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Problem : What relationship does the aggregate supply curve show?

The aggregate supply curve shows the relationship between the price level and the quantity of goods and services supplied in an economy.

Problem : What is the equation for the aggregate supply curve in the short run?

The equation for the aggregate supply curve in the short run is Y = Ynatural + a(P - Pexpected).

Problem : What does each of the terms mean in the equation for the short-term aggregate supply curve and what does the equation mean overall?

The equation for the short run aggregate supply curve, is Y = Ynatural + a(P - Pexpected). In this equation, Y is output, Ynatural is the natural rate of output that exists when all productive factors are used at their normal rates, a is a constant greater than zero, P is the price level, and Pexpected is the expected price level. This equation means that output deviates from the natural rate of output when the price level deviates from the expected price level.

Problem : What is the slope of both the short run aggregate supply curve and of the long run aggregate supply curve?

The slope of the short-term aggregate supply curve is (1/a); the long-term aggregate supply curve is vertical and therefore has no slope.

Problem : Give one reason for why the long-term aggregate supply curve is vertical and four models for why the short-term aggregate supply curve is upward sloping.

The long run aggregate supply curve is vertical because output in the long run is fixed by the factors of production, namely capital and labor. Four models for why the short run aggregate supply curve is upward sloping are the sticky-wage model, the worker-misperception model, the imperfect-information model, and the sticky-price model.
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