# How do I represent this indifference curve graphically?

I am not able to visualize this indifference curve.

I consume only two goods: sugar and milk.

I will prefer a bundle X of sugar and milk over a bundle Y only if $x_{sugar} > y_{sugar}$, and $x_{milk} > y_{milk}$.

If $Y_{sugar} > x_{sugar}$ and $y_{milk} > x_{milk}$, then I prefer Y bundle over X.

If neither case is true, I am indifferent between the two bundles.

How do I plot this on a graph? I need to solve a question, and I believe being able to draw a graph will be helpful!

This is how I visualize it. Is this representation correct? The problem is that there are no indifference "curves" but indifference "areas". Consider the following graph: For a reference bundle $A$ (equivalent to $\{2,3\}$), the gray regions indicate the areas of indifference, based on your definition of preferences (the black lines are part of the indifference areas).

Thus, by selecting any bundle, you can find the indifference "areas" by plotting the vertical and horizontal lines across that point. Areas to the North-West and South-East will always be the indifference "areas".

For reference, this is the R code to generate the graph:

remove(list = ls())

a=2
b=3

plot(c(0,5), c(0,5), type = "n", xlab = "Sugar", ylab = "Milk", xaxs="i", yaxs="i")
rect(0, b, a, 5, border = NA, col = "grey60")
rect(a, 0, 5, b, border = NA, col = "grey60")
abline(h = b, col = 1, lwd = 2)
abline(v=a, col = 1, lwd = 2)
points(a, b, type="p", pch=19, col="black", bg=NA, cex=2)
text(1, 4, "Indifferent",cex = 1.3)
text(3.5, 1.5, "Indifferent",cex = 1.3)
text(1, 1.5, "Worse off",cex = 1.3)
text(3.5, 4, "Better off",cex = 1.3)
text(2.2, 3.3, "A",cex = 1.3)

• You are welcome. Pick any point other than A. Then, compare the x and y axis values with those of A. The text in the region tells you how that bundle that you picked compares with A. For instance, pick (4,4). This bundle has more sugar and milk. Therefore, it is preferred to A. The individual is better off with that new bundle. – luchonacho Feb 23 '17 at 17:42
• Any feedback from downvoters is mostly appreciated. Thanks. – luchonacho May 11 '17 at 6:02