Imagine we have an economy with two goods, X and Y. We will indicate the level of endowment of goods X and Y to country H (Home) using X_H and Y_H, respectively.

The endowment of X_H units of X and Y_H units of Y gives country H a certain level of satisfaction or utility. If H had fewer units of Y, for example Y'_H, then to achieve the same level of satisfaction H will need more units of X, as indicated by X'_H.

Likewise, with fewer units of X, more units of Y are needed to maintain the same level of satisfaction.

If we connect all the points that give H this same level of satisfaction (or utility), we will have a curve, I_H, known as the indifference curve.

(1)

If H is able to move to a point above the line I_H, for example by increasing endowment of both X and Y to X''_H and Y''_H respectively, then H's level of satisfaction has increased, and can be represented by another indifference curve I''_H.

There are many other such curves above and below I_H, all connecting points of equal satisfaction.

Like H, country F (Foreign) has indifference curves. We'll denote F's endowment of goods X and Y with X_F and Y_F, and F's indifference curve with I_F.