Most micro diagrams show indifference curves and budget lines in the plane, as if the object of interest were a flat map. The map is really a projection \(\mathbb{R}^3 \to \mathbb{R}^2\): we plot \((x_1,x_2)\) and suppress the utility coordinate, even though the graph \((x_1,x_2,U(x_1,x_2))\) lives in three dimensions. Those curves are level sets of \(U(x_1,x_2)\) seen after that collapse. We rarely draw the height, so it is easy to forget what “moving along an indifference curve” or “tangent to the budget” means in the geometry of the surface. I think that missing picture is an underappreciated source of confusion when we lean on two-dimensional graphs alone.
The interactive view below is the same tool as the standalone project ev-cv-3d (also hosted here): a coloured utility “hill”, horizontal slices as indifference curves, the budget as a vertical curtain, and the Marshallian optimum on the surface. It is meant as intuition alongside the usual 2D EV/CV diagrams, not as a substitute for welfare measured in money units.
Interactive embedded below. The frame is fixed-height so the chart can stay in place while the controls pane scrolls independently.
If your browser blocks the embed, open the standalone interactive.