Problem 27 - Calculus Early Transcendentals: Pearson New International Edition

Question

Suppose that the government pumps an extra \(\$ 1\) billion into the economy. Assume that each business and individual saves \(25 \%\) of its income and spends the rest, so of the initial \(\$ 1\) billion, \(75 \%\) is respent by individuals and businesses. Of that amount, \(75 \%\) is spent, and so forth. What is the total increase in spending due to the government action? (This is called the multiplier effect in economics.)

Step-by-Step Solution

Answer

The total increase in spending is \$4 billion.

Step 1: Identify the Initial Injection

The government injects an initial amount of \( \$1 \text{ billion} \) into the economy. This is our starting point for the calculation of the multiplier effect.

Step 2: Determine the Marginal Propensity to Consume

Individuals and businesses spend \( 75\% \) of their income. Therefore, the Marginal Propensity to Consume (MPC) is \( 0.75 \). This means for every extra dollar received, \( \$0.75 \) will be spent.

Step 3: Calculate the Multiplier

The multiplier in economic terms is calculated using the formula: \[ \text{Multiplier} = \frac{1}{1 - \text{MPC}} \] Substituting the value of MPC, we get: \[ \text{Multiplier} = \frac{1}{1 - 0.75} = \frac{1}{0.25} = 4 \]

Step 4: Calculate the Total Increase in Spending

The total increase in spending is the initial injection multiplied by the multiplier. Therefore, \[ \text{Total Increase in Spending} = \text{Initial Injection} \times \text{Multiplier} = \\(1 \text{ billion} \times 4 = \\)4 \text{ billion} \]

Key Concepts

Marginal Propensity to Consume

The Marginal Propensity to Consume (MPC) is a crucial concept in economics, representing the portion of additional income that a consumer is likely to spend rather than save. In our exercise, it's determined that individuals and businesses spend 75% of their income. This gives us an MPC of 0.75, indicating that for every extra dollar received, $0.75 will be spent on goods and services. Understanding MPC is vital as it directly influences the multiplier effect. A higher MPC means more money is circulated in the economy with each transaction, leading to potentially more significant economic growth. This cycle makes the MPC a key factor when considering fiscal policies and consumer behavior. Key points to remember about MPC:

• MPC measures spending change relative to income change.
• It ranges between 0 and 1, with 0 indicating no spending and 1 meaning all extra income is spent.
• Higher MPC can lead to a stronger multiplier effect.

Economics

Economics is the social science that studies how individuals, businesses, governments, and nations choose to allocate their resources. It explores complex interactions and the decision-making processes involved in producing, consuming, and distributing goods and services. In the context of our exercise, economics helps us understand the impact of government spending on the overall economy by examining concepts like the multiplier effect and MPC. These insights inform decisions regarding fiscal policy and its potential for stimulating economic growth. Important aspects of economics include:

• Resource allocation: Efficiently distributing scarce resources to satisfy needs and wants.
• Market dynamics: Understanding supply and demand interactions.
• Policy implications: Using economic theories and data to shape governance and business strategies.

By understanding these aspects, policymakers can better estimate the potential outcomes of their fiscal interventions.

Government Spending

Government spending plays a pivotal role in influencing economic activity. It involves expenditures on goods and services intended to boost the economy. By injecting funds into the economy, the government can stimulate demand, encourage production, and support employment. In our example, the government introduces an initial injection of $1 billion. This action is designed to elevate economic activity by promoting spending and investment. Government spending can create a ripple effect starting from the initial fund allocation and extending throughout various economic sectors. Critical roles of government spending include:

• Infrastructure development: Funding public goods that facilitate commerce and economic growth.
• Stabilization policies: Adjusting spending to mitigate economic fluctuations and manage inflation.
• Income redistribution: Providing welfare programs to support underserved communities.

Such interventions can strengthen the economy when carefully tuned to the prevailing economic conditions.

Economic Multiplier

The concept of the economic multiplier illustrates how an initial change in spending can lead to a more significant overall impact on the economy. It hinges on the idea that spending doesn't stop with the initial transaction but continues as recipients spend the incoming funds, setting off a chain reaction of expenditure throughout the economy.In simple terms, the multiplier is determined using the formula: \[ \text{Multiplier} = \frac{1}{1 - \text{MPC}} \] This reflects the amplified effect that an injection of funds can have, dependent on the marginal propensity to consume. In our case, with an MPC of 0.75, the multiplier is calculated as 4. Understanding the economic multiplier is essential because of:

• Its role in assessing the effectiveness of fiscal policy: Knowing the multiplier helps predict the impact of government spending.
• Its influence on economic forecasting: It aids in estimating changes in GDP based on spending adjustments.
• Its implications for investment decisions: Businesses can anticipate increased demand due to government interventions.

This concept reveals the power of spending to drive broader economic advancement.