Consumption Function

The consumption function is an equation that expresses a positive relationship between income and consumption.

Consumption is the purchase of goods and services by households. Disposable income is income remaining after deduction of taxes and other mandatory expenses and addition of government transfers, which households can spend or save. The consumption function is the relationship between consumption and disposable income. It is represented by an equation that models the factors that alter consumer spending—the total individual and household purchases of consumer goods and services. The equation indicates a reliance on changing incomes. Keynesian economics uses the concept of the consumption function in order to understand the factors that alter consumer spending.

This relationship is typically outlined with a graph of the linear equation:
$\text{C}=a+(\text{MPC}\times Y_d)$
C represents the total sum of consumer spending; $a$ represents required purchases even without disposable income, such as food and shelter (graphically speaking, it is the $y$-intercept). The marginal propensity to consume (MPC) is the change in consumer spending that occurs in response to an incremental change in disposable income. Disposable income is represented by $Y_{d}$. MPC is the slope of the consumption function.
The equation is a linear equation that expresses consumption as a function of income. The consumption function shows the positive relationship between the two, which means consumption will increase as income increases. The MPC will be a value between zero and 1. Assume a person receives an additional $100 in income; their only options are to spend or save the$100. For example, if a consumer has an $\text{MPC} = 0.75$, they would spend $75 and save$25.

An increase in disposable income will increase consumption (which, in turn, is a reason for an increase in aggregate demand). Potential increases in consumption include a raise in current or expected future income or a decrease in taxes. All of these factors will increase disposable income. Another factor that will increase consumption will be the desire to save less. This is essentially an increase in MPC, which increases the slope of the consumption function. If these factors move in the opposite direction, it will lead to a decrease in consumption.

Marginal Propensity to Consume

The marginal propensity to consume is the proportion or percentage of the additional disposable income that a person decides to spend on consumption.

Marginal propensity to consume (MPC) is the portion of disposable income a consumer decides to spend on consumption rather than savings. MPC changes with changes in income.

In the consumption function, MPC is also viewed as the change in C divided by the change in $Y_{d}$. The formula for MPC is $\text{MPC}=\Delta \text{C}/\Delta Y$, where $\Delta \text{C}$ is the change in consumption and $\Delta Y$ is the change in disposable income. If an individual receives a windfall of $100 and spends$60 of it, their MPC is 0.6.

MPC is not the same for all consumers. Those with lower disposable income spend a higher percentage of their income on consumption than those who make more money. In other words, poorer households spend more of their disposable income (if they have access to disposable income).

Marginal Propensity to Save

The marginal propensity to save is the proportion or percentage of the additional disposable income that a person decides to save.
The marginal propensity to save (MPS) is the change in consumer savings that occurs in response to an incremental change in disposable income. A person's desire to save changes based on income, as well as other factors. The value of MPS must also be between zero and 1, and $\text{MPC}\;+\text{MPS}=1$ because a person will either save or spend the increase in income. If an agent has a MPC of 1, he or she will spend all of their disposable income on consumption and will not save any of it. The two terms added together cannot have a larger value than the marginal disposable income. MPS is calculated by dividing the change in savings by the change in income: $\text{MPS}=\Delta \text{S}/\Delta Y$ . If a household earns $50 and saves$20, the marginal propensity to save is 0.4. Saving is dependent on one's level of income and living standards.