ECON10003 Chap.3 Short-Run Output and the Keynesian Cross
Short-Run Output and the Keynesian Cross
In the simple Keynesian model, consumption contains autonomous spending and an income-induced component governed by the marginal propensity to consume. Investment and government purchases are treated as autonomous in the basic setup. Expand consumption with disposable income, collect all autonomous terms and identify the coefficient on output. That slope must lie below one for a stable finite multiplier in the simple model.
Let consumption equal 80 plus 0.75 times income after taxes of 100, with investment 120 and government purchases 150. Planned expenditure becomes 275 plus 0.75 times output. Planned expenditure is a behavioural schedule, not the accounting identity for realised expenditure. Equilibrium is the point at which unintended inventory change is zero. Short-run equilibrium requires output to equal planned aggregate expenditure.
When planned spending exceeds production, inventories fall unexpectedly and firms have reason to increase output; the reverse applies when spending is lower. Set the output variable equal to the expenditure equation, move induced spending to the left and divide by one minus the marginal propensity to consume.
Using planned expenditure of 275 plus 0.75Y gives 0.25Y equal to 275, so equilibrium output is 1,100. Substitution returns planned spending of 1,100, completing the check. The result depends on fixed prices, spare capacity and the stated autonomous components. It does not describe long-run productive capacity. An autonomous expenditure increase becomes income, part of which is consumed again.
The geometric series produces an expenditure multiplier of one divided by one minus the marginal propensity to consume. Calculate the multiplier, apply it to the autonomous change and verify the sign. For a lump-sum tax change, the first-round consumption effect introduces the negative tax multiplier.
With an MPC of 0.75, the spending multiplier is 4. A government-purchase increase of 20 raises equilibrium output by 80; a tax increase of 20 lowers it by 60 under the simple assumptions. The multiplier is model-dependent. Imports, taxes, price adjustment, interest responses and capacity constraints can shrink or reshape the realised effect.
What this chapter covers
- 01
Planned expenditure has an intercept and slope
- 02
Equilibrium output solves a fixed point
- 03
The multiplier traces repeated spending rounds
Worked application: Planned expenditure has an intercept and slope
- 1Define variables, units, timing and the governing relation.
- 1Substitute the supplied values while preserving signs and denominators.
- 1Reconcile the result with the identity or equilibrium condition.
- 3Interpret the magnitude and name one model boundary.
Key terms
- Planned expenditure has an intercept and slope
- Substitute consumption before solving for equilibrium. In the simple Keynesian model, consumption contains autonomous spending and an income-induced component governed by the marginal propensity to consume. Investment and government purchases are treated as autonomous in the basic setup.
- Equilibrium output solves a fixed point
- Set production equal to planned aggregate expenditure. Short-run equilibrium requires output to equal planned aggregate expenditure. When planned spending exceeds production, inventories fall unexpectedly and firms have reason to increase output; the reverse applies when spending is lower.
- The multiplier traces repeated spending rounds
- Separate the initial shock from the total output response. An autonomous expenditure increase becomes income, part of which is consumed again. The geometric series produces an expenditure multiplier of one divided by one minus the marginal propensity to consume.
Short-Run Output and the Keynesian Cross FAQ
Where should a worked answer state the limit of planned expenditure has an intercept and slope?
In the simple Keynesian model, consumption contains autonomous spending and an income-induced component governed by the marginal propensity to consume. Investment and government purchases are treated as autonomous in the basic setup. Expand consumption with disposable income, collect all autonomous terms and identify the coefficient on output. That slope must lie below one for a stable finite multiplier in the simple model.
Planned expenditure is a behavioural schedule, not the accounting identity for realised expenditure. Equilibrium is the point at which unintended inventory change is zero. Finish by reconciling the result with the declared relation and unit.
How does equilibrium output solves a fixed point connect evidence to a consequential action?
Using planned expenditure of 275 plus 0.75Y gives 0.25Y equal to 275, so equilibrium output is 1,100. Substitution returns planned spending of 1,100, completing the check. The result depends on fixed prices, spare capacity and the stated autonomous components. It does not describe long-run productive capacity. Put the changed input through every line before comparing the new equilibrium.
Which rival interpretation puts the most pressure on the multiplier traces repeated spending rounds?
Separate the initial shock from the total output response Calculate the multiplier, apply it to the autonomous change and verify the sign. For a lump-sum tax change, the first-round consumption effect introduces the negative tax multiplier. An independent identity, boundary value or dimensional check should expose an inconsistent answer.
What should be defined before planned expenditure has an intercept and slope enters the analysis?
In the simple Keynesian model, consumption contains autonomous spending and an income-induced component governed by the marginal propensity to consume. Investment and government purchases are treated as autonomous in the basic setup. Let consumption equal 80 plus 0.75 times income after taxes of 100, with investment 120 and government purchases 150. Planned expenditure becomes 275 plus 0.75 times output.
Move the equation across examples only after redefining variables, timing and quotation convention.
Why might two sources disagree about equilibrium output solves a fixed point?
Set the output variable equal to the expenditure equation, move induced spending to the left and divide by one minus the marginal propensity to consume. The result depends on fixed prices, spare capacity and the stated autonomous components. It does not describe long-run productive capacity. Report the omitted market, adjustment path or behavioural channel after the numerical interpretation.
Exam move
Set up a calculation ledger for Short-Run Output and the Keynesian Cross, with separate columns for definition, algebra, substitution, reconciliation and interpretation. Index the entries by planned expenditure has an intercept and slope, equilibrium output solves a fixed point, the multiplier traces repeated spending rounds, and write units beside every supplied value.
Rework each relation after changing one input, preserving signs and denominators line by line. Put the answer back into the identity or equilibrium condition; a result that does not reconcile is not ready for economic interpretation. Attempt the chapter questions with the formula sheet closed, then compare operations rather than final digits. Mark where an accounting statement ends and a behavioural assumption begins.
Finish by stating the magnitude, unit, direction and horizon in words. Add one channel the model omits so mathematical consistency is not mistaken for a complete forecast.
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