Quantitative Economics
This is a repository about the book " An Introduction to R for Quantitative Economics" by Vikram Dayal.
Chapter Three - Getting data into R
In this chapter, three datasets are described and made avalaible to further use in the next chapters.
First, we load the needed packages to read the three datasets:
library(readr)
library(readxl)
library(xlsx)
1. Chhatre and Agrawal (2009) Data
This dataset is about carbon storage and livelihood benefits from forest commons.
ifri_car_liv <- read_csv("/Users/MAC/Documents/AmbienteR/Quantitative-Economics/Chapter 3 Getting data into R/Raw data/carbon_livelihoods_dataset1.zip Folder/ifri_car_liv.csv")
Some basic commands in R are displayed:
head - it looks at the top rows of the dataset;
head(ifri_car_liv)
brackets [ ] - it chooses specific rows and columns;
str - it displays the structure of the data.
str(ifri_car_liv)
2. Graddy (2006) Data
This dataset is about the prices paid by individual buyers at the Fulton fish market in New York.
Fulton <- read_table2("/Users/MAC/Documents/AmbienteR/Quantitative-Economics/Chapter 3 Getting data into R/Raw data/fulton.zip Folder/Fulton.txt")
head(Fulton)
str(Fulton)
3. Crude Oil Price Data
This dataset brings oil crude prices since 1861.
Oil_prices <- read_excel("/Users/MAC/Documents/AmbienteR/Quantitative-Economics/Chapter 3 Getting data into R/Raw data/Crude Oil Price Data/bp-stats-review-2021-all-data.xlsx", sheet = "Oil - Crude prices since 1861", skip = 3)
head(Oil_prices)
str(Oil_prices)
Warning: it's necessary to convert the "Year" column from character to numeric:
Oil_prices$Year <- lapply(Oil_prices$Year, as.integer)
Oil_prices$Year <- as.numeric(Oil_prices$Year)
Chapter Four - Supply and Demand
In this chapter, demand and supply functions are mathematical and graphical treated with the mosaic package. Also in this chapter, the equilibrium between supply and demand is calculated.
1. A little bit of theory
1.1 Demand function
The demand is usually defined as a schedule of quantities that buyers are willing and able to purchase at a schedule of prices in a given time interval, ceteris paribus.
Actually, the demand function is influenced by many variables: the price of the good, the prices of related goods (compliments and substitutes), incomes of the buyers, the tastes and preferences of the buyers, the period of time and a variety of other possible variables.
Indeed, an individual's demand function for a good (good X) might be written as:
Qx = f(Px, P(related goods), income (M), preferences, . . . ), where:
• Qx = the quantity of good X demanded
• Px = the price of demand for the good X
• P(related goods) = the prices of compliments or substitutes
• Income(M) = the income of the buyers
• Preferences = the preferences or tastes of the buyers
For the sake of simplicity, the demand function is based on an inverse or negative relationship between the price and quantity of a good purchased. Thus, let the quantity demanded Qx be given by:
Qx = αd − βd.Px, where:
αd = all relevant non-specified factors that affect demand for the product; and
βd = slope of the demand curve. The coefficient is negative in accordance with the law of demand. Actually, the related good may be either a complement or a substitute. If it is a complement, the coefficient of its price would be negative. If it is a substitute, the coefficient of its price would be positive.
1.2 Supply function
On the other side, supply is a schedule of quantities that will be produced and offered for sale at a schedule of prices in a given time period, ceteris paribus.
A supply function is a model that represents the behavior of the producers and/or sellers in a market.
Indeed, an individual's supply function of a good (good X) might be written as:
Qx = f(Px, P(inputs), technology, number of sellers, laws, taxes, expectations . . . #S), where:
• Qx = quantity of the good X supplied
• Px = price of supply of the good X
• P(inputs) = prices of the inputs (factors of production used)
• Technology is the method of production (a production function), laws and regulations may impose more costly methods of production
• taxes and subsidies alter the costs of production
• #S represents the number of sellers in the market
For the sake of simplicity, the supply function is based on a direct or positive relationship between the price and quantity of a good supplied. Thus, let the quantity demanded Qx be given by:
Qx = αs + βs.Px, where:
αs = all relevant non-specified factors that affect demand for the product; and
βs = slope of the supply curve. The coefficient of Px is positive following the general rule that price and quantity supplied are directly related.
1.3 Supply and demand law
The price of any good adjusts to bring the quantity supplied and the quantity demanded of the good into equilibrium.
At equilibrium, demand = supply, i.e. D = S. This gives us the equilibrium price:
Px = (αd − αs)/(βd + βs)
2. Loading the Mosaic Package
The mosaic package is designed to facilitate the use of R in statistics and calculus instruction by providing a number of functions that (a) make many common tasks fit into a common template, and (b) simplify some tasks that would otherwise be too complicated for beginners.
install.packages("mosaic")
library(mosaic)
3. Plotting the demand curve
First of all, we set up an inverse demand function in order to place the independent variable on the y-axis and the dependent variable on the x-axis. So, let the price demanded be given by pD = (125 − 6q) / 8, where aD = 125, bD = 6 and cD = 8.
Next, we use the makeFun Mosaic function which creates the demand function below:
pD <- makeFun(( aD - ( bD * q ) ) / cD ~ q, aD = 125, bD = 6, cD = 8)
D denotes demand, p denotes price, q denotes quantity and a, b, and c are parameters; aD is the parameter related to the demand function. Note the use of the tilde (~): the expression to the left of it is a function of the variable on the right of it.
