Question

In year one, Adam earns \(\$ 1,000\) and saves \(\$ 100 .\) In year 2 Adam gets a \(\$ 500\) raise so that he earns a total of \(\$ 1,500 .\) Out of that \(\$ 1,500,\) he saves \(\$ 200 .\) What is \(\triangle\) dam's MPC out of his \(\$ 500\) raise? a. 0.50 b. 0.75 c. 0.80 d. 1.00

Short answer

Adam's MPC out of his $500 raise is 0.80, which is option c.

Step-by-step solution

Understand Marginal Propensity to Consume (MPC)

Marginal Propensity to Consume (MPC) is the ratio of the change in consumption to the change in income. It measures how much consumption changes when income changes.

Identify Changes in Income and Savings

Adam's income in Year 1 was \( \\( 1,000 \) and he earned \( \\) 1,500 \) in Year 2. Therefore, the change in income is \( \Delta Y = \\( 1,500 - \\) 1,000 = \\( 500 \).In Year 1, Adam saved \( \\) 100 \) and in Year 2, he saved \( \\( 200 \). Thus, the change in savings is \( \Delta S = \\) 200 - \\( 100 = \\) 100 \).

Calculate Change in Consumption

The change in consumption can be found using the change in savings. Since the total change in income is \( \\( 500 \) and the increased savings is \( \\) 100 \), the increase in consumption \( \Delta C \) is given by:\[ \Delta C = \Delta Y - \Delta S = \\( 500 - \\) 100 = \$ 400 \]

Calculate MPC

Now, use the formula for MPC:\[ MPC = \frac{\Delta C}{\Delta Y} = \frac{\\( 400}{\\) 500} = 0.80 \]

Conclusion

Based on the calculation, Adam's MPC out of his \( \$ 500 \) raise is 0.80. Therefore, the correct answer is option c, 0.80.

Key concepts

Understanding Change in Income

In economics, understanding how income changes is crucial to grasp concepts such as the Marginal Propensity to Consume (MPC). Income can fluctuate due to various factors like salary increments, bonuses, or job changes. These modifications lead to a change in the amount of money an individual earns.

In the original exercise, Adam received a raise, which increased his income from \(1,000 to \)1,500. This change in income is calculated as the difference between what he earned in year two and what he earned in year one:

• Year 1 Income: \(1,000
• Year 2 Income: \)1,500
• Change in Income (\( \Delta Y \)): \( \(1,500 - \)1,000 = $500 \)

It's essential to track these changes because they directly impact how much more, or less, someone may choose to spend or save, influencing their overall financial behavior.

Understanding Change in Savings

Change in savings refers to how much more or less money a person saves when their income changes. It's an important measure to observe how saving habits adjust with changing financial conditions. Savings is the money set aside after all the expenditures have been accounted for.

In this scenario, as Adam’s income increased from year one to year two, his savings also experienced a change. Here's how we determine the change in savings:

• Year 1 Savings: \(100
• Year 2 Savings: \)200
• Change in Savings (\( \Delta S \)): \( \(200 - \)100 = $100 \)

Detecting a change in savings helps comprehend how effectively income variations translate into changes in saving patterns, which is essential for financial planning and understanding consumption behavior.

Determining Change in Consumption

Change in consumption is about understanding how much more people spend when their income changes. This spending behavior is key in calculating the Marginal Propensity to Consume (MPC).

For Adam, with the rise in income, there was also a shift in how much he spent (or consumed). To ascertain this, we subtract the increase in savings from the total income change:

• Total Change in Income: \( \(500 \)
• Increase in Savings: \( \)100 \)
• Change in Consumption (\( \Delta C \)): \( \Delta Y - \Delta S = \(500 - \)100 = $400 \)

This calculation is vital, as a higher MPC indicates that a larger portion of any additional income is spent rather than saved, affecting economic demand and growth considerations.