Principles of Macroeconomics / Unit 9 MAC 0823 worked example, 60 to 90 seconds
Solving for Equilibrium Algebraically
The idea
The schedule finds equilibrium by search; algebra finds it directly. Set output equal to expenditure, substitute the expenditure line, collect the output terms on one side and solve. The advantage is that any parameter can then be changed and the new equilibrium recomputed without rebuilding a table.
In practice
With the course's economy, set GDP equal to 2,700 plus 0.6 of GDP. Subtracting 0.6 of GDP from both sides leaves 0.4 of GDP equal to 2,700, so GDP is 2,700 divided by 0.4, which is 6,750. That matches the schedule. Now raise government purchases by 100, to 1,100. The autonomous total becomes 2,800, and GDP becomes 2,800 divided by 0.4, which is 7,000. A change of 100 in autonomous spending moved equilibrium by 250.
Where people slip
The dividing figure is one minus the slope, not the slope. Dividing by the slope instead is the most common error here, and it produces an answer that is wrong in a plausible-looking direction.
Your place on the trail
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