Marginal Propensity to Save (MPS)

An economic metric displaying the change in savings rates at various income levels

Author: David Bickerton
David Bickerton
David Bickerton
Asset Management | Financial Analysis

Previously a Portfolio Manager for MDH Investment Management, David has been with the firm for nearly a decade, serving as President since 2015. He has extensive experience in wealth management, investments and portfolio management.

David holds a BS from Miami University in Finance.

Reviewed By: Himanshu Singh
Himanshu Singh
Himanshu Singh
Investment Banking | Private Equity

Prior to joining UBS as an Investment Banker, Himanshu worked as an Investment Associate for Exin Capital Partners Limited, participating in all aspects of the investment process, including identifying new investment opportunities, detailed due diligence, financial modeling & LBO valuation and presenting investment recommendations internally.

Himanshu holds an MBA in Finance from the Indian Institute of Management and a Bachelor of Engineering from Netaji Subhas Institute of Technology.

Last Updated:November 25, 2023

What Is Marginal Propensity To Save (MPS)?

The "Propensity to Save" schedule displays the savings levels at various income levels.

It demonstrates how people tend to save at different income levels. MPS is used to quantify the link between income changes and savings.

It refers to the portion of a salary increase that a consumer saves rather than spending on products and services.

The MPS is an economic measure that shows how much money is conserved or how much money is lost due to economic leakage.

In the Keynesian model of Economics, leakage refers to that portion of the money not used to purchase goods and services. It thus is withdrawn and not reinvested in the economy and breaks from the circular flow of income and expenditure.

Key Takeaways

  • The Marginal Propensity to Save (MPS) reveals how alterations in income impact individuals' saving habits.

  • MPS is influenced by a variety of factors, including government policies, income levels, prevailing interest rates, and individual preferences.

  • MPS is calculated by dividing the change in saving by the change in income, providing insights into the economic relationship between these two variables.

  • MPS plays a pivotal role in the multiplier effect, influencing the extent to which changes in autonomous spending affect overall economic activity.

Understanding Marginal Propensity to Save (MPS)

It is a statistic employed in economics to assess how savings change in response to changes in income.

A part of each additional dollar in household income is allocated to savings.

The MPS demonstrates how excess cash is used by the household sector, focusing on how much is saved.

Because saving is complementary to consuming, it draws attention to significant aspects of a household's activity and spending habits.

Note

For example, if a person receives an extra $1 and the marginal propensity to save is 25%, 25 cents will be saved, and the remaining 75 cents will be spent on consumption.

Understanding how changes in income impact savings and consumption requires knowledge of the MPS.

  • The slope of the line contrasts income (X-axis) with saving (Y-axis).
  • In typical circumstances, its value ranges from 0 to 1.
  • If all of the extra money is saved, that is,

ΔC = 0, then MPS=1

However, if all the extra income is spent, or if ΔS = 0, then MPS = 0 (since the numerator becomes 0).

  • Because S cannot exceed Y, MPS cannot exceed 1.

Note

A high MPS indicates that a larger share of additional income is saved, whereas a low MPS shows that a larger portion is consumed.

When the MPS is larger, minor variations in income cause huge changes in savings and vice versa.

An individual's MPS grows with income since they can better meet their requirements as their income rises.

In other words, as a person becomes wealthy, the likelihood that they will spend each extra dollar decreases.

What is the purpose of determining MPS?

By examining MPS, economists may assess how wage increases can impact savings.

The marginal propensity to save significantly impacts the multiplier's value.

Economists can use household income and savings data to calculate households' MPS by income level.

This calculation is important because MPS is not constant and may vary depending on income level.

As a result, each more dollar has a lower likelihood of spending on additional purchases, and the MPS increases with income frequently. As wealth rises, so does the ability to satisfy needs and wants.

It's still conceivable, though, for a consumer's savings and consumption habits to alter in reaction to an increase in income.

Note

A higher paycheck enables one to conveniently pay for living expenditures, giving one more room to save. Higher pay also opens up access to more expensive items and services.

This could involve moving to a new, more expensive home or buying a higher-end or luxury automobile.

Knowing individuals' MPS allows economists to predict how government or investment spending changes affect saving.

