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006_homework2_format.Rmd
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---
title: "Homework 2"
author:
- XXXXXXXX (Only code no name)
- XXXXXXXX (Only code no name)
- XXXXXXXX (Only code no name)
- XXXXXXXX (Only code no name)
- XXXXXXXX (Only code no name)
- XXXXXXXX (Only code no name)
date: ''
output:
word_document:
toc: yes
toc_depth: '3'
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = FALSE,
warning = FALSE,
message = FALSE,
fig.align = "center")
```
# Financial markets I
## Exercise 2
This exercises is taken from:
**Oliver Blanchard (2017) Macroeconomics (7 Edition)** > Chapter 4 Financial Markets I > Questions and Problems > Exercise 2
Suppose that the houselhold nominal income for an economy, $Y_t$, is $\$50,000$ billions and the nominal demand for money, $M_t^d$, in this economy is given by:
$$M_t^d = Y_t*(0.2 - 0.8i_t)$$
Where $i_t$ is the nominal interest rate fixed by the central bank.
1. What is the demand for money when the interest rate is $i_t = 0.01 (1\%)$ and $i_t = 0.05 (5\%)$? **(3.5 points)**
2. What will be the impact on the demand of money, $M_t^d$, if the nominal income, $Y_t$, declines by $20\%$? **(3.5 points)**
3. What is the relation between the demand of money, $M_t^d$, and the nominal income, $Y_t$? **(3.5 points)**
4. What is the relation between the demand of money, $M_t^d$, and the nominal interest rate fixed by the central bank, $i_t$? **(3.5 points)**
5. Explain what the central bank should do to the interest rate, $i_t$, if it needs to increase the demand of money, $M_t^d$. **(3.5 points)**
## Data from Colombia in relation to the financial market
### Demand for central bank money
In the appendix of *Chapter 4 Financial Markets I* from the book **Oliver Blanchard (2017) Macroeconomics (7 Edition)** there is an explanation about the demand for central bank money.
- Enter into the Bank of the Republic (Colombia) using the route:
**http://www.banrep.gov.co/** > Estadísticas > Tasas de interés y sector financiero > 3. Agregados monetarios, encaje y cartera > Agregados monetarios > Descargar y consultar: Efectivo, Base monetaria, M3 y sus componentes - Mensual > Exportar
6. Make a plot of **Efectivo** ($CU_t^d$ in the model), **Reserva Bancaria** ($R_t^d$ in the model) and **Total** as the sum of **Efectivo** plus **Reserva Bancaria** ($H_t^d$ in the model) for *Colombia* where the x-axis corresponds to the date and y-axis corresponds to the values of **Efectivo**, **Reserva Bancaria** and **Total**. **(3.5 points)**
### Nominal interest rate fixed by the central bank
Section *4-3 Determining the interest rate II* mentions the **federals fund rate** as the $i_t$ for the model in the USA. In Colombia $i_t$ is know as **“Tasa de intervención del Banco de la República”**.
- Enter into the Bank of the Republic (Colombia) using the route:
**http://www.banrep.gov.co/** > Estadísticas > Tasas de interés y sector financiero > 1. Tasas de interés de política monetaria > Tasas de interés de política monetaria > Descargar y consultar: Serie diaria (desde 04/01/1999)
7. Make a plot of **Tasa de intervención de política monetaria** ($i_t$ in the model) for *Colombia* where the x-axis corresponds to the date and y-axis corresponds to the value of **Tasa de intervención de política monetaria**. **(3.5 points)**
# Goods and financial markets: The IS-LM model
## Goods market and real variables
- Enter into the World Bank's Human Development Indicators database using the link:
<**https://databank.worldbank.org/source/world-development-indicators**>
- In *Country* select *Colombia*
- In *Series* select *GDP (constant LCU)*, *Households and NPISHs Final consumption expenditure (constant LCU)*, *Gross capital formation (constant LCU)* and *General government final consumption expenditure (constant LCU)*
- In *Time* select *VIEW RECENT YEARS: 50*
- Apply changes and download the data using *Download options > Excel* at the upper right corner of the platform
8. Make a plot of *GDP (constant LCU)* ($Y_t$ in the model expressed in real terms), *Households and NPISHs Final consumption expenditure (constant LCU)* ($C_t$ in the model expressed in real terms), *Gross capital formation (constant LCU)* ($I_t$ in the model expressed in real terms) and *General government final consumption expenditure (constant LCU)* ($G_t$ in the model expressed in real terms) for *Colombia* where the x-axis corresponds to the date and y-axis corresponds to the values of *GDP (constant LCU)*, *Households and NPISHs Final consumption expenditure (constant LCU)*, *Gross capital formation (constant LCU)* and *General government final consumption expenditure (constant LCU)*. **(3.5 points)**
## Exercise 5
This exercises is based on:
**Oliver Blanchard (2017) Macroeconomics (7 Edition)** > Chapter 5 Goods and Financial Markets; The IS-LM model > Questions and Problems > Exercise 5
Consider the following numerical example of the IS-LM model:
$$C_t = 100 + 0.3Y_{tD}$$
$$I_t = 150 + 0.2Y_t - 1000i_t$$
$$T_t = 100$$
$$G_t = 200$$
$$\overline{i}_t = 0.01 (1\%)$$
$$(\frac{M}{P})^d = 2Y_t - 4000i_t$$
9. Find the equation for aggregate demand. **(3.5 points)**
10. Derive the IS relation. **(3.5 points)**
11. Derive the LM relation assuming that the central bank fix $\overline{i}_t = 0.01 (1\%)$. Remember that the LM relation will be an horizontal line. **(3.5 points)**
12. Solve for the equilibrium values of $Y_t$, $i_t$, $C_t$, $I_t$ and $(\frac{M}{P})^s$. **(3.5 points)**
13. Suppose that the central bank fix the money supply to $(\frac{M}{P})^s = 1500$. What is the impact of this monetary policy on the IS and LM curves? **(3.5 points)**
14. Find the new equilibrium values of $Y_t$, $i_t$, $C_t$ and $I_t$ when $(\frac{M}{P})^s = 1500$. **(4 points)**