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---
title: 'The Goods Market in an Open Economy'
author: "Luis Francisco Gomez Lopez"
date: 2021-03-10 09:12:36 GMT -05:00
output:
beamer_presentation:
colortheme: dolphin
fonttheme: structurebold
theme: AnnArbor
ioslides_presentation: default
slidy_presentation: default
bibliography: macro_faedis.bib
link-citations: yes
header-includes:
- \usepackage{booktabs}
- \usepackage{longtable}
- \usepackage{array}
- \usepackage{multirow}
- \usepackage{wrapfig}
- \usepackage{float}
- \usepackage{colortbl}
- \usepackage{pdflscape}
- \usepackage{tabu}
- \usepackage{threeparttable}
- \usepackage{threeparttablex}
- \usepackage[normalem]{ulem}
- \usepackage{makecell}
- \usepackage{xcolor}
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE,
warning = FALSE,
message = FALSE,
fig.align = "center")
```
```{r}
library(tidyverse)
library(latex2exp)
library(readxl)
library(knitr)
library(kableExtra)
```
# Contents
- Please Read Me
- Purpose
- Demand for goods in an open economy
- IS curve in an open economy
- Marshall–Lerner condition
- IS curve and the Balance of Payments (BOP)
- Acknowledgments
- References
# Please Read Me
- Check the message __Welcome greeting__ published in the News Bulletin Board.
- Dear student please edit your profile uploading a photo where your face is clearly visible.
- The purpose of the virtual meetings is to answer questions and not to make a summary of the study material.
- This presentation is based on [@blanchard_macroeconomics_2017, Chapter 18]
# Purpose
Analyze the equilibrium of the goods market of an open economy.
# Demand for goods in an open economy
- The demand of goods in an open economy is:
+ $\widehat{Z} \equiv \widehat{C} + \widehat{I} + \widehat{G} + \widehat{X} - \varepsilon*\widehat{IM}$
+ If we include behavioral equations we have[^1]: $$\widehat{Z} = \widehat{C}(\widehat{Y}-\widehat{T}) + \widehat{I}(\widehat{Y}, r) + \widehat{G} + \widehat{X}(\widehat{Y}^*,\varepsilon) - \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$$
+ Where exports and imports, $\widehat{X}$ and $\widehat{IM}$, depend on the **real multilateral** exchange rate, $\varepsilon$. Also exports depend on **GDP** inside the territory, $\widehat{Y}$, and imports depend on **GDP** outside the territory, $\widehat{Y}^*$
+ Furthermore, we multiply $\widehat{IM}$ by $\varepsilon$ to express the term $\varepsilon*\widehat{IM}$ in the domestic currency[^2].
[^1]: We are not going to include the **risk premium**, $x$, to facilitate the analysis.
[^2]: If the different **nominal** exchange rates, that are included in $\varepsilon$, are expressed as the amount of **units of national currency** that must be given in exchange for a **unit of foreign currency** then you have to multiply and not divide the imports by $\varepsilon$.
# Demand for goods in an open economy
- The demand of goods in an open economy is:
+ $\widehat{Z} \equiv \widehat{C} + \widehat{I} + \widehat{G} + \widehat{X} - \varepsilon*\widehat{IM}$
+ If we include behavioral equations we have: $$\widehat{Z} = \widehat{C}(\widehat{Y}-\widehat{T}) + \widehat{I}(\widehat{Y}, r) + \widehat{G} + \widehat{X}(\widehat{Y}^*,\varepsilon) - \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$$
+ $\widehat{C}$, $\widehat{I}$ and $\widehat{G}$ include both products that are produced within the economy and products that are produced in the rest of the world.
+ Therefore these variables can depend on $\varepsilon$. In that sense, we assume that if $\varepsilon$ increases, the products produced by the **rest of the world** are replaced by products produced **within** the economy and together $\widehat{C}$, $\widehat{I}$ and $\widehat{G}$ do not change.
