Utility maximization consumer

Introduction: In consumer behavior it is assumed that a consumer wants to maximize his utility.

  • $p_1$ is the price of good $x$
  • $p_2$ is the price of good $y$
  • $I$ is the available income

Consider the utility maximization problem

\mbox{subject to}&p_1x+p_2y=I,\\
\mbox{where} &  x \in D_1 \ \mbox{and} \ y \in D_2.

An extremum location $(x,y)=(c,d)$, where $c \in D_1$ and $d \in D_2$ that is not a boundary point, satisfies the following system of equations:

p_1x + p_2 y &=&I.