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Lesson M04.L02: The Consumption Function and Marginal Propensity to Consume

Module: Macroeconomics in the Short-Run: The Basic Keynesian Model Level: intro Duration: 30 minutes Learning Objective: Derive and interpret the consumption function C = a + bY; calculate the MPC and MPS; apply to Australian household data. Data as of: 2024 Provenance: OpenStax Macro 3e | ABS National Accounts | RBA

Explanation

In the Keynesian model, consumption (C) is the largest component of aggregate demand. Understanding how households decide how much to spend is central to the model.

The consumption function is the relationship between household disposable income (Y) and planned consumption spending:

C = a + bY

Where: - C = planned consumption spending (AUD) - a = autonomous consumption โ€” the amount households spend regardless of income (e.g., they borrow or draw on savings to cover basic necessities even with zero income). a > 0 - b = the Marginal Propensity to Consume (MPC) โ€” the fraction of each additional dollar of disposable income that households spend (rather than save). 0 < b < 1 - Y = household disposable income (AUD)

Marginal Propensity to Consume (MPC):

MPC = ฮ”C รท ฮ”Y

If Australian households receive an extra $1.00 in income and spend $0.85 of it, MPC = 0.85.

Marginal Propensity to Save (MPS):

MPS = 1 โˆ’ MPC

Because every dollar of income is either spent or saved: MPC + MPS = 1

Australian context: The ABS and RBA track the household saving ratio (saving as a share of disposable income). In 2024, Australia's household saving ratio was around 3โ€“5%, implying MPS โ‰ˆ 0.03โ€“0.05 and MPC โ‰ˆ 0.95โ€“0.97 on average. However, during COVID-19 (2020), the saving ratio surged to over 20% as households could not spend (lockdowns) and precautionary saving rose โ€” demonstrating that MPC can change with economic conditions.

Worked Example

Given data for a representative Australian household: - Monthly disposable income (Y) = $6,500 - Monthly autonomous consumption (a) = $1,200 (rent, utilities, food at minimum level regardless of income) - MPC (b) = 0.75

Step 1 โ€” Write the consumption function: C = 1,200 + 0.75Y

Step 2 โ€” Calculate consumption at Y = \(6,500:** C = 1,200 + 0.75 ร— 6,500 C = 1,200 + 4,875 C = **\)6,075/month

Step 3 โ€” Calculate saving: Saving = Y โˆ’ C = 6,500 โˆ’ 6,075 = $425/month

Step 4 โ€” Calculate MPS: MPS = 1 โˆ’ MPC = 1 โˆ’ 0.75 = 0.25 Check: Saving รท Income = 425 รท 6,500 = 6.5% (the average saving rate at this income level)

Step 5 โ€” Income rises by $1,000 (to \(7,500). How much does consumption change?** ฮ”C = MPC ร— ฮ”Y = 0.75 ร— 1,000 = **\)750 more spending New consumption = 6,075 + 750 = \(6,825** New saving = 7,500 โˆ’ 6,825 = **\)675 (saving also rises: ฮ”MPS ร— ฮ”Y = 0.25 ร— 1,000 = $250 extra saving)

Common Misconception

Misconception: The MPC equals the average propensity to consume (i.e., the share of total income spent on consumption).

Correction: The average propensity to consume (APC) is C รท Y โ€” total consumption as a share of total income. The MPC is ฮ”C รท ฮ”Y โ€” how much consumption changes for each extra dollar of income. These are different. Because of autonomous consumption (the intercept a), the APC is higher at low incomes (households consume more than their income) and falls as income rises. The MPC is constant in the simple linear model, equal to the slope b. Mixing them up leads to errors in multiplier calculations.

Practice Prompts

  1. An Australian household has autonomous consumption of $800/month and an MPC of 0.80. Write their consumption function and calculate consumption when monthly income is \(5,000. โ†’ **Answer:** C = 800 + 0.80 ร— 5,000 = 800 + 4,000 = **\)4,800/month**. MPS = 1 โˆ’ 0.80 = 0.20. Saving = 5,000 โˆ’ 4,800 = $200/month.

  2. Income rises from $5,000 to $6,200. Using the MPC of 0.80, how much does consumption increase, and how much does saving increase? โ†’ Answer: ฮ”Y = \(1,200. ฮ”C = 0.80 ร— 1,200 = **\)960 more consumption. ฮ”S = 0.20 ร— 1,200 = $240** more saving. Check: 960 + 240 = 1,200 โœ“.

  3. During the COVID-19 lockdowns of 2020, Australia's household saving ratio jumped from around 7% to over 20%. What does this imply happened to the MPS and MPC during this period? โ†’ Answer: The saving ratio is the average propensity to save. A jump to 20%+ implies the MPS rose significantly โ€” households were saving a much larger fraction of their income. Correspondingly, the MPC fell โ€” households spent less out of each dollar of income. This demand compression is a key reason why GDP fell so sharply in mid-2020.

Visual โ€” The Consumption Function and the MPC

Consumption function: \(C = a + bY\) Income, Y Consumption, C a 45ยฐ line: C = Y C = a + bY Break-even point rise run MPC = b Above 45ยฐ line: dissaving Below 45ยฐ line: saving Saving gap Dissaving gap

Figure: The consumption function has intercept \(a\) and slope \(b\), the marginal propensity to consume. Where the consumption line lies above the 45ยฐ line households dissave; where it lies below the 45ยฐ line households save.

Further Resources