To find the equilibrium levels of output and price, we need to equate the planned aggregate expenditure (AEPlanned) with the aggregate supply (AS). The equilibrium condition is where AEPlanned equals AS, which determines both the output and price level.
Given: AEPlanned = 150 – 4P + 0.6Y AS: P = (-22.5 + 0.2Y) (w/20), where W = 20 (initial wage rate)
We will substitute the AS equation into the AEPlanned equation and solve for the equilibrium output (Y) and price level (P).
AEPlanned = AS 150 – 4P + 0.6Y = -22.5 + 0.2Y + (20/20) (Substituting W = 20)
Solving for Y: 0.6Y – 0.2Y = -22.5 + 150 + 1 0.4Y = 128.5 Y = 321.25
Now that we have the equilibrium output (Y), we can find the equilibrium price level using the AS equation: P = -22.5 + 0.2Y P = -22.5 + 0.2 * 321.25 P = -22.5 + 64.25 P = 41.75
In the short run, when there is a reduction in housing prices leading to a decrease in household wealth and a change in autonomous expenditure by -15, the new planned aggregate expenditure becomes:
New AEPlanned = AEPlanned + Change in autonomous expenditure New AEPlanned = (150 – 4P + 0.6Y) + (-15)
Substitute the equilibrium output (Y = 321.25) and equilibrium price (P = 41.75) into the equation:
New AEPlanned = (150 – 4 * 41.75 + 0.6 * 321.25) – 15 New AEPlanned = 246.5
Now we compare the new AEPlanned with the AS equation to find the new equilibrium price level:
New AEPlanned = AS 246.5 = -22.5 + 0.2Y + (20/20)
Solving for Y: 0.2Y = 246.5 + 22.5 – 1 0.2Y = 268 Y = 1340
Now we can find the new equilibrium price using the AS equation: P = -22.5 + 0.2Y P = -22.5 + 0.2 * 1340 P = -22.5 + 268 P = 245.5
The change in equilibrium price is: 245.5 – 41.75 = 203.75
The economy experiences an inflationary gap because the new equilibrium output (1340) is greater than the long-run equilibrium output (321.25). The size of the output gap is the difference between the new equilibrium output and the long-run equilibrium output:
Output Gap = New Equilibrium Output – Long-Run Equilibrium Output Output Gap = 1340 – 321.25 = 1018.75
Question 15: Comparison and Conclusion
In this scenario, we analyzed the equilibrium levels of output and price in an AD-AS model. Initially, with a wage rate of 20, the economy’s equilibrium output was determined to be 321.25, and the equilibrium price was 41.75. However, a reduction in housing prices and a decrease in autonomous expenditure by 15 led to a new short-run equilibrium with an output of 1340 and a price of 245.5. This resulted in an inflationary output gap of 1018.75 units.
By examining these changes in the AD-AS model, we gained insights into how adjustments in various economic factors can impact output, price levels, and the type of output gap experienced by the economy. Such analyses are essential for understanding the effects of policy changes and external shocks on macroeconomic variables.
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