U is convex to the origin and we can have a system (that is, a family or an infinitely large number) of them. A higher (the one farther away from the origin) curve represents a greater total satisfaction for the nation and is therefore preferred to the one which is lower (that is, nearer the origin). Further, the difference between the levels of satisfaction represented by two indifference curves cannot be measured in absolute terms.
Similarly, no two indifference curves of a nation can intersect each other. Limitations: Community indifference curves suffer from several limitations which inherently flow from their assumptions. Reference Timing: They are drawn with reference to a point of time, and are, therefore, subject to continuous revision. Information: In practice, the information needed for drawing these curves is never fully available.
Most of the time, these curves have to be drawn and used only for the purpose of abstract reasoning and illustration. Adding up Individual Preferences: Community indifference curves are to be derived by addition of indifference curves of individual members of the society. This brings in problems of interpersonal comparison of utility, differences in tastes and incomes, and the like. Addition of individual curves to get community indifference curves is possible only if tastes and preferences of all members of society are identical. Income Distribution: Community indifference curves are drawn with reference to a given distribution of income. However, when international trade takes place, income distribution within the community undergoes a change. This happens because international trade causes a shift in the production pattern and, therefore, changes in the prices of factors of production. Since individual members of society get their incomes by supplying to the market productive resources owned by them, therefore, incomes of some groups increase while those of others may even decline.
Moreover, the nation as a whole also becomes richer. All these developments lead to a shift in the tastes and preferences of the community. Existence of State: The State is a part of the community and its demand pattern contributes to the location and slope of the community indifference curves. However, the State does not determine its preference only on the basis of economic considerations. Non-economic considerations also play an important role in its preference map.