# Demand for goods in an open economy
- The demand for goods in an open economy is divided between:
+ Demand for goods **within the territory** that can be produced **within the territory** or in the **rest of the world**: $\widehat{C}(\widehat{Y}-\widehat{T}) + \widehat{I}(\widehat{Y}, r) + \widehat{G}$
+ Demand for goods from the **rest of the world** produced **within the territory**: $\widehat{X}(\widehat{Y}^*,\varepsilon)$
+ Demand for goods **within the territory** produced in the **rest of the world**: $\varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$
- Additionally it is important to mention that for a given period it can happen that:
+ $\widehat{X}(\widehat{Y}^*,\varepsilon) > \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$ (**Trade surplus**)
+ $\widehat{X}(\widehat{Y}^*,\varepsilon) < \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$ (**Trade deficit**)
+ $\widehat{X}(\widehat{Y}^*,\varepsilon) = \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$
# Demand for goods in an open economy
```{r, out.width = '90%'}
ggplot(data = tibble(x = c(0, 5, 0, 5),
y = c(5, 0, -1, -6))
) +
#First plot
geom_point(aes(x = x, y = y),
color = "blue",
size = 3) +
geom_segment(aes(x = 0, y = 0,
xend = 5, yend = 0)) +
geom_segment(aes(x = 0, y = 0,
xend = 0, yend = 5)) +
geom_segment(aes(x = 0, y = 1.5,
xend = 4, yend = 3.5,
),
color = 'red') +
annotate(geom = 'text',
x = 4, y = 3.75,
label = TeX('$\\widehat{Z} = \\widehat{C}(\\widehat{Y}_R-\\widehat{T}) + \\widehat{I}(r,\\widehat{Y}_R) + \\widehat{G}')) +
annotate(geom = 'text',
x = 5.25, y = 0,
label = TeX('$\\widehat{Y}_R$')) +
annotate(geom = 'text',
x = 0, y = 5.25,
label = TeX('$\\widehat{Z}')) +
#Second plot
geom_segment(aes(x = 0, y = -6,
xend = 0, yend = -1)) +
geom_segment(aes(x = 0, y = -6,
xend = 5, yend = -6)) +
geom_segment(aes(x = 0, y = -4.5,
xend = 4, yend = -2.5,
),
color = 'red') +
geom_segment(aes(x = 0, y = -5,
xend = 4, yend = -4,
),
color = 'green') +
annotate(geom = 'text',
x = 5.25, y = -6,
label = TeX('$\\widehat{Y}$')) +
annotate(geom = 'text',
x = 0, y = -0.75,
label = TeX('$\\widehat{Z}')) +
annotate(geom = 'text',
x = 4, y = -2.25,
label = TeX('$\\widehat{Z} = \\widehat{C}(\\widehat{Y}_R-\\widehat{T}) + \\widehat{I}(r,\\widehat{Y}_R) + \\widehat{G}')) +
annotate(geom = 'text',
x = 4, y = -3.75,
label = TeX('$\\widehat{Z} = \\widehat{C}(\\widehat{Y}_R-\\widehat{T}) + \\widehat{I}(r,\\widehat{Y}_R) + \\widehat{G} - \\epsilon\\widehat{M}(\\widehat{Y}_R,\\epsilon)')) +
theme_void()
```
# Demand for goods in an open economy
```{r, out.width = '90%'}
ggplot(data = tibble(x = c(0, 5, 0, 5, 0, 2, 2),
y = c(5, 0, -1, -4, -6, -4, 2.5))
) +
#First plot
geom_point(aes(x = x, y = y),
color = "blue",
size = 3) +
geom_segment(aes(x = 0, y = 0,
xend = 5, yend = 0)) +
geom_segment(aes(x = 0, y = 0,
xend = 0, yend = 5)) +
geom_segment(aes(x = 0, y = 1.5,
xend = 4, yend = 3.5,
),
color = 'red') +
geom_segment(aes(x = 0, y = 1,
xend = 4, yend = 2,
),
color = 'green') +
geom_segment(aes(x = 0, y = 2,
xend = 4, yend = 3,
),
color = 'purple') +
annotate(geom = 'text',
x = 4, y = 3.75,
