<p>In Calstrom-Fuerst-Ghironi (2004) &quot;Does It Matter (for Equilibrium Determinacy) What Price Index the Central Bank Targets?&quot;, they used a standard two-sector NK model, and the optimal price setting condition reads (equation 14):</p>
<p><span class="math-container">$\frac{P_{t}^{j}}{P_{t}}=\frac{1}{Z_{t}^{j}}\frac{W_{t}^{j}}{P_{t}}$</span>,</p>
<p>where <span class="math-container">$P_{t}^{j}$</span> is the price index for sector j, <span class="math-container">$P_{t}$</span> is aggregate price level, <span class="math-container">$W_{t}^{j}$</span>  is wage for sector j, <span class="math-container">$Z_{t}^{j}$</span>  is the marginal cost in sector j, so that <span class="math-container">$1/{Z_{t}^{j}}$</span> is the markup of price over marginal cost.</p>
<p>I do not understand how this equation is derived. My understanding is that in multi-sector models we still have pricing equation to be in the form of <span class="math-container">$P_{t}^{j}=\frac{\epsilon}{\epsilon-1}\frac{E_{t}[\cdots]}{E_{t}[\cdots]}$</span>.</p>
<p>The equation in Calstrom-Fuerst-Ghironi (2004) also showed up in another paper of theirs using multi-sector NK model. In both papers, they say refer to Yun (1996), but I do not see a form like this in Yun (1996).</p>
<p>Any help is greatly appreciated!</p>

CC BY-SA 4.0
2020-09-29T00:14:39.453Z
In particular, isn't nominal marginal cost just $W_{t}^{j}$ (their production technology is $Y_{t}^{j} = L_{t}^{j}$).
TomG
CC BY-SA 4.0
2020-09-29T00:29:15.120Z
Could you please include hyperlinks to those papers?
1muflon1
CC BY-SA 4.0
2020-09-29T00:33:15.527Z
My bad, their two papers are linked below:
http://faculty.washington.edu/ghiro/CaFuGhiroJET0506.pdf

http://faculty.washington.edu/ghiro/CaFuGhiroHeRelPrices082206.pdf
TomG
<macroeconomics><new-keynesian-economics>
Calvo Price setting in a Multi-sector NK Model
TomG
# Calvo Price setting in a Multi-sector NK Model

(Asked by: username_0 on 2020-09-29)

In Calstrom-Fuerst-Ghironi (2004) "Does It Matter (for Equilibrium Determinacy) What Price Index the Central Bank Targets?", they used a standard two-sector NK model, and the optimal price setting condition reads (equation 14):

$\frac{P\_{t}^{j}}{P\_{t}}=\frac{1}{Z\_{t}^{j}}\frac{W\_{t}^{j}}{P\_{t}}$,

where $P\_{t}^{j}$ is the price index for sector j, $P\_{t}$ is aggregate price level, $W\_{t}^{j}$ is wage for sector j, $Z\_{t}^{j}$ is the marginal cost in sector j, so that $1/{Z\_{t}^{j}}$ is the markup of price over marginal cost.

I do not understand how this equation is derived. My understanding is that in multi-sector models we still have pricing equation to be in the form of $P\_{t}^{j}=\frac{\epsilon}{\epsilon-1}\frac{E\_{t}[\cdots]}{E\_{t}[\cdots]}$.

The equation in Calstrom-Fuerst-Ghironi (2004) also showed up in another paper of theirs using multi-sector NK model. In both papers, they say refer to Yun (1996), but I do not see a form like this in Yun (1996).

Any help is greatly appreciated!

**Tags:** macroeconomics, new-keynesian-economics

> **Comments:**
> **username_0**: In particular, isn't nominal marginal cost just $W_{t}^{j}$ (their production technology is $Y_{t}^{j} = L_{t}^{j}$).  
> **username_1**: Could you please include hyperlinks to those papers?  
> **username_0**: My bad, their two papers are linked below: http://faculty.washington.edu/ghiro/CaFuGhiroJET0506.pdf  http://faculty.washington.edu/ghiro/CaFuGhiroHeRelPrices082206.pdf  

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## 0 answers

