Question

Suppose that the equation for a particular short-run AS curve is P = 20 + 0.5Q, where P is the price level and Q is real output in dollar terms. What is Q if the price level is 120? Suppose that the Q in your answer is the full-employment level of output. By how much will Q increase in the short run if the price level unexpectedly rises from 120 to 132? By how much will Q increase in the long run due to the price level increase?

Short answer

The output level corresponding to the price level 120 is Q = $200.

If the price level rises from 120 to 132, the output level increases by $24 in the short-run.

Although the output level (Q) does not increase, it remains unchanged at $200 in the long-run.

Step-by-step solution

The calculation for the output level 

The equation for the short-run aggregate supply curve is:

P = 20 + 0.5Q

Now, the output level corresponding to P= 120 is:

120=20+0.5Q

0.5Q=120-20

Q=200

Hence, the full-employment output level is Q = $200, when the price level is 120.

The output level corresponding to the price level 132 is:

Now, the output level corresponding to P= 120 is:

132=20+0.5Q

0.5Q=132-20

Q=224

Hence, the output level is Q = $224, when the price level is 132.

So, when the price level rises from 120 to 132, the output level rises by $24.

In the long-run, the price and output levels are uncorrelated, and the potential output level will be produced in the economy. So when the price level rises, the output level does not rise but remains unchanged at Q = $200.