Title: Autonomous expenditure — a clear explainer
Definition
– Autonomous expenditure: spending in an economy that does not change in response to the economy’s current real income (output). In macroeconomic models, these are the components of aggregate demand that are treated as independent of current national income.
Why it matters (key points)
– Autonomous spending provides a baseline level of demand even when income is low.
– In Keynesian analysis, a change in autonomous expenditure triggers a multiplied change in aggregate output via the spending (or fiscal) multiplier.
– Typical items treated as autonomous include some government purchases, basic necessities (autonomous consumption), planned investment that doesn’t respond to current income, and exports.
Autonomous vs induced spending
– Induced spending: consumption or investment that rises or falls as disposable income changes (for example, people spend more when their income increases).
– Autonomous spending: needs or plans that exist independently of current income levels (for example, minimum household food and shelter expenses, or government spending on defense).
How an autonomous expense behaves in practice
– The “need” that defines an autonomous expenditure often stays the same, but the way it is financed or the quality purchased can vary with income (e.g., food can be bought cheaply or expensively; if income is short, households may use savings, borrow, or receive transfers).
– Although modeled as independent of income, in reality autonomous expenditures can be affected by interest rates, taxes, trade policy, and other non-income factors.
Checklist: how to identify an autonomous expenditure
– Is the spending necessary to maintain a baseline function or minimum standard of living?
– Would the spending be incurred even if current income falls?
– Can the amount be financed by savings, borrowing, or government transfers if current income is insufficient?
– Is the planned spending decision not closely tied to short-term changes in national income?
If most answers are “yes,” treat the item as autonomous for macroeconomic analysis.
Worked numeric example: multiplier effect (simple Keynesian case)
Assumptions:
– Closed economy (no imports), no taxes, fixed price level.
– Marginal propensity to consume (MPC) = 0.8 (MPC = fraction of an extra
dollar of disposable income that a household spends on consumption.
Simple Keynesian multiplier (closed economy, no taxes)
Formula:
– Multiplier k = 1 / (1 − MPC)
Assumptions (repeat briefly for clarity): closed economy (no imports), no taxes, constant price level, and constant marginal propensity to consume (MPC).
Worked numeric example
– Given MPC = 0.8.
– Multiplier k = 1 / (1 − 0.8) = 1 / 0.2 = 5.
– Suppose autonomous government spending (ΔG) increases by $100 million.
– Total change in equilibrium output (ΔY) = k × ΔA, where ΔA is the change in autonomous expenditure.
– ΔY = 5 × $100 million = $500 million.
Interpretation: the initial $100 million of autonomous spending generates additional rounds of induced consumption until the increase in income is five times the initial injection, under the stated assumptions.
Extension: taxes and imports (open economy, proportional tax and import leakages)
When some income is taken away by taxes or spent on imports, the multiplier is smaller because those are leakages—portions of income that do not return to domestic consumption.
General formula with a proportional tax rate t and marginal propensity to import m:
– k = 1 / [1 − MPC × (1 − t) + m]
Worked numeric example with taxes and imports
– MPC = 0.8, tax rate t = 0.25, marginal propensity to import m = 0.10.
– Effective marginal spending domestically = MPC ×
(continuing)
(1 − t) − m = 0.8 × (1 − 0.25) − 0.10 = 0.8 × 0.75 − 0.10 = 0.60 − 0.10 = 0.50.
Thus the effective marginal propensity to spend domestically (the fraction of each additional dollar of income that re-enters domestic demand) is 0.50. Use that in the multiplier formula:
k = 1 / [1 − effective marginal domestic spending] = 1 / (1 − 0.50) = 1 / 0.50 = 2.0.
Worked numeric example (rounds)
– Autonomous increase in spending ΔA = $100.
– Round 0 (initial injection): +$100 income.
– Taxes = t × 100 = $25.
– Disposable income = $75.
– Consumption (total) = MPC × disposable =
= 0.8 × 75 = $60. Imports on the new income = m × income = 0.10 × 100 = $10. So domestic consumption (the part that re-enters domestic demand) = $60 − $10 = $50. That equals the effective marginal domestic spending fraction (0.50) × $100.
Continue the round-by-round accounting using the effective domestic spending fraction = 0.50:
– Round 0 (initial): Income = +$100 → Domestic spending that feeds next round = 0.50 × 100 = $50.
– Round 1: Income = +$50. Taxes = 0.25 × 50 = $12.50. Disposable = $37.50. Consumption total = 0.8 × 37.5 = $30. Imports = 0.10 × 50 = $5. Domestic consumption (re-entering) = $30 − $5 = $25 (also 0.50 × 50).
– Round 2: Income = +$25. Domestic spending next = 0.50 × 25 = $12.50.
– Round 3: Income = +$12.50. Domestic spending next = 0.50 × 12.50 = $6.25.
– And so on (each round is half the previous).
Sum of the rounds (geometric series):
Total change in income ΔY = 100 + 50 + 25 + 12.5 + … = 100 × (1 / (1 − 0.5)) = 100 × 2.0 = $200.
