Question

What is the marginal propensity to consume if: a. Consumption increases by \(\$ 75\) when disposable income rises by \(\$ 100\) ? b. Consumption falls by \(\$ 50\) when disposable income falls by \(\$ 100\) ? c. Saving equals \(\$ 20\) when disposable income equals \(\$ 100\) and saving equals \(\$ 40\) when disposable income equals \(\$ 300\) ?

Short answer

Answer: In case a, the MPC is 0.75. In case b, the MPC is 0.5. In case c, the MPC is 0.9.

Step-by-step solution

Case a: Consumption increases by \(75 when disposable income rises by \)100

To find the MPC in case a, divide the change in consumption (\(75) by the change in disposable income (\)100): MPC = \(\frac{\Delta C}{\Delta Y}\) = \(\frac{75}{100}\) = 0.75

Case b: Consumption falls by \(50 when disposable income falls by \)100

To find the MPC in case b, divide the change in consumption (-\(50) by the change in disposable income (-\)100): MPC = \(\frac{\Delta C}{\Delta Y}\) = \(\frac{-50}{-100}\) = 0.5

Case c: Saving = \(20 when disposable_ income = \)100, and saving = \(40 when disposable_income =\)300

To find the MPC in case c, we first need to find the change in consumption, which we can do by finding the change in saving and using the fact that the sum of consumption and saving equals disposable income. Step 1: Calculate the change in saving and the change in disposable income. \(\Delta S = 40 - 20 = 20\); \(\Delta Y = 300 - 100 = 200\). Step 2: Find the change in consumption. Since the sum of consumption and saving equals disposable income, the change in consumption and the change in saving must together equal the change in disposable income: \(\Delta C + \Delta S = \Delta Y\). So, we can find the change in consumption as follows: \(\Delta C = \Delta Y - \Delta S = 200 - 20 = 180\). Step 3: Calculate the MPC. MPC = \(\frac{\Delta C}{\Delta Y}\) = \(\frac{180}{200}\) = 0.9

Key concepts

Consumption Function

The consumption function is a key concept in understanding economic behavior. It describes the relationship between consumption and disposable income, meaning how people adjust their spending habits as their income changes.
The basic idea is that as disposable income rises, people consume more. Conversely, when their disposable income drops, consumption falls too. This relationship is captured by the marginal propensity to consume (MPC), which measures the proportion of extra disposable income that a consumer spends on goods and services.
Mathematically, the consumption function can be expressed as:

• C = a + bY

where:

• \(C\) is consumption,
• \(a\) is autonomous consumption (consumption when income is zero),
• \(b\) is the marginal propensity to consume, and
• \(Y\) is disposable income.

The MPC is a critical component of the consumption function. For instance, if

• the MPC = 0.75,
• this suggests that for every extra dollar of income received, 75 cents will be spent on consumption,

and

• 25 cents will be saved.

In practical terms, assessing MPC involves examining how changes in disposable income reflect in consumption patterns, as demonstrated in various scenarios of disposable income changes.

Disposable Income

Disposable income is essentially the amount of money a household has left to spend or save after paying taxes. It's a critical factor in determining consumer behavior, as it directly influences how much households consume and save.
Understanding disposable income helps to identify the potential for spending within an economy. When households have high disposable income, they tend to spend more, stimulating economic growth. Conversely, when disposable income is low, spending often declines, potentially slowing down the economic activity.
It's important to differentiate between two related concepts:

• Gross Income: The total income earned, including wages, salaries, bonuses, and other earnings.
• Net Income (Disposable Income): The amount left after taxes and mandatory contributions have been deducted from gross income.

If a person's disposable income increases by $100, and they choose to spend $75 of it, their MPC is 0.75. This scenario highlights how disposable income directly impacts consumption choices, embodying the interaction between earning, spending, and saving decisions.

Saving Behavior

Saving behavior refers to the extent and manner in which individuals or households save their disposable income rather than spending it. It reflects their financial preferences and economic outlooks.
People save for various reasons, including:

• Building an emergency fund,
• Preparing for future expenses (like education or retirement), and
• Investing to generate future income.

From an economic standpoint, saving is linked to consumption through the equation that disposable income equals consumption plus saving (

• \(Y = C + S\)

where:

• \(Y\) is disposable income,
• \(C\) is consumption, and
• \(S\) is saving.

Thus, the marginal propensity to save (MPS) is the fraction of the additional income saved rather than spent. If the MPS is 0.25, for every additional dollar of income, 25 cents would be saved, and the remaining 75 cents would be spent.
In the context of the exercise, understanding saving behavior is crucial in calculating changes in consumption. As seen in the solution, examining how savings change with disposable income allows us to infer consumption behavior, thus uncovering the marginal propensity to consume. This interplay highlights how interconnected saving and consumption behaviors are in financial decision-making.