A community indifference curve is an illustration of different combinations of commodity

Commodity

In economics, a commodity is the generic term for any marketable item produced to satisfy wants or needs. Economic commodities comprise goods and services....

 quantities that would bring a whole community

Community

The term community has two distinct meanings:*a group of interacting people, possibly living in close proximity, and often refers to a group that shares some common values, and is attributed with social cohesion within a shared geographical location, generally in social units larger than a household...

 the same level of utility. The model can be used to describe any community, such as a town or an entire nation. In a community indifference curve, the indifference curves of all those individuals are aggregated

Aggregate data

In statistics, aggregate data describes data combined from several measurements.In economics, aggregate data or data aggregates describes high-level data that is composed of a multitude or combination of other more individual data....

 and held at an equal and constant level of utility

Utility

In economics, utility is a measure of customer satisfaction, referring to the total satisfaction received by a consumer from consuming a good or service....

.

Solving for a CIC

A community indifference curve (CIC) provides the set of all aggregate endowments (x-bar, y-bar) = (x1 + x2, y1, + y2) needed to achieve a given distribution of utilities, (u1-bar, u2-bar). The community indifference curve can be found by solving for the following minimization problem:



Min y-bar s.t. U1(x1, y1,) ≥ u1-bar and U2(x-bar – x1,y-bar – y1) ≥ u2-bar


CICs assume allocative efficiency amongst members of the community. Allocative Efficiency provides that MRS1xy = MRS2 xy.
The CIC comes from solving for y-bar in terms of x-bar, y-cic(x-bar).

Community indifference curves are an aggregate of individual indifference curves.