From 569404773ea89dd6bdc76d5715f7564f984eb011 Mon Sep 17 00:00:00 2001 From: jdebacker Date: Fri, 6 Sep 2024 10:49:13 -0400 Subject: [PATCH] fix firm eq --- docs/book/content/calibration/firms.md | 2 ++ docs/book/content/calibration/taxes.md | 2 +- 2 files changed, 3 insertions(+), 1 deletion(-) diff --git a/docs/book/content/calibration/firms.md b/docs/book/content/calibration/firms.md index 2a05f2f..a4ef222 100644 --- a/docs/book/content/calibration/firms.md +++ b/docs/book/content/calibration/firms.md @@ -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 $m$. diff --git a/docs/book/content/calibration/taxes.md b/docs/book/content/calibration/taxes.md index eab6ac0..1bdb2ec 100644 --- a/docs/book/content/calibration/taxes.md +++ b/docs/book/content/calibration/taxes.md @@ -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