ECON2000 Chap.8 Keynesian Cross and IS-MP
Keynesian Cross and IS-MP
The Keynesian Cross solves a price-fixed goods market by setting planned aggregate expenditure equal to output. Consumption, investment, government purchases and net exports contribute autonomous and income-induced components. The expenditure slope produces a multiplier, while unintended inventories explain adjustment toward equilibrium.
Interest-sensitive spending then turns repeated Keynesian-Cross equilibria into the downward-sloping IS curve. The MP curve represents the monetary-policy rule, and its intersection with IS determines output and the policy rate for a given inflation rate. The chapter solves equilibrium algebraically, traces autonomous-spending changes and distinguishes a shift of IS or MP from movement along an existing policy rule.
What this chapter covers
- 01
Planned aggregate expenditure
- 02
Consumption and investment components
- 03
Goods-market equilibrium
- 04
Multiplier
- 05
Inventory adjustment
- 06
IS derivation
- 07
MP rule
- 08
IS-MP equilibrium
Worked example · free
Solving the Keynesian Cross
- +1Set Y equal to 180 plus 0.70Y.
- +2Rearrange to 0.30Y = 180, giving equilibrium output of 600.
- +1The multiplier is 1 divided by 0.30, equal to 3.333.
- +2The spending increase raises output by 15 times 3.333, equal to 50, so new output is 650.
Key terms
- Autonomous spending
- Planned expenditure that does not vary directly with current income in the specified model.
- Induced spending
- The part of planned expenditure that changes with current income.
- Multiplier
- The equilibrium output change produced by one unit of autonomous spending change.
- IS curve
- The combinations of interest rates and output consistent with goods-market equilibrium.
- MP rule
- A monetary-policy schedule assigning the policy rate to macroeconomic conditions.
Keynesian Cross and IS-MP FAQ
Why does planned expenditure determine output?
With prices fixed and production responding to demand, firms adjust output when intended spending differs from production. Planned expenditure above output depletes inventories and encourages expansion; planned expenditure below output accumulates inventories and prompts cuts. Adjustment ends where the two are equal.
What determines the multiplier?
The induced expenditure slope determines how much each income round feeds into the next. A higher marginal response creates a larger multiplier, while taxes and imports provide leakages that reduce it. Stability requires the slope to remain below one.
How is the IS curve derived?
For each interest rate, solve the Keynesian Cross after interest-sensitive consumption and investment are set. A higher rate lowers those components and produces a lower equilibrium output. Connecting the resulting rate-output pairs traces the downward-sloping IS curve.
What shifts the MP curve?
A change in the central bank's policy rule or stance shifts MP. A rate change prescribed by movement in inflation or output along the existing rule is not a separate shift. Keeping the trigger explicit prevents moving both the curve and the point for one event.
Exam move
Build planned expenditure from its components before using a memorised multiplier. Solve equilibrium algebraically, then explain the unintended-inventory mechanism in words. Practise changes in government purchases, taxes, autonomous consumption, investment confidence and net exports, identifying whether each alters the intercept or slope. Derive IS by repeating the goods-market solution at several interest rates.
Add MP only after IS is understood, and label inflation as fixed at this stage. For each shock, write the entry equation beside it, shift one justified curve and report output and interest-rate directions. Reserve final inflation conclusions for the full AD-AS model. Create an expenditure worksheet with separate rows for consumption, investment, government purchases and net exports.
Mark each term autonomous or induced and calculate the total slope after tax and import leakages. Solve the same economy by algebra and by graph, then use unintended inventories to explain the direction of adjustment from output above and below equilibrium. Vary the interest rate and record the resulting goods-market output pairs to derive IS rather than memorising its direction.
Add a policy rule only after the IS schedule is complete. Practise fiscal expansion, confidence loss, foreign-demand change and monetary-rule shift one at a time. For each, identify the first equation affected and whether the change shifts a curve or moves the equilibrium along it. Check that the interest-rate direction is consistent with the MP slope.
Finish by stating that inflation is held fixed in the IS-MP exercise, preventing a premature full-model conclusion. Do one reverse exercise after each standard problem. Instead of receiving a shock and finding the new equilibrium, start from a lower output and higher interest rate and propose a curve change consistent with both directions. Check the proposal against the underlying expenditure and policy equations.
Reverse drills show whether you understand the mapping rather than only following arrows forward, and they expose cases where several shocks could fit the same observed outcome.
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