MPS is used to determine the expenditures multiplier using the formula given:

1 / MPS

We can learn how fluctuations in consumers' MPS affect the rest of the economy through the expenditures multiplier.

If the MPS is smaller, the multiplier is higher; therefore, government expenditure or investment changes will have a bigger economic impact.

Saving Function

Saving is the excess income over and above consumption during an accounting year. This is because disposable income is either consumed or saved.

Thus,

Y= S + C

S = Y - C

It is also called “postponed consumption.”

Savings might be in the form of rising bank deposits, buying assets, or holding on to more cash.

People's preferences for future consumption over present consumption, their prospects for future income, and the interest rate all impact how much they save.

Note

Saving is essential to a country's economic development due to the relationship between saving and investment.

Some people must be inclined to refrain from spending all of their money if there is to be a rise in productive wealth.

On the other hand, people must be ready to invest in boosting productive capacity; progress cannot be made solely via saving.

The saving function shows the functional relationship between saving and income. It shows how much will be saved at different levels of income.

S = f(Y)

Where

  • S= Saving (Dependent variable)
  • Y= National Income (Independent Variable)
  • f= Functional Relationship

An example of a saving schedule:

Example of Savings Schedule

Income (Y) ($ Million) Consumption (C) ($Million) Savings (S = Y - C) ($ Millions)
0 40 -40
100 120 -20
200 200 0
300 280 20
400 360 40
500 440 60
600 520 80

The propensity to save is the tendency of people to save at various levels of income in an economy.

The tendency to save has two components. They are Marginal Propensity to Save(MPS) and Average Propensity to Save (APS).

The MPS is the slope of the saving function.

A higher MPS means the saving function will be steeper, indicating that more will be saved at each income level. A lower MPS means the saving function will be flatter, indicating that less will be saved at each income level.

Calculation of Marginal Propensity to Save (MPS)

The Marginal Propensity to Save (MPS) is calculated by dividing the change in saving by the change in income.

MPS = Change in Saving (ΔS) / Change in Income (ΔY) 

For example, a person's MPS would be 0.2, or 20%, if their income and savings rose by $100 and $20, respectively.

An example schedule to demonstrate the calculation of MPS:

Calculation Of MPS Example

Income (Y)(₹) Consumption(C)(₹) Savings(S)(₹) ΔS ΔY APS (S/Y) MPS(ΔS/ΔY)
0 50 -50 - - -
50 75 -25 25 50 -0.5 0.5
100 100 0 25 50 0 0.5
200 150 50 50 100 0.25 0.5
300 200 100 50 100 0.33 0.5
400 250 150 50 100 0.375 0.5
500 300 200 50 100 0.4 0.5

Even if income is ₹0, some consumers will be there, known as autonomous consumption. An individual would use past savings for it.

If income is ₹50 and consumption is ₹75, consumption>income, therefore past savings will have to be used. This will result in a negative APS.

At the break-even point, income equals consumption, and savings will be ₹0. The APS is also 0 at this point. With every rise in income, consumption and savings also rise. The value of MPS remains constant throughout the saving function.

The constant value of the saving curve indicates that it is a straight line since MPS calculates the saving curve's slope.

The value of MPS always varies between 0 and 1.

The MPS of 1 implies that all additional income has been saved, while the MPS of 0 indicates that all extra income has been spent.

Factors Influencing the Marginal Propensity to Save (MPS)

The MPS deals with income levels and how saving patterns differ depending on an individual’s income. Various factors come into play ranging from different government & taxation policies to the region's demographics.

Several factors can influence the MPS, including

1. Government policy 

Changes in tax or government spending can affect disposable income and, therefore, the MPS.

2. Income levels

Customers will purchase all essentials at low-income levels. Any additional revenue will likely all be spent. When increased income levels cover all essentials, saving is an affordable addition.

3. The diminishing marginal utility of income 

Additional money has less value as income levels increase, making customers less likely to know what to buy with it and save a higher proportion of it.

The Keynesian consumption function demonstrates that the marginal propensity to consume declines as incomes increase, increasing the marginal propensity to save.

Note

The Keynesian consumption function was given by John Maynard Keynes, who gave the concept of the consumption function.

4. Interest rates 

Lower interest rates decrease the opportunity cost of saving, leading to higher MPS, whereas higher interest rates increase the cost of saving, leading to lower MPS.

