Question

The economy is described by the aggregate-demand curve Y = 100 - P and the short-run aggregate-supply curve Y = -12.5 + (1/2)P.

a) If the economy is in long-run equilibrium, what are the long-run level of output and price level?
b) Suppose that a new tax on consumption is implemented, leading demand to shift by a factor of β. Which direction do you expect the AD curve to shift? Through which of the channels discussed in the lecture will we see this shift?
c) Suppose β = 0.33, (in other words, AD shifts by 33%). Calculate the new short-run equilibrium.

Answer 1

To find the long-run output and price level in equilibrium, set the AD curve equal to the SRAS curve, yielding a price level of 75 and output of 25. A new tax will shift the AD curve left, indicating a decrease in demand. When β = 0.33, the AD shifts by 33%, affecting the equilibrium; solving the new equations provides the new output and price level.

Step-by-step explanation:

Long-Run Equilibrium

To find the long-run level of output and price level when the economy is in long-run equilibrium, we need to set the aggregate-demand (AD) curve equal to the short-run aggregate-supply (SRAS) curve and solve for the price level, P.

AD curve: Y = 100 - P
SRAS curve: Y = -12.5 + (1/2)P

Setting them equal to each other:
100 - P = -12.5 + (1/2)P
Adding P to both sides and adding 12.5 to both sides, we get:
112.5 = (3/2)P
Dividing both sides by (3/2), we find:
P = 75, and therefore Y = 25.

Shift in Aggregate-Demand Curve

A new tax on consumption will decrease the aggregate demand, shifting the AD curve to the left. This shift can be seen through the channels of decreased consumer spending.

Short-Run Equilibrium with β = 0.33

To find the new short-run equilibrium:

New AD curve with β = 0.33: Y = (100 - P) × (1 - 0.33)

Plugging in the new AD into the equilibrium condition:
(100 - P) × (1 - 0.33) = -12.5 + (1/2)P

Solving for P will give us the new price level and substituting it into the AD or SRAS equation will provide the new output, Y.