To see what price in the inverse demand function corresponds to a quantity of 20, we type in the value of q as follows:
pD(20)
[1] 0.625
So, when q = 20, pD = 0.625.
We will now plot the first inverse demand function:
curve(expr = pD, from = 0, to = 30, ylim = c(0, 20), lty = 1, lwd = 1.5, main = "1st Demand Curve", col = "blue", xlab = "Quantity", ylab = "Price")
Assuming a general increase in incomes, each individual would choose to buy more "q" at every price. To express the shift in the demand curve due to the general increase in income, we make and plot a second demand function, given by pD2 = (125 − 6q) / 8, where aD = 150, bD = 6 and cD = 8. The only difference to pD is that aD is now equal to 150.
pD2 <- makeFun(( aD - ( bD * q )) / cD ~ q, aD = 150, bD = 6, cD = 8)
To see what price in the inverse demand function corresponds to a quantity of 20, we type in the value of q as follows:
pD2(20)
[1] 3.75
So, when q = 20, pD2 = 3.75
We will now plot the second inverse demand function:
curve(expr = pD2, from = 0, to = 30, ylim = c(0, 20), lty = 1, lwd = 1.5, main = "2nd Demand Curve", col = "red", xlab = "Quantity", ylab = "Price")
We can now plot both the demand curves pD and pD2 together:
curve(expr = pD, from = 0, to = 30, ylim = c(0, 20), lty = 1, lwd = 1.5, main = "1st and 2nd Demand Curves", col = "blue", xlab = "Quantity", ylab = "Price") curve(pD2, add = TRUE, lwd = 2, col = "red")
4. Plotting the supply curve
We set up a supply function where the quantity supplied is given by pS = (12 + 2q) / 5, where aD = 12, bD = 2 and cD = 5.
pS <- makeFun((aS + (bS * q))/cS~q, aS = 12, bS = 2, cS = 5)
We will now plot the supply function:
curve(expr = pS, from = 0, to = 30, ylim = c(0, 20), lty = 1, lwd = 1.5, main = "Supply Curve", col = "violet", xlab = "Quantity", ylab = "Price")
Finally, we can plot both supply and demand curves together:
curve(expr = pD, from = 0, to = 30, ylim = c(0, 20), lty = 1, lwd = 1.5, main = "Supply and Demand Curves", col = "blue", xlab = "Quantity", ylab = "Price") curve(pD2, add = TRUE, lwd = 2, col = "red") curve(pS, add = TRUE, lwd = 2, col = "violet")
A rightward shift in demand increases equilibrium price and equilibrium quantity. Although we can see the equilibrium from the point of intersection of D and S, we may want to calculate the equilibrium price and quantity.
5. Market equilibrium
Market equilibrium is found at the point where the supply curve intersects the demand curve. At equilibrium price, quantity supplied is equal to quantity demanded. Then:
((aD - (bD * q))/cD) - ((aS + (bS * q))/cS))
We use the findZeros function and apply it to the excess demand at the initial (before the demand curve shifted) equilibrium quantity:
q.equil_0 <- findZeros(((aD - (bD * q))/cD) - ((aS + (bS * q))/cS) ~ q, aD = 125, bD = 6, cD = 8, aS = 12, bS = 2, cS = 5)
To find what quantity corresponds to the initial equilibrium quantity, we type:
q.equil_0
[1] 12
In the same way, to find what price corresponds to the initial equilibrium price, we type:
pD(q.equil_0)
[1] 6.625
We also use the findZeros function and apply it to the excess demand at the final (after the demand curve shifted) equilibrium quantity:
q.equil_1 <- findZeros(((aD - (bD * q))/cD) - ((aS + (bS * q))/cS) ~ q, aD = 150, bD = 6, cD = 8, aS = 12, bS = 2, cS = 5)
To find what quantity corresponds to the final equilibrium quantity, we type:
q.equil_1
[1] 14
In the same way, to find what price corresponds to the final equilibrium price, we type:
pD(q.equil_1)
[1] 3.75
6. A little bit of practice
6.1 Fish Data
Kathryn Graddy collected data on price and quantities in the Fulton fish market, a large market in New York, and reported the results of her study of the prices paid by individual buyers. We can bring the Fulton fish market dataset into R as follows:
Fish <- read.csv2("/Users/MAC/Documents/AmbienteR/Quantitative-Economics/Chapter 3 Getting data into R/Raw data/fulton.zip Folder/Fulton.csv")
inspecting the dataset
head(Fish)
str(Fish)
Notice that both price and quantity variables are linearized. Later, we will deal with this topic.
For now, we plot price against quantity in a scatter plot. In order to do that we use a function or command that is in the Mosaic package, namely xyplot:
xyplot(LogPrice ~ LogQuantity, data = Fish, main = "Fish Market Data", sub = "Equilibrium price versus equilibrium quantity", col = "red", xlab = "Quantity", ylab = "Price")
Since both supply and demand were changing, we cannot “identify” a supply or demand curve only from the above scatter plot.
However, Graddy found that stormy weather shifted the supply curve. So we can identify the demand curve using that information. In other words, stormy weather serves as an ‘instrumental variable.
Thus, we will plot price against stormy variable (stormy weather, that is if the weather was stormy or not on fishing day). We ‘jitter’ the stormy variable, that is add some random noise to help distinguishing different observations. We also ask for type = p for points and = r for regression line:
xyplot(LogPrice ~ jitter(Stormy), data = Fish, type = c("p","r"), main = "Fish Market Data", sub = "Price versus Stormy Weather")