label = TeX('$\\widehat{Z} = \\widehat{C}(\\widehat{Y}_R-\\widehat{T}) + \\widehat{I}(r,\\widehat{Y}_R) + \\widehat{G}')) +
annotate(geom = 'text',
x = 4, y = 2.25,
label = TeX('$\\widehat{Z} = \\widehat{C}(\\widehat{Y}_R-\\widehat{T}) + \\widehat{I}(r,\\widehat{Y}_R) + \\widehat{G} - \\epsilon\\widehat{M}(\\widehat{Y}_R,\\epsilon)')) +
annotate(geom = 'text',
x = 4, y = 3.25,
label = TeX('$\\widehat{Z} = \\widehat{C}(\\widehat{Y}_R-\\widehat{T}) + \\widehat{I}(r,\\widehat{Y}_R) + \\widehat{G} - \\epsilon\\widehat{IM}(\\widehat{Y}_R,\\epsilon) + \\widehat{X}(\\widehat{Y}^*,\\epsilon)$')) +
annotate(geom = 'text',
x = 5.25, y = 0,
label = TeX('$\\widehat{Y}_R$')) +
annotate(geom = 'text',
x = 0, y = 5.25,
label = TeX('$\\widehat{Z}')) +
#Second plot
geom_segment(aes(x = 0, y = -6,
xend = 0, yend = -1)) +
geom_segment(aes(x = 0, y = -4,
xend = 5, yend = -4)) +
geom_segment(aes(x = 0, y = -2,
xend = 4, yend = -6),
color = 'orange') +
geom_segment(aes(x = 2, y = 2.5,
xend = 2, yend = -4),
linetype = 'dashed') +
annotate(geom = 'text',
x = 5.25, y = -4,
label = TeX('$\\widehat{Y}_R$')) +
annotate(geom = 'text',
x = 0.25, y = -0.75,
label = TeX('$\\widehat{X}(\\widehat{Y}^*,\\epsilon) - \\epsilon\\widehat{IM}(\\widehat{Y}_R,\\epsilon)$')) +
annotate(geom = 'text',
x = 0.5, y = -3.5,
label = 'Trade surplus') +
annotate(geom = 'text',
x = 3.25, y = -4.5,
label = 'Trade deficit') +
annotate(geom = 'text',
x = -0.1, y = -4,
label = '0') +
theme_void()
```
# IS curve in an open economy
- *IS* curve:
+ $\widehat{Y} = \widehat{Z}$
+ $\widehat{Y} = \widehat{C}(\widehat{Y}_R-\widehat{T}) + \widehat{I}(r,\widehat{Y}) + \widehat{G} + \widehat{X}(\widehat{Y}^*,\varepsilon) - \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$
- The **equilibrium condition** in the Goods Market for an Open Economy can by achieve with:
+ $\widehat{X}(\widehat{Y}^*,\varepsilon) > \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$
+ $\widehat{X}(\widehat{Y}^*,\varepsilon) < \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$
+ $\widehat{X}(\widehat{Y}^*,\varepsilon) = \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$
+ With a **trade surplus**, **trade deficit** or **without them** the Goods Market can be in equilibrium.
# IS curve in an open economy
- **Example** of the **equilibrium condition** in the Goods Market with $\widehat{X}(\widehat{Y}^*,\varepsilon) < \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$ (**Trade deficit**)[^3]
```{r, out.width = '65%'}
ggplot(data = tibble(x = c(0, 5, 0, 5, 0, 2, 8/3, 8/3),
y = c(5, 0, -1, -4, -6, -4, 8/3, -14/3))
) +
#First plot
geom_point(aes(x = x, y = y),
color = "blue",
size = 3) +
geom_segment(aes(x = 0, y = 0,
xend = 5, yend = 0)) +
geom_segment(aes(x = 0, y = 0,
xend = 0, yend = 5)) +
geom_segment(aes(x = 0, y = 0,
xend = 4, yend = 4)) +
geom_segment(aes(x = 0, y = 2,
xend = 4, yend = 3,
),
color = 'purple') +
annotate(geom = 'text',
x = 4, y = 4.25,
label = TeX('$\\widehat{Y} \\equiv \\widehat{Y}_R$')) +
annotate(geom = 'text',
x = 4, y = 3.25,
label = TeX('$\\widehat{Z} = \\widehat{C}(\\widehat{Y}_R-\\widehat{T}) + \\widehat{I}(r,\\widehat{Y}_R) + \\widehat{G} - \\epsilon\\widehat{IM}(\\widehat{Y}_R,\\epsilon) + \\widehat{X}(\\widehat{Y}^*,\\epsilon)$')) +
