Consumption Function

Consumption Function

Definition

The consumption function shows the functional relationship between consumption expenditure (C) and disposable income levels (Y). It tells us how much households want to spend on consumption at various income levels.

Equation

A Keynesian linear consumption function can be written as:

Where

C = Total Consumption Expenditure (what households spend)

C₀ = Autonomous Consumption — consumption when Y = 0 (constant intercept)

c = Marginal Propensity to Consume (MPC) — slope of consumption function

Y = Disposable Income (income available after taxes)

Numerical Example

If C₀ = 200 and c = 0.7, then C = 200 + 0.7Y

when Y = 1000:  C = 200 + 0.7×1000 = 200 + 700 = USD 900

Thus, out of USD 1000, the household will consume USD 900, and the rest of the amount, i.e., USD 100, will be saved. Therefore, households disposable income is the sum of consumption and savings.

Autonomous Consumption — The Intercept Term ‘C₀‘

Autonomous Consumption (C₀) is the minimum level of consumption that occurs even when disposable income (Y) is zero. It is the intercept of the consumption function on the vertical axis. It is called ‘autonomous’ because it does not depend on income.

Equation

In a consumption function

C₀ represents autonomous consumption. It is found when Y = 0.

Example

Given: C = 200 + 0.7Y
When Y = 0:  C = 200 + 0.7(0) = USD 200
Interpretation: Even if the household has zero income, it must still spend USD 200 on basic necessities (food, shelter, clothing). This spending is financed from previous savings or borrowing.

Properties of Autonomous Consumption

• Always Positive: Autonomous consumption (C₀ > 0) is always positive because people must consume to survive, even with no income.
• Dissaving at Y = 0: When Y = 0 and C = C₀ > 0, households draw down savings or borrow — they ‘dissave’ to fund autonomous consumption.
• Vertical Intercept: On the C-Y graph, ‘ C₀ ‘ determines where the consumption function starts — the point where it crosses the vertical axis.

Induced Consumption — ‘cY‘

Definition

Induced consumption (cY) is that part of consumption which depends on disposable income. As income increases, induced consumption increases and vice versa. It is found by multiplying MPC with disposable income.

Equation

In the consumption function   c. Y is induced consumption.

Example

Given: C = 200 + 0.7Y
When Y = USD 1000:  C = 200 + 0.7(1000) = USD 900
Interpretation: Here, induced consumption is USD 700 if the household has a USD 1000 income. Autonomous consumption is USD 200, which does not depend on income.

Properties of Induced Consumption

• Depends on income: Higher income leads to higher induced consumption, while lower income leads to lower induced consumption.
• Increasing function of income: It becomes zero when income is zero. Mathematically, cY=0 when Y=0
• Determined by MPC: A higher MPC means a larger portion of additional income is spent on consumption

Marginal Propensity to Consume (MPC)

Definition

MPC (Marginal Propensity to Consume) is the change in consumption (ΔC) resulting from a one-unit change in disposable income (ΔY). It is the slope of the consumption function. Keynes argued: 0 < MPC < 1

Formula

MPC = ΔC / ΔY = c   (slope of consumption function)

Example

Given the consumption schedule: when Y rises from USD 1000 → USD 1100,  C rises from USD 950 → USD 1020

ΔC = C₂ − C₁, ΔY = Y₂ − Y₁   MPC = ΔC / ΔY = (1020 − 950) / (1100 − 1000) = 70 / 100 = 0.70
Interpretation: For every USD 1 increase in income, households spend USD 0.70 on consumption and save the remaining   USD 0.30. In other words, a USD 100 rise in income leads to an increase in consumption by USD 70 each time.

Properties

• 0 < MPC < 1: MPC is always between 0 and 1. People spend part but not all of an income increase.
• Constant in Linear CF: In the linear Keynesian function C = C₀ + cY, MPC = c is constant at all income levels.
• Slope of CF Curve: On the consumption graph, MPC = slope = rise/run = ΔC/ΔY. A steeper line means a higher MPC.

Average Propensity to Consume (APC)

Definition

APC (Average Propensity to Consume) is the fraction of total disposable income that is spent on consumption. It shows the proportion of income consumed at a given income level. Keynes argued APC falls as income rises.

