Question

What is the significance of the ${45}^{\circ }$ line that is often included in the consumption function diagram?

Short answer

The significance of the 45-degree line in the consumption function diagram is that it helps us determine the point at which consumption expenditure equals disposable income (C = Y_d). This point is essential in identifying the equilibrium level of output in a simple, closed economy operating below full employment, where equilibrium occurs when aggregate demand equals aggregate supply. In a Keynesian cross model, the intersection of the consumption function and the 45-degree line demonstrates the desired aggregate demand in an economy, which will be equal to the total output. Hence, the 45-degree line plays a crucial role in analyzing the equilibrium output and understanding the economic behavior of a closed economy.

Step-by-step solution

Understand the consumption function

In macroeconomics, the consumption function shows the relationship between the consumption expenditure and the disposable income of households. It can be represented by the equation: $C=a+b{Y}_d$ where C represents consumption expenditure, a is the autonomous consumption (the amount of consumption when the disposable income is zero), b is the marginal propensity to consume (MPC), and Y_d is the disposable income. With this equation, we can plot C against Y_d to obtain the consumption function diagram.

Plot the consumption function diagram

The typical consumption function graph has the disposable income (Y_d) on the horizontal axis and the consumption expenditure (C) on the vertical axis. By plotting the consumption function equation on this graph, we can see that it will have a positive slope due to the marginal propensity to consume being a positive number (provided that households consume more when their disposable income increases).

Add the 45-degree line to the graph

The 45-degree line in this context is a straight line that starts at the origin and has a slope of 1, meaning that it represents all points where the consumption expenditure is equal to the disposable income (C = Y_d). When we add this line to the consumption function diagram, we can compare the actual consumption expenditure against the disposable income for any given level of Y_d.

Understand the significance of the 45-degree line

The significance of the 45-degree line in the consumption function diagram is that it helps us determine the point at which consumption expenditure equals disposable income. This point is essential in identifying the equilibrium level of output in a simple, closed economy operating below full employment, where equilibrium occurs when aggregate demand equals aggregate supply. In a Keynesian cross model, the intersection of the consumption function and the 45-degree line demonstrates the desired aggregate demand in an economy, which will be equal to the total output. No tendency for the economy to move away from this point exists, as households will be spending exactly what they are earning, resulting in no excess demand or supply. Thus, the 45-degree line plays a crucial role in analyzing the equilibrium output and understanding the economic behavior of a closed economy.

Key concepts

Macroeconomics

Macroeconomics is a branch of economics that focuses on the behavior and performance of an economy as a whole. It considers larger-scale factors such as national income, inflation, unemployment, and economic growth. In macroeconomics, models and theories are created to understand and predict how economies operate on a grand scale and how different sectors of the economy relate to one another.

One of the fundamental concepts in macroeconomics is the examination of how households consume goods and services, as well as the decisions they make about saving and spending. This consumer behavior has direct implications on overall economic health, influencing policies and decisions made by governments and organizations.

Consumption Expenditure

Consumption expenditure refers to the total amount of money spent by households on goods and services for personal use. It is a primary component of aggregate demand in an economy. Consumption expenditure includes spending on durable goods, such as automobiles and appliances; non-durable goods like food and clothing; and services like healthcare and education.

The level of consumption expenditure is a critical indicator for economists as it provides insights into consumer confidence, disposable income levels, and the overall health of the economy. A rise in consumption expenditure typically signals economic growth, whereas a decline may indicate economic hardship or recession.

Disposable Income

Disposable income, represented by the symbol Y_d in economic models, is the amount of money that households have available for spending and saving after income taxes have been accounted for. It is an important factor in determining consumption patterns, as it represents the income that consumers can freely allocate to meet their needs and desires.

Disposable income has direct implications on economic activities; more disposable income generally leads to increased consumption expenditure and economic growth, whereas less disposable income can result in lower spending and potential economic contraction.

Marginal Propensity to Consume

The marginal propensity to consume (MPC) is a measure of how much consumption expenditure changes when there is a change in disposable income. Specifically, it represents the proportion of each additional dollar of disposable income that households are likely to spend on consumption rather than saving.

In mathematical terms, MPC can be calculated using the formula
$MPC=\frac{\mathrm{\Delta }C}{\mathrm{\Delta }{Y}_d}$ where $\mathrm{\Delta }C$ is the change in consumption expenditure and $\mathrm{\Delta }{Y}_d$ is the change in disposable income. MPC values range between 0 and 1 - with higher values indicating a greater likelihood of spending additional income.

Equilibrium Output

Equilibrium output in an economy occurs at the level of production where the quantity of goods produced equals the quantity of goods consumed, or in macroeconomic terms, where aggregate supply equals aggregate demand. At this point, output is stable, and there is neither upward nor downward pressure on the level of production.

Identifying the equilibrium output is crucial for understanding where an economy stands regarding its resource utilization and whether it is operating under, at, or above its potential output. In Keynesian economics, achieving equilibrium output is associated with full employment and efficient resource allocation.

Keynesian Cross Model

The Keynesian cross model is a simple analytic tool used to demonstrate the relationship between aggregate demand and aggregate supply, ultimately illustrating how equilibrium output is determined in an economy. A fundamental feature of this model is the inclusion of the 45-degree line, which represents all points where consumption equals disposable income.

The point where the consumption function - the relationship between expenditure and income - intercepts the 45-degree line indicates the level of economic output at which consumers are spending all their income. This intersection shows the equilibrium point in the economy where there is no excess supply or demand, and it is used by economists to predict the effects of changes in fiscal policy.