That matches the multiplier formula used earlier:
k = 1 / [1 − effective marginal domestic spending] = 1 / (1 − 0.50) = 2.0,
so ΔY = k × ΔA = 2.0 × $100 = $200.
Compact formula and derivation (assumptions noted)
– Assumptions: marginal propensity to consume (MPC) = 0.8; tax rate t = 0.25 (proportional taxes); marginal propensity to import m = 0.10 (imports proportional to income); no other leakages or endogenous policy responses; prices and interest rates fixed for the short run.
– Effective marginal domestic spending per additional dollar of income = MPC × (1 − t) − m.
– Multiplier k = 1 / [1 − (MPC × (1 − t) − m)] = 1 / [1 − MPC(1 − t) + m].
– Total change in equilibrium income from an autonomous spending change ΔA: ΔY = k × ΔA.
Practical checklist for applying this method
1. Specify the endogenous/induced behavior: MPC, tax rule (t), and import propensity (m). Use consistent definitions (fractions of income).
2. Compute effective marginal domestic spending =
2. Compute effective marginal domestic spending = MPC × (1 − t) − m. Use consistent units (fractions of income). This is the fraction of each extra dollar of income that feeds back into domestic spending (consumption net of taxes and imports).
3. Compute the spending multiplier k:
k = 1 / [1 − (effective marginal domestic spending)]
= 1 / [1 − MPC(1 − t) + m].
This gives the total change in equilibrium income per dollar change in autonomous spending.
4. Apply the multiplier to the autonomous spending change:
ΔY = k × ΔA,
where ΔA is the change in autonomous expenditure (investment, government spending, autonomous consumption, etc.).
Worked numeric example
– Assumptions: MPC = 0.80 (marginal propensity to consume), t = 0.20 (proportional tax rate), m = 0.10 (marginal propensity to import). These are fractions of income.
– Step 2: effective marginal domestic spending = 0.80 × (1 − 0.20) − 0.10
= 0.80 × 0.80 − 0.10
= 0.64 − 0.10
= 0.54.
– Step 3: multiplier k = 1 / (1 − 0.54) = 1 / 0.46 ≈ 2.174.
– Step 4: if autonomous investment rises by ΔA = $100 million,
ΔY = 2.174 × $100 million ≈ $217.4 million.
Interpretation: a $100 million autonomous spending increase raises equilibrium income by about $217.4 million under the model’s assumptions.
Checks, edge-cases, and caveats
– If effective marginal domestic spending ≥ 1, the denominator (1 − effective) is ≤ 0. That implies an infinite or negative multiplier and signals a breakdown of the simple model (unbounded income response or unstable dynamics). Real economies have constraints that prevent this.
– The derivation assumes short-run fixed prices and interest rates, no endogenous policy responses, linear proportional tax and import rules, and no other leakages. Violations (e.g., monetary policy reaction, price changes, capacity limits, changing MPC) will alter results.
– Imports, taxes, and saving all reduce the multiplier; higher MPC raises it.
– For open economies, import propensities and foreign spending can materially change multiplier magnitudes and distributional effects.
–
– Practical steps to compute a simple open-economy multiplier — checklist and worked example
1. Decide the model specification. For a short-run Keynesian open-economy with proportional lump-sum-tax rate t, marginal propensity to consume (MPC) c, and marginal propensity to import m, use the linear identity:
Y = C + I + G + X − M, with C = a + c(1 − t)Y and M = mY.
This yields the multiplier:
k = 1 / [1 − c(1 − t) + m].
Definitions: MPC (marginal propensity to consume) = fraction of an additional unit of disposable income spent on consumption; marginal propensity to import (MPM) = fraction of an additional unit of income spent on imports.
2. Collect data or choose parameters. Typical sources: national accounts for G, I, X, M; consumption and disposable income series to estimate c; import and GDP series to estimate m; tax revenue and GDP to infer an average t or use a statutory rate if appropriate.
3. Estimate parameters (simple OLS regressions are common short-cut):
– Estimate c by regressing consumption (C) on disposable income (Yd = Y − T): C = a + cYd.
– Estimate m by regressing imports (M) on income: M = mY + error.
– Compute t = T/Y (total taxes over GDP) for an average proportional rate (note: this conflates progressive taxes and other non-linearities).
4. Plug estimates into k = 1 / [1 − c(1 − t) + m] to get the short-run multiplier.
5. Simulate an autonomous spending shock ΔA (A = autonomous consumption a + I + G + X). The change in equilibrium output is ΔY = k × ΔA.
Worked numeric example:
– Suppose c = 0.80, t = 0.20, and m = 0.10.
– Denominator = 1 − 0.80*(1 − 0.20) + 0.10 = 1 − 0.80*0.80 + 0.10 = 1 − 0.64 + 0.10 = 0.46.
– Multiplier k = 1 / 0.46 ≈ 2.174.
– A $100 autonomous increase in government spending raises income ΔY ≈ 2.174 × $100 = $217.40.