Formula

APC = C / Y = C₀/Y + c   (falls as Y rises because C₀/Y falls)

Example

At Y = USD 1000,  C = USD 950:  APC = 950/1000 = 0.95   (95% of income consumed)
At Y = USD 1800,  C = USD 1510:  APC = 1510/1800 = 0.84   (84% of income consumed)
Interpretation: As income rises from USD 1000 to USD 1800, the proportion of income consumed falls from 95% to 84%. APC is declining — confirming Keynes’s non-proportional consumption theory.

Properties

• APC Declines with Income: As income rises, APC falls because the autonomous part ‘C0′ becomes smaller relative to income.
• APC = C/Y (Ratio): Unlike MPC, which measures change, APC measures the level — total consumption as a fraction of total income.
• Non-Proportional: Falling APC means the consumption function is non-proportional: as Y doubles, C less than doubles.

Consumption Schedule and Diagram

Explanation Through Consumption Schedule

Table 1: Consumption Schedule (C = 250 + 0.7Y)

Key: APC falls (0.95→0.84) as Y rises  |  MPC = 0.70 constant throughout  |  MPC < APC at all income levels  |  Savings increase with income.

Explanation

• Consumption Rises with Income — but Less Than Proportionately: As income increases by USD 100 at each step (from USD 1000 to USD 1800), consumption also rises — but only by USD 70. For every USD 100 rise in Y, C rises by USD 70 and Savings rise by USD 30. This confirms households do not spend 100% of additional income.
• MPC is Constant = 0.70 Throughout: For each USD 100 increase in income, consumption increases by exactly USD 70, giving MPC = 70/100 = 0.70 at every income level. A constant MPC means the consumption function is LINEAR — it plots as a straight line on the C-Y graph.
• APC is Declining (0.95 → 0.84): When income is low (USD 1000), APC = 0.95 — households consume 95% of income. As income rises to USD 1800, APC falls to 0.84 — only 84% is consumed. This decline in APC is the hallmark of Keynes’s NONPROPORTIONAL consumption function.
• MPC < APC at All Income Levels: Notice: MPC = 0.70 is always less than APC (which ranges from 0.84 to 0.95). This is because APC includes the autonomous component (C₀/Y). Mathematically: APC = C₀ /Y + MPC > MPC (since C0 /Y > 0).

Explanation Through Diagram

Figure 1: Keynesian Linear Consumption Function — Graph (C = 250 + 0.7Y)

Explanation

• The 45° Reference Line (OZ): The line OZ passes through the origin at a 45° angle. At every point on OZ, C = Y — all income is consumed and savings = zero. It serves as a reference line to compare actual consumption against income.
• The Consumption Function Curve (CC’): CC’ is the actual consumption function C = C0 + cY. It starts above the origin on the vertical axis (because of autonomous consumption ‘a’) and rises with income but is less steep than OZ (because MPC < 1). The curve is a straight line (linear) because MPC is constant.

• Dissaving Region (CC’ above OZ): At low-income levels, the CC’ curve lies ABOVE the OZ line. This means C > Y — households are consuming more than their income. They finance this excess consumption by drawing down accumulated savings or borrowing from abroad.
• Breakeven Point (CC’ crosses OZ): The CC’ curve eventually crosses the OZ line at a specific income level Y*. At this point (E), C = Y exactly, so savings = 0. This is the breakeven income.
• Saving Region (CC’ below OZ — widening gap): Beyond Y*, the CC’ curve lies BELOW the OZ line. This means C < Y — households save the difference. An important observation: the gap between OZ and CC’ WIDENS as income grows, because savings increase with income.

Shifting of the Consumption Function

Any factor that changes consumption other than income is known as a shift factor of CF. These are also the factors that determine the propensity to consume at the same income. level.

Shift Factors of Consumption Function — Upward Shifts

Any factor — other than income — that increases consumption shifts the entire CC’ curve UPWARD (increasing autonomous consumption ‘C₀’, raising the intercept).

