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fix firm eq
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jdebacker committed Sep 6, 2024
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2 changes: 2 additions & 0 deletions docs/book/content/calibration/firms.md
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Expand Up @@ -7,12 +7,14 @@ The [OG-Core firm theory documentation](https://pslmodels.github.io/OG-Core/cont

The production function is given as:

```{math}
:label: EqFirmsCESprodfun
\begin{split}
Y_{m,t} &= F(K_{m,t}, K_{g,m,t}, L_{m,t}) \\
&\equiv Z_{m,t}\biggl[(\gamma_m)^\frac{1}{\varepsilon_m}(K_{m,t})^\frac{\varepsilon_m-1}{\varepsilon_m} + (\gamma_{g,m})^\frac{1}{\varepsilon_m}(K_{g,m,t})^\frac{\varepsilon_m-1}{\varepsilon_m} + \\
&\quad\quad\quad\quad\quad(1-\gamma_m-\gamma_{g,m})^\frac{1}{\varepsilon_m}(e^{g_y t}L_{m,t})^\frac{\varepsilon_m-1}{\varepsilon_m}\biggr]^\frac{\varepsilon_m}{\varepsilon_m-1} \quad\forall m,t
\end{split}
```

This production function has the following parameters:
* $\varepsilon_m$ is the elasticity of substitution between capital, labor, and infrastructure in sector $m$.
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2 changes: 1 addition & 1 deletion docs/book/content/calibration/taxes.md
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Expand Up @@ -5,7 +5,7 @@ The government is not an optimizing agent in `OG-ZAF`. The government levies tax


## Personal income taxes
The government sector influences households through two terms in the household budget constraint {eq}`EqHHBC`---government transfers $TR_{t}$ and through the total tax liability function $T_{s,t}$, which can be decomposed into the effective tax rate times total income {eq}`EqTaxCalcLiabETR2`. In this chapter, we detail the household tax component of government activity $T_{s,t}$ in `OG-ZAF`.
The government sector influences households through two terms in the household budget constraint {eq}`EqHHBC`---government transfers $TR_{t}$ and through the total tax liability function $T_{s,t}$, which can be decomposed into the effective tax rate times total income. In this chapter, we detail the household tax component of government activity $T_{s,t}$ in `OG-ZAF`.

```{math}
:label: EqHHBC
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