annotate(geom = 'text',
x = 5.25, y = 0,
label = TeX('$\\widehat{Y}_R$')) +
annotate(geom = 'text',
x = 0, y = 5.25,
label = TeX('$\\widehat{Z}\\;\\widehat{Y}')) +
#Second plot
geom_segment(aes(x = 0, y = -6,
xend = 0, yend = -1)) +
geom_segment(aes(x = 0, y = -4,
xend = 5, yend = -4)) +
geom_segment(aes(x = 0, y = -2,
xend = 4, yend = -6),
color = 'orange') +
geom_segment(aes(x = 8/3, y = 8/3,
xend = 8/3, yend = -14/3),
linetype = 'dashed') +
annotate(geom = 'text',
x = 5.25, y = -4,
label = TeX('$\\widehat{Y}_R$')) +
annotate(geom = 'text',
x = 0.25, y = -0.75,
label = TeX('$\\widehat{X}(\\widehat{Y}^*,\\epsilon) - \\epsilon\\widehat{IM}(\\widehat{Y}_R,\\epsilon)$')) +
annotate(geom = 'text',
x = 0.5, y = -3.5,
label = 'Trade surplus') +
annotate(geom = 'text',
x = 3.25, y = -4.5,
label = 'Trade deficit') +
annotate(geom = 'text',
x = -0.1, y = -4,
label = '0') +
theme_void()
```
[^3]: Remember that it can exist equilibriums where $\widehat{X}(\widehat{Y}^*,\varepsilon) \geq \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$
# Marshall–Lerner condition
- The **real** balance trade or **real** net exports, is defined as $\widehat{NX} \equiv \widehat{X} - \widehat{IM}$
+ Using the **behavioral equations** we have that $\widehat{NX} = \widehat{X}(\widehat{Y}^*,\varepsilon) - \varepsilon\widehat{IM}(\widehat{Y},\varepsilon)$
- A natural question that arises is how $\widehat{NX}$ depends on the **real multilateral** exchange rate, $\varepsilon$. If that question can be answered, we can also determine how $\varepsilon$ is related with the **real** GDP, $\widehat{Y}$.
- To answer this question we need to use the concept of **derivative** from differential calculus and the concept of **elasticity** from microeconomics.[^4]
[^4]: If you don't have these tools, please skip this section and focus on the numerical example at the end of the explanation
# Marshall–Lerner condition
- To know the relationship between $\widehat{NX}$ and $\varepsilon$ we must know what determines the sign of $\frac{d\widehat{NX}}{d\varepsilon}$:
\footnotesize
$$\begin{split}
\frac{d\widehat{NX}}{d\varepsilon} & = \frac{d\widehat{X}(\widehat{Y}^*,\varepsilon)}{d\varepsilon} - \frac{d\varepsilon\widehat{IM}(\widehat{Y},\varepsilon)}{d\varepsilon} \\
& = \frac{d\widehat{X}(\widehat{Y}^*,\varepsilon)}{d\varepsilon} - \left[\widehat{IM}(\widehat{Y},\varepsilon) + \varepsilon\frac{d\widehat{IM}(\widehat{Y},\epsilon)}{d\varepsilon}\right] \\
& = \frac{d\widehat{X}(\widehat{Y}^*,\varepsilon)}{d\varepsilon} - \widehat{IM}(\widehat{Y},\varepsilon)\left[1 + \frac{d\widehat{IM}(\widehat{Y},\varepsilon)}{d\varepsilon}\frac{\varepsilon}{\widehat{IM}(\widehat{Y},\varepsilon)}\right] \\
& = \frac{\widehat{X}(\widehat{Y}^*,\varepsilon)}{\varepsilon}\frac{d\widehat{X}(\widehat{Y}^*,\varepsilon)}{d\varepsilon}\frac{\varepsilon}{\widehat{X}(\widehat{Y}^*,\varepsilon)} - \widehat{IM}(\widehat{Y},\varepsilon)\left[1 + \frac{d\widehat{IM}(\widehat{Y},\varepsilon)}{d\varepsilon}\frac{\varepsilon}{\widehat{IM}(\widehat{Y},\varepsilon)}\right]
