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To identify the shape of the LRAS curve, we'll start by analyzing the main characteristics of the long-run aggregate supply in the context of an economy. In the long run, all factors of production are variable, meaning that we can adjust the amounts of labor and capital employed in the production process. When the economy is operating at potential output, it means that it is using all of its resources efficiently. The LRAS curve is, therefore, vertical because it represents potential output or full employment.

The LRAS curve is vertical because it represents the potential output an economy can reach when resources are fully employed and efficiently utilized. In the long run, changes in the overall price level have no effect on the total amount of goods and services that an economy can produce. This is because, in the long run, factors of production (such as labor and capital) can adjust to changes in the price level. For example, if the price level increases, firms may initially respond by producing more goods and services to take advantage of higher profits. However, over time, workers will demand higher wages, and suppliers will increase the prices of raw materials. These factors will increase production costs, offsetting the initial increase in prices. As a result, in the long run, the economy will return to its potential output level, and the output will not be affected by changes in the price level.

The long-run aggregate supply curve is vertical because it represents the maximum output an economy can produce when labor and capital are fully utilized at their most efficient levels. In the long run, changes in the overall price level do not affect the total amount of goods and services that an economy can produce, which is why the LRAS curve is vertical and not affected by changes in the price level.