
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2022-09-25T19:39:53.780Z
$C_j$ is the equilibrium value. It's the sum of all $C_{ij}$ equilibrium values. It will show up in the denominator when you apply log-linearization there.
BrsG
<log-linearization>
how to log-linearize a utility function?
user14261785
# how to log-linearize a utility function?

(Asked by: username_0 on 2022-09-25)

This is a part of Online Appendix to Business Cycle Dynamics under Rational Inattention (Mackowiak and Wiederholt, 2015).

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I don't understand why C\_j is supposed to be a denominator. Could anyone give me an explanation? I learned log-linearization but this is non-sense to me. I understand the product of labor and wage part but don't get any sense why C\_j appear at numerator in a consumption log-linearizatino term.

**Tags:** log-linearization

> **Comments:**
> **username_1**: The approach to log-linearization of utility functions is no different than that for other expressions. And with expressions as tricky as (35) there is no way to just see the solution.  There is no substitute for doing the math. What have you tried?  
> **username_0**: @username_1 Thanks for your comment. I tried to derive (36) from (35) but my equation did not have a C_j as a denominator. I'm aware of the basic concept of log-linearization but don't understand why there C_j is supposed to be.  
> **username_1**: $C_j$ is the equilibrium value. It's the sum of all $C_{ij}$ equilibrium values. It will show up in the denominator when you apply log-linearization there.  

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## 0 answers