\end{split}$$
# Marshall–Lerner condition
- To know the relationship between $\widehat{NX}$ and $\varepsilon$ we must know what determines the sign of $\frac{d\widehat{NX}}{d\varepsilon}$:
\footnotesize
$$\begin{split}
\frac{d\widehat{NX}}{d\varepsilon} & =
\widehat{IM}(\widehat{Y},\varepsilon)\left[\frac{\widehat{X}(\widehat{Y}^*,\varepsilon)}{\varepsilon\widehat{IM}(\widehat{Y},\varepsilon)}\frac{d\widehat{X}(\widehat{Y}^*,\varepsilon)}{d\varepsilon}\frac{\varepsilon}{\widehat{X}(\widehat{Y}^*,\varepsilon)} - \frac{d\widehat{IM}(\widehat{Y},\varepsilon)}{d\varepsilon}\frac{\varepsilon}{\widehat{IM}(\widehat{Y},\varepsilon)} - 1\right] \\
& = \widehat{IM}(\widehat{Y},\varepsilon)\left[\frac{\widehat{X}(\widehat{Y}^*,\varepsilon)}{\varepsilon\widehat{IM}(\widehat{Y},\varepsilon)}\eta_{\widehat{X},\varepsilon} - \eta_{\widehat{IM},\varepsilon} - 1\right]
\end{split}$$
Where $\eta_{\widehat{X},\varepsilon} \equiv \frac{d\widehat{X}(\widehat{Y}^*,\varepsilon)}{d\varepsilon}\frac{\varepsilon}{\widehat{X}(\widehat{Y}^*,\varepsilon)}$ and $\eta_{\widehat{IM},\varepsilon} \equiv \frac{d\widehat{IM}(\widehat{Y},\varepsilon)}{d\varepsilon}\frac{\varepsilon}{\widehat{IM}(\widehat{Y},\varepsilon)}$
# Marshall–Lerner condition
- $\eta_{\widehat{X},\varepsilon}$ is the elasticity of the **real multilateral** exchange rate with respect to the **real** exports and $\eta_{\widehat{IM},\varepsilon}$ is the elasticity of the **real multilateral** exchange rate with respect to the **real** imports.
- The sign of $\frac{d\widehat{NX}}{d\varepsilon}$ is determined by:
$$\frac{d\widehat{NX}}{d\varepsilon} =
\left\{
\begin{array}{ll}
>0 & \mbox{if } \frac{\widehat{X}(\widehat{Y}^*,\varepsilon)}{\varepsilon\widehat{IM}(\widehat{Y},\varepsilon)}\eta_{\widehat{X},\varepsilon} - \eta_{\widehat{IM},\varepsilon} > 1 \\
=0 & \mbox{if } \frac{\widehat{X}(\widehat{Y}^*,\varepsilon)}{\varepsilon\widehat{IM}(\widehat{Y},\varepsilon)}\eta_{\widehat{X},\varepsilon} - \eta_{\widehat{IM},\varepsilon} = 1 \\
<0 & \mbox{if } \frac{\widehat{X}(\widehat{Y}^*,\varepsilon)}{\varepsilon\widehat{IM}(\widehat{Y},\varepsilon)}\eta_{\widehat{X},\varepsilon} - \eta_{\widehat{IM},\varepsilon} < 1
\end{array}
\right.$$
- If $\frac{\widehat{X}(\widehat{Y}^*,\varepsilon)}{\varepsilon\widehat{IM}(\widehat{Y},\varepsilon)}\eta_{\widehat{X},\varepsilon} - \eta_{\widehat{IM},\varepsilon} > 1$ then $\frac{d\widehat{NX}}{d\varepsilon} > 0$ and this situation is known as the **Marshall–Lerner condition**. Also if this condition is fulfilled then there is a positive relation between $\varepsilon$ and $\widehat{Y}$.
# Marshall–Lerner condition
- Numerical example of the **Marshall–Lerner condition**
+ Let us assume that $\varepsilon$ increases by 1% and we want to know how much $\widehat{X}$ and $\widehat{IM}$ decrease or increase in percentage terms.
+ The concept of **elasticity** allows us to answer the previous question where it indicates that happens to a dependent variable in percentage terms when an independent variable increases by 1% starting from some initial values of the dependent and independent variable.
