🎮 3D Utility Maximization

This 3D visualization extends the standard two-good utility maximization problem to three goods. The budget constraint is now a plane in three-dimensional space rather than a line, and the indifference curves become indifference surfaces. The consumer's problem is to find the point on the budget plane that lies on the highest possible indifference surface.

With Cobb-Douglas preferences U = X^α · Y^β · Z^(1-α-β), the optimal solution allocates income in proportion to the exponents: fraction α to X, β to Y, and (1-α-β) to Z. This elegant result generalizes directly from the two-good case. Rotate the 3D view to see how the indifference surface is tangent to the budget plane at the optimum.