Question

In an economy, when income increases from \(\$ 400\) billion to \(\$ 500\) billion, consumption expenditure changes from \(\$ 420\) billion to \(\$ 500\) billion. Calculate the marginal propensity to consume, the change in saving, and the marginal propensity to save.

Short answer

MPC = 0.8, ∆Saving = $20 billion, MPS = 0.2.

Step-by-step solution

- Understanding Marginal Propensity to Consume (MPC)

The marginal propensity to consume (MPC) is calculated as the change in consumption expenditure divided by the change in income. Let's denote the change in consumption expenditure as \(\text{∆C} \) and the change in income as \(\text{∆Y} \).

- Calculate Change in Consumption Expenditure

The initial consumption expenditure is \$ 420\ billion and the new consumption expenditure is \$ 500\ billion. Thus, \(\text{∆C} = 500 - 420 = 80\).

- Calculate Change in Income

The initial income is \$ 400\ billion and the new income is \$ 500\ billion. Thus, \(\text{∆Y} = 500 - 400 = 100\).

- Calculate MPC

Using the formula \( \text{MPC} = \frac{∆C}{∆Y} \), plug in the values: \( \text{MPC} = \frac{80}{100} = 0.8 \).

- Understanding Change in Saving

Change in saving can be calculated using \( \text{∆S} = \text{∆Y} - \text{∆C} \).

- Calculate Change in Saving

Plug in the values: \(\text{∆S} = 100 - 80 = 20\). The change in saving is \$ 20\ billion.

- Understanding Marginal Propensity to Save (MPS)

The marginal propensity to save (MPS) is calculated as the change in saving (∆S) divided by the change in income (∆Y).

- Calculate MPS

Using the formula \( \text{MPS} = \frac{∆S}{∆Y} \), plug in the values: \(\text{MPS} = \frac{20}{100} = 0.2 \).

Key concepts

marginal propensity to save

The marginal propensity to save (MPS) indicates how much of the extra income a person saves rather than spends. It is the ratio of the change in saving to the change in income. In our exercise, after we calculated the increase in income (\text{∆Y} = 100) and the increase in saving (\text{∆S} = 20), we found that the MPS can be calculated as: \( \text{MPS} = \frac{∆S}{∆Y} = \frac{20}{100} = 0.2 \). This means that for every additional dollar earned, 20 cents is saved.

change in saving

Understanding the change in saving (\text{∆S}) is crucial for analyzing how income variations affect saving behavior. In the given problem, the formula to determine the change in saving is \( \text{∆S} = \text{∆Y} - \text{∆C} \). Here: \ • Change in Income (\text{∆Y}) = \$ 500 \ billion - \$ 400 \ billion = \$ 100 \ billion
• Change in Consumption (\text{∆C}) = \$ 500 \ billion - \$ 420 \ billion = \$ 80 \ billion.
Substituting these values into the formula: \( \text{∆S} = 100 - 80 = 20 \), we get that the change in saving is \$ 20 \ billion.

income change calculation

Calculating the change in income (\text{∆Y}) is a fundamental step in understanding economic variables like MPC and MPS. To find the change in income in our problem, we take the difference between the new income and the initial income. Here, the income increases from \$ 400 \ billion to \$ 500 \ billion. The calculation is: \( \text{∆Y} = 500 - 400 = 100 \). This \$ 100 \ billion increase in income is essential for calculating both the marginal propensity to consume and the marginal propensity to save. \ Breaking down each step and understanding this change helps simplify complex economic concepts.