+ Let us assume that $\widehat{X}(\widehat{Y}^*,\varepsilon) = \varepsilon\widehat{IM}(\widehat{Y},\varepsilon) > 0$ so $\frac{\widehat{X}(\widehat{Y}^*,\varepsilon)}{\varepsilon\widehat{IM}(\widehat{Y},\varepsilon)} = 1$.
+ Also assume that $\eta_{\widehat{X},\varepsilon} = 0.9$ and $\eta_{\widehat{IM},\varepsilon} = -0.8$. This means that if $\varepsilon$ increases by 1% then $\widehat{X}$ increases by 0.9% and $\widehat{IM}$ decreases by -0.8%.
+ In this case $\frac{\widehat{X}(\widehat{Y}^*,\varepsilon)}{\varepsilon\widehat{IM}(\widehat{Y},\varepsilon)}\eta_{\widehat{X},\varepsilon} - \eta_{\widehat{IM},\varepsilon} = 1*0.9 - (-0.8) = 1.7 > 1$. Therefore, the **Marshall–Lerner condition** is fulfilled for this particular **numerical example**, $\frac{d\widehat{NX}}{d\varepsilon} > 0$.
# IS curve and the Balance of Payments (BOP)
- The **IS** curve for an open economy represents the equilibrium in the Goods Market:
\footnotesize
$$\begin{split}
\widehat{Y} & = \widehat{C}(\widehat{Y}_R-\widehat{T}) + \widehat{I}(r,\widehat{Y}) + \widehat{G} + \widehat{X}(\widehat{Y}^*,\varepsilon) - \varepsilon\widehat{IM}(\widehat{Y},\varepsilon) \\
\widehat{Y} & = \widehat{C}(\widehat{Y}_R-\widehat{T}) + \widehat{I}(r,\widehat{Y}) + \widehat{G} + \widehat{NX}(\widehat{Y}^*,\widehat{Y},\varepsilon) \\
\widehat{Y} - \widehat{C}(\widehat{Y}_R - \widehat{T}) & = \widehat{I}(r,\widehat{Y}) + \widehat{G} + \widehat{NX}(\widehat{Y}^*,\widehat{Y},\varepsilon) \\
\widehat{Y} - \widehat{C}(\widehat{Y}_R - \widehat{T}) - \widehat{T} & = \widehat{I}(r,\widehat{Y}) - (\widehat{T} - \widehat{G}) + \widehat{NX}(\widehat{Y}^*,\widehat{Y},\varepsilon)
\end{split}$$
- In an open economy the income of individuals **within** a territory includes the income obtained **within** the territory and represented by $\widehat{Y}$ as well as other income from the **rest of the world**.
- We are going to include this aspect using elements from the **Balance of Payments (BOP)** and taking into account [@international_monetary_fund_balance_2009]
# IS curve and the Balance of Payments (BOP)
\tiny
```{r}
read_excel(path = '009_bp_resumen_IQY.xlsx',
sheet = 1,
range = 'A11:V53') %>%
select(1:2) %>%
set_names(nm = c('Account', 'Value (Millons USD)')) %>%
slice(1:6, 13:21, 24, 27:28, 31, 34:41) %>%
kable(format = 'latex',
digits = 2, caption = 'Balance of Payments (BOP) for Colombia in 2000') %>%
kable_styling(latex_options = 'scale_down') %>%
row_spec(c(1, 13, 27), bold = TRUE, color = 'white', background = '#e31a1c') %>%
row_spec(c(4, 7, 10, 14, 17, 20, 23, 26), bold = TRUE, color = 'white', background = '#18BC9C') %>%
footnote(general = 'Banco de la República - Colombia',
general_title = 'Source: ',
number = 'Methodology: Sixth version of the Balance of Payments Manual of the International Monetary Fund (IMF)',
alphabet = 'The Capital account does not appear because the sources of information currently available do not allow the identification and registration of capital transfers for Colombia',
footnote_as_chunk = TRUE)
```
# IS curve and the Balance of Payments (BOP)
- The **Primary Income** (**Ingreso primario (Renta factorial)**) and the **Secondary Income** (**Ingreso secundario (Transferencias corrientes)**) represents the other income from the **rest of the world**.
