How to read this
The firm starts at . When rises, the change splits into substitution along the old isoquant to and scale down the new expansion path to . The two-step split is bookkeeping: as rises gradually, both effects happen at once.
- Press ▶ Step by step: first , then .
- Press ▶ Raise w₁ smoothly, then drag : at every point the blue and red arrows add up to the black one, the direction of the path.
- Try Leontief: no substitution, only scale.
Technology
Prices
Input space
isoquants for and ; old and new isocost line; dotted rays: old and new expansion paths. The bars on the axis add up: substitution + scale = total.
now: isoquant, isocost line and (dotted) expansion path at the current ; faint: the same at the start. The bars on the axis grow together: substitution + scale = total, accumulated so far.
Why output falls
A higher input price shifts marginal cost up, so the profit-maximising output falls. MC after, thin: MC before, AC after.
A higher input price shifts marginal cost up, so the profit-maximising output falls, gradually, as rises. MC now, thin: at the start, dotted: at the end, AC now.