How to read this
At the prices the cheapest bundle is . Keeping while changes would cost the black line . But the firm substitutes, so the true cost (blue) lies below that line and touches it at . A function below all its tangent lines is concave (C4).
- Drag in the plot: the slope where they touch is , Shephard's lemma (C5).
- Scale both prices by : cost scales with them, input demand does not (C3, H3).
Technology
Scale
Reference prices and output
Price scaling
Cost as a function of
: inputs adjust; cost if inputs stay at ; the shaded gap is the saving from substitution. Move the pointer over the plot to compare prices; drag (or tap) to move .