R: Find intersection of two vectors

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]