The long-run aggregate supply curve is vertical because it is at the full-employment or potential output. Because the economy's potential output is determined by the availability and productivity of real resources, not by the price level. That means that even if demand increases, firms can't hire new workers and expand because everyone is already working.
Amartya Sen, Indian economist who was awarded the 1998 Nobel Prize in Economic Sciences for his contributions to welfare economics and social choice theory and for his interest in the problems of society's poorest members
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