Question

Explain why the sum of the MPC and the MPS for any given change in disposable income must always be equal to 1 .

Short answer

The sum of the Marginal Propensity to Consume (MPC) and the Marginal Propensity to Save (MPS) for any given change in disposable income must always be equal to 1 because disposable income (YD) is divided into two parts: the amount consumed (C) and the amount saved (S). When considering a change in disposable income (ΔYD) and dividing this change into corresponding changes in consumption (ΔC) and savings (ΔS), the following relationship holds: \[1 = \frac{ΔC}{ΔYD} + \frac{ΔS}{ΔYD}\] This relationship confirms that the sum of MPC and MPS equals 1, demonstrating the fundamental principle in macroeconomics between consumption, savings, and disposable income.

Step-by-step solution

Define Marginal Propensity to Consume (MPC)

The Marginal Propensity to Consume (MPC) is the fraction of an additional unit of disposable income that is spent on consumption. Mathematically, it is represented as the change in consumption (ΔC) divided by the change in disposable income (ΔYD): \[MPC = \frac{ΔC}{ΔYD}\]

Define Marginal Propensity to Save (MPS)

The Marginal Propensity to Save (MPS) is the fraction of an additional unit of disposable income that is saved. Mathematically, it is represented as the change in savings (ΔS) divided by the change in disposable income (ΔYD): \[MPS = \frac{ΔS}{ΔYD}\]

Relate MPC and MPS to disposable income

A household's disposable income (YD) is divided into two parts: the amount consumed (C) and the amount saved (S). Therefore, we can represent the relationship between disposable income, consumption, and savings as: \[YD = C + S\]

Derive the relationship between MPC and MPS

Now, let's consider a change in disposable income (ΔYD) and divide this change into the corresponding changes in consumption (ΔC) and savings (ΔS): \[ΔYD = ΔC + ΔS\] Now, divide both sides of the equation by ΔYD: \[\frac{ΔYD}{ΔYD} = \frac{ΔC}{ΔYD} + \frac{ΔS}{ΔYD}\] Since the left side of the equation is equal to 1 (as any number divided by itself is equal to 1), we can rewrite the equation as: \[1 = MPC + MPS\]

Conclusion

We have shown that the sum of the Marginal Propensity to Consume (MPC) and the Marginal Propensity to Save (MPS) for any given change in disposable income must always be equal to 1. This result is a fundamental principle in macroeconomics, and it demonstrates the relationship between consumption, savings, and disposable income.

Key concepts

Consumption

When we talk about consumption in economics, we are referring to the amount of goods and services purchased by households. It is a significant component of the economy because it directly reflects consumer preferences and spending behavior.
Consumption plays a crucial role in measuring economic health, as high levels generally indicate a thriving economy, whereas low levels might suggest an economic downturn.
Understanding consumption is essential since it forms a large part of a country’s GDP. Consumption is not just about spending whims but is often influenced by disposable income. When people have more income after taxes (disposable income), they tend to spend more, showcasing a direct correlation.
Therefore, economists closely monitor consumption patterns as these can signify broader economic trends and often lead to policy changes if the figures suggest economic stagnation or recession.

• Consumption contributes to GDP.
• Directly correlated to disposable income.
• Reflects consumer confidence.

Savings

Savings, the portion of disposable income that is not consumed, plays a pivotal role in the lives of individuals and the broader economy.
It acts as a financial cushion, promoting long-term financial security. Savings can be understood in terms of Marginal Propensity to Save (MPS), which is formally defined as the fraction of additional income that is saved rather than spent on consumption.
Simply put, when someone earns extra income and decides to save a portion of it, this action is quantified through the MPS.
It's calculated as the change in savings divided by the change in disposable income, similar to the MPC. An increase in savings tends to reduce immediate consumption but can provide a pool of resources for future investment.

• Key for financial stability.
• Tied to long-term economic growth.
• Closely related to the Marginal Propensity to Save (MPS).

Disposable Income

Disposable income is the amount of money that households have available for spending and saving after income taxes have been accounted for. It is the backbone of consumer spending and is crucially connected to both consumption and savings. This concept helps understand how different economic factors such as taxation and wages impact individual and national economies.
The more disposable income people have, the more they can potentially contribute to economic growth through spending and saving. Analyzing disposable income gives insight into economic policies' effectiveness, especially those related to taxation and wage adjustments.

• Net income after taxes.
• Strongly influences consumption and savings.
• Indicator of economic health.

Macroeconomics

Macroeconomics is the branch of economics that studies the behavior of the economy as a whole. It encompasses various concepts like consumption, savings, and disposable income. Macroeconomics aims to understand how all these elements interact to influence economic growth, inflation, and employment. Within macroeconomics, the relationship between consumption and savings is vital for identifying stable economic policies. By analyzing data like GDP, inflation rates, and unemployment figures, economists can recommend policies that stimulate economic balance and growth.
This field often guides government and central bank policies that attempt to stabilize the economy through fiscal and monetary measures. It provides a big-picture view of the economy, helping to strategize national and international trade and financial approaches.

• Analyzes whole-economy behavior.
• Informs fiscal and monetary policy.
• Interconnects with individual savings and consumption patterns.