5. Consumer sentiment 

High consumer sentiment can lead to higher MPS, as individuals and households may feel more confident about their financial futures and be more likely to save.

6. Personal preferences 

Not everyone is a rational being. Approximately 25% of people may not save when rational utility maximization may imply they should because they do not adhere to the life-cycle hypothesis models. 

Some people are more susceptible to present-income bias than others. This indicates that people prioritize consumption in the immediate present over saving for the future.

Note

The life cycle hypothesis examines individuals' saving and spending habits throughout their lives and demonstrates the connection between aging and saving.

7. Demographics 

The MPS tends to be higher for older individuals, who are more likely to save for retirement. Similarly, the MPS tends to be higher for individuals with higher income and education levels, who are more likely to have the resources and knowledge to save effectively.

8. Life-cycle hypothesis 

According to theories of life-cycle spending, people want to spread out their consumption over time.

People will often have a larger predisposition to save during their middle working years as they save money for retirement.

  • Risk-averse - Risk loving: Risk-averse people are more likely to save extra money, plan for being laid off, etc. People who enjoy taking risks might not want to save.
  • Cultural factors: The MPS is likely higher in cultures where saving is highly valued. Conversely, the MPS will be lower in cultures where consumption is highly valued.

In addition to the above factors, social security, retirement benefits, and economic stability also affect MPS. 

People with a sense of security regarding their future tend to save more. The higher the social security and retirement benefits, the greater the MPS. 

Similarly, in a stable economy, people save more as they have more confidence in their future income and job security.

Marginal Propensity to Save (MPS) in Multiplier Effect

The effect on GDP of a change in autonomous spending.

As famous economist R.F. Kahn propounded, the investment multiplier is denoted by ‘k.’

k = Change in income/change in initial investment=  ΔY / ΔI

The MPC and MPS are the two key components of the Multiplier effect. 

The MPS is the proportion of increased income saved, and the MPC is the increased income consumed. The MPS and MPC interact to determine the Multiplier effect.

There is a direct relationship between MPC and the value of multipliers.

Note

The value of k increases when the MPC rises, and vice versa

MPC means consumption expenditure, and one’s expenditure is another’s income.

MPS has an indirect relationship with the value of the multiplier.

The value of k decreases when MPS increases and vice versa.

A smaller Multiplier impact is produced by higher MPS, whereas lower MPS obtains a larger Multiplier effect.

k= ΔY / ΔI

  • S = I at equilibrium
  • S = Y - C
  • I = Y - C

k= ΔY / ΔY - ΔC

Dividing the numerator and denominator by Y, we get

k = (ΔY / ΔY) / (ΔY / ΔY) - (ΔC / ΔY)

ΔC / ΔY = MPC

k= 1/1-MPC

MPC + MPS = 1

Hence, 1- MPC = MPS

k = 1 / MPS

Importance of Marginal Propensity to Save (MPS)

An essential Keynesian economic idea known as the MPS clarifies how changes in income impact saving and consumption. Additionally, it is used to forecast how changes in governmental policy would affect saving and consumption.

It is also used to examine how changes in interest rates affect saving and consumption.

The MPS and the notion of Marginal Propensity to Invest (MPI), which quantifies the fraction of an individual's or household's excess income invested instead of consumed or saved, are closely linked concepts.

The MPS is also very important in figuring out the multiplier impact.

Note

The impact of a shift in autonomous expenditure on the GDP is known as the multiplier effect. The Multiplier effect's two essential elements are the MPC and MPS.

The MPS indicates how much more money is saved, while the MPC determines how much more is spent.

The interaction between the MPS and MPC determines the Multiplier effect. A lesser Multiplier impact is produced by higher MPS, whereas lower MPS obtains a larger one.

The MPS is also an essential indicator of economic stability and growth.

A higher MPS indicates that individuals and households are saving more money, which may promote increased investment and economic growth.

Note

Contrarily, a lower MPS shows that people and families are consuming more, which might result in higher consumption levels but may also be a symptom of economic instability.

Marginal Propensity to Save FAQs

Researched and authored by Harveen Kaur Ahluwalia | LinkedIn 

Reviewed and edited by Parul Gupta LinkedIn

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