R: Find intersection of two vectors - r

Question

I have two vectors. I need to find the intersection between these two, and do a nice plot of it.
So, here is a very simple data frame example:
df <- data.frame( id <- c(1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2),
p <-c(5,7,9,11,13,15,17,19,21,23,20,18,16,14,12,10,8,6,4,2 ),
q <-c(3,5,7,13,19,31,37,53,61,67,6,18,20,24,40,46,66,70,76,78))
colnames(df) <- c("id","price","quantity")
supply <- df[df$id == 1,]
demand <- df[df$id == 2,]
plot( x = supply$quantity, y = supply$price, type = "l", ylab = "price", xlab = "quantity")
lines(x = demand$quantity , y = demand$price, type = "l")
grid()
Now, I can plot them and find the intersection manually, but can you make R calculate the intersection between these two lines?
The data can take huge jumps, and the lines can go from very step to nearly horizontal.

Answer 1

Be careful creating your data frame. You want =, not <-. Also, make id a factor, for clarity.
df <- data.frame(
id = factor(rep(c("supply", "demand"), each = 10)),
price = c(5,7,9,11,13,15,17,19,21,23,20,18,16,14,12,10,8,6,4,2 ),
quantity = c(3,5,7,13,19,31,37,53,61,67,6,18,20,24,40,46,66,70,76,78)
)
First we define common, frequent points to evaluate the quantity at.
quantity_points <- with(
df,
seq(min(quantity), max(quantity), length.out = 500)
)
Now split the dataset into supply/demand parts.
by_id <- split(df[, c("price", "quantity")], df$id)
Then we use approx to calculate the price at each of these quantities, for supply and demand separately.
interpolated_price <- lapply(
by_id,
function(x)
{
with(
x,
approx(
quantity,
price,
xout = quantity_points
)
)$y
}
)
Finally, the crossing point is where the absolute value of the supply price minus the demand price is minimised.
index_of_equality <- with(interpolated_price, which.min(abs(supply - demand)))
quantity_points[index_of_equality]