• Fall in Price Level (Real Balance Effect): Lower prices increase the real purchasing power of households’ money income. Even at the same nominal income, households can buy more — shifting CF upward.
• Fall in Interest Rate: Lower interest rates make borrowing cheaper and saving less rewarding. Households borrow more for consumer durables and save less — boosting consumption.
• Availability of Easy Credit: When banks relax lending standards, households can borrow more easily for spending on big items (cars, appliances) – raising consumption above what income alone would support.
• Transfer Payments: Transfer payments (subsidies, welfare) provide extra funds that raise the purchasing power of households and income consumption.
• Cut in Direct Taxes: Tax cuts raise disposable income, which increases consumption at every income level.
• Rise in Wealth / Asset Values: An increase in stock prices, property values, or financial wealth makes households feel richer (wealth effect). They increase consumption at every income level.
• Equal Income Distribution: More equal distribution raises the MPC of the economy (the poor have a higher MPC).
• Expected Inflation: Higher inflation expectations prompt households to buy NOW before prices rise further.
• Windfall gains: One-time unexpected benefits like winning a lottery shift CF upward.

Shift Factors of Consumption Function — Downward Shifts

Factors that reduce consumption — other than income — shift the entire CC’ curve DOWNWARD (decreasing autonomous consumption ‘C₀’, lowering the intercept).

• Rise in Price Level: Higher prices reduce real purchasing power. Even at the same nominal income, households can buy less — shifting CF downward.
• Rise in Interest Rate: Higher interest rates make borrowing expensive and saving more attractive. Households reduce consumer borrowing and increase savings, reducing consumption.
• Non-Availability of Easy Credit: Credit tightening (banks raising loan requirements and reducing credit card limits) prevents households from financing consumption beyond income, reducing consumption.
• Rise in Direct Taxes: Tax increases reduce disposable income, reduce purchasing power, and decrease consumption at every income level.
• Transfer Payments: Cuts in transfer payments reduce purchasing power. Decrease consumption at every income level.
• Fall in Wealth / Asset Values: A stock market crash or fall in property values reduces household wealth (negative wealth effect). Households cut back on consumption at every income level.
• Unequal Distribution: More unequal distribution reduces the economy’s MPC (rich have lower MPC).
• Expected Inflation: Lower inflation expectations mean less urgency to buy now — households defer spending.

Relationship Between APC and MPC

Mathematical Relationship

Starting from the Keynesian Consumption Function

Step 1: Derive APC

Step 2: Compare APC and MPC

 ,  ,

Step 3: Why APC Falls as Y Rises

As Y ↑ → C₀/Y ↓  → APC = C₀/Y + c  ↓    (because ‘c’ is constant, the falling C₀/Y pulls APC down).

Numerical check:  

 ✓

Finding APC & MPC Graphically

Explanation

APC at Point A

Draw ray from ORIGIN O to point A. APC = slope of ray OA = C₁/Y₁ = 950/1000 = 0.95

APC at Point B

Draw ray from ORIGIN O to point B. APC = slope of ray OB = C₂/Y₂ = 1370/1600 = 0.856. Slope OB < slope OA  → APC falls!

MPC at Point A

Draw TANGENT tt’ at point A. MPC = slope of tangent = ΔC/ΔY = 0.70

MPC at Point B

Draw TANGENT JJ’ at point B. For linear CF, tangent slope = CF slope = 0.70 (constant). For non-linear CF, MPC changes.

MPC vs APC — Complete Relationship Summary

Key Takeaways of Consumption Function

C = C₀ + cY

The Keynesian consumption function is linear. ‘C0’ is autonomous consumption (intercept); ‘c’ is MPC (slope).

MPC = ΔC/ΔY = 0.7

MPC is the slope — for every USD 1 rise in income, USD 0.70 is consumed. In the linear model, MPC is constant throughout.

APC = C/Y — Falling

APC declines as income rises (from 0.95 to 0.84), confirming the non-proportional nature of Keynesian consumption.

APC > MPC always

Mathematically: APC = C0/Y + MPC. Since C0/Y > 0, APC always exceeds MPC at every positive income level.

Shifts in CF

Income moves along CF. All other factors (prices, taxes, interest rates, wealth) shift the entire CF up or down by changing ‘C0′.

Suggestions for Further Readings

• Absolute Income Hypothesis