A change that shifted the long-run aggregate supply curve to the right would not necessarily shift the short-run aggregate supply curve to the right.

False - Increase in the amount of capital employed can shift both

Explanation:

In the long-run aggregate supply curve is vertical and only labor, capital and technology cause the aggregate supply curve to shift.

In the short-run, the aggregate supply curve is upward sloping and can be affected by only one factor of production (capital)

What shifts the long-run aggregate supply curve to the right include; an increase in the amount of labor or capital employed or the discovery of new technology (innovation).

In the short run however, only an increase in capital employed move the aggregate supply curve outward.

Therefore, only an increase in the amount of capital employed can shift both the short and long run aggregate supply curve to the right