- If the **Primary Income** (**Ingreso primario (Renta factorial)**) is represented by $\widehat{NI}$ and the **Secondary Income** (**Ingreso secundario (Transferencias corrientes)**) is represented by $\widehat{NT}$ we can rewrite the **IS** curve for an open economy as:
\footnotesize
$$\begin{split}
(\widehat{Y} + \widehat{NI} + \widehat{NT} - \widehat{T}) - \widehat{C}(\widehat{Y}_R - \widehat{T}) & = \widehat{I}(r,\widehat{Y}) - (\widehat{T} - \widehat{G}) + \widehat{NX}(\widehat{Y}^*,\widehat{Y},\varepsilon) + \widehat{NI} + \widehat{NT} \\
\widehat{S}^{pr} & = \widehat{I}(r,\widehat{Y}) - \widehat{S}^{pu} + \widehat{CA} \\
\widehat{S}^{pr} + \widehat{S}^{pu} - \widehat{I}(r,\widehat{Y}) & = \widehat{CA}
\end{split}$$
- Where $\widehat{S}^{pr} \equiv (\widehat{Y} + \widehat{NI} + \widehat{NT} - \widehat{T}) - \widehat{C}(\widehat{Y}_R - \widehat{T})$ is the **real** private savings in an open economy, $\widehat{S}^{pu} \equiv \widehat{T} - \widehat{G}$ is the **real** public savings in an open economy and $\widehat{CA} \equiv \widehat{NX}(\widehat{Y}^*,\widehat{Y},\varepsilon) + \widehat{NI} + \widehat{NT}$ is the **current account**.
# IS curve and the Balance of Payments (BOP)
- In that sense, if the Goods Market is in equilibrium then the difference between savings and investment is equal to the **current account**.
\footnotesize
$$\begin{split}
(\widehat{Y} + \widehat{NI} + \widehat{NT} - \widehat{T}) - \widehat{C}(\widehat{Y}_R - \widehat{T}) & = \widehat{I}(r,\widehat{Y}) - (\widehat{T} - \widehat{G}) + \widehat{NX}(\widehat{Y}^*,\widehat{Y},\varepsilon) + \widehat{NI} + \widehat{NT} \\
\widehat{S}^{pr} & = \widehat{I}(r,\widehat{Y}) - \widehat{S}^{pu} + \widehat{CA} \\
\widehat{S}^{pr} + \widehat{S}^{pu} - \widehat{I}(r,\widehat{Y}) & = \widehat{CA}
\end{split}$$
- Where $\widehat{S}^{pr} \equiv (\widehat{Y} + \widehat{NI} + \widehat{NT} - \widehat{T}) - \widehat{C}(\widehat{Y}_R - \widehat{T})$ is the **real** private savings in an open economy, $\widehat{S}^{pu} \equiv \widehat{T} - \widehat{G}$ is the **real** public savings in an open economy and $\widehat{CA} \equiv \widehat{NX}(\widehat{Y}^*,\widehat{Y},\varepsilon) + \widehat{NI} + \widehat{NT}$ is the **current account**.
# Acknowledgments
- To my family that supports me
- To the taxpayers of Colombia and the __[UMNG students](https://www.umng.edu.co/estudiante)__ who pay my salary
- To the __[Business Science](https://www.business-science.io/)__ and __[R4DS Online Learning](https://www.rfordatasci.com/)__ communities where I learn __[R](https://www.r-project.org/about.html)__
- To the __[R Core Team](https://www.r-project.org/contributors.html)__, the creators of __[RStudio IDE](https://rstudio.com/products/rstudio/)__ and the authors and maintainers of the packages __[tidyverse](https://CRAN.R-project.org/package=tidyverse)__, __[tidyquant](https://CRAN.R-project.org/package=tidyquant)__, __[latex2exp](https://CRAN.R-project.org/package=latex2exp)__,
__[readxl](https://CRAN.R-project.org/package=readxl)__, __[knitr](https://CRAN.R-project.org/package=knitr)__,
__[kableExtra](https://CRAN.R-project.org/package=kableExtra)__ and __[tinytex](https://CRAN.R-project.org/package=tinytex)__ for allowing me to access these tools without paying for a license
- To the __[Linux kernel community](https://www.kernel.org/category/about.html)__ for allowing me the possibility to use some __[Linux distributions](https://static.lwn.net/Distributions/)__ as my main __[OS](https://en.wikipedia.org/wiki/Operating_system)__ without paying for a license
# References