Question

Show why a \(\$ 10\) billion reduction in government purchases of goods and services will have a larger effect on real GDP than a \(\$ 10\) billion reduction in government transfers by completing the accompanying table for an economy with a marginal propensity to consume \((M P C)\) of \(0.6 .\) The first and second rows of the table are filled in for you: on the left side of the table, in the first row, the \(\$ 10\) billion reduction in government purchases decreasesa. When government purchases decrease by \(\$ 10\) billion, what is the sum of the changes in real GDP after the 10 rounds? b. When the government reduces transfers by \(\$ 10\) billion, what is the sum of the changes in real GDP after the 10 rounds? c. Using the formula for the multiplier for changes in government purchases and for changes in transfers, calculate the total change in real GDP due to the \(\$ 10\) billion decrease in government purchases and the \(\$ 10\) billion reduction in transfers. What explains the difference? (Hint: The multiplier for government purchases of goods and services is \(1 /(1-M P C)\). But since each \(\$ 1\) change in government transfers only leads to an initial change in real GDP of \(M P C \times \$ 1\), the multiplier for government transfers is \(M P C /(1-M P C) .)\)

Short answer

Compare the differences and explain the results. Answer: The effect of a decrease in government purchases and a decrease in government transfers on real GDP depends on the multipliers for changes in those variables. The multiplier for changes in government purchases is greater than the multiplier for government transfers, which means the decrease in government purchases has a larger negative effect on real GDP compared to the decrease in government transfers.

Step-by-step solution

Find the change in real GDP for each round

First, we need to calculate the change in real GDP for each round following the decrease in government purchases and transfers. The change in real GDP for a given round can be calculated as follows: Change in real GDP = initial change * MPC^round Note that the initial change in government purchases is given as \(\$ 10\) billion, and the initial change in government transfers is given as \(-\$ 10\) billion.

Sum the changes in real GDP for the given 10 rounds

Next, for both scenarios, we will sum up the changes in real GDP after the 10 rounds to find the total change in real GDP at the end of the 10 rounds. Total change in real GDP = Sum of changes in real GDP for each round For government purchases: Sum of real GDP changes = \(-10 \times (1 + 0.6 + 0.6^2 + 0.6^3 + ... + 0.6^{10})\) For government transfers: Sum of real GDP changes = \(-10 \times 0.6 \times (1 + 0.6 + 0.6^2 + 0.6^3 + ... + 0.6^{10})\)

Calculate the multipliers for changes in government purchases and transfers

Now, we will calculate the multipliers for changes in government purchases and transfers using the provided formulas. Multiplier for changes in government purchases: \(1 /(1-MPC) = 1/(1-0.6)\) Multiplier for changes in government transfers: \(MPC /(1-MPC) = 0.6/(1-0.6)\)

Calculate the total change in real GDP using the multipliers

Next, we will use the multipliers to calculate the total change in real GDP due to the \(\$ 10\) billion decrease in government purchases and the \(\$ 10\) billion reduction in transfers. Total change in real GDP (government purchases) = initial change * multiplier = \(-10\) billion * multiplier for changes in government purchases Total change in real GDP (government transfers) = initial change * multiplier = \(-10\) billion * 0.6 * multiplier for changes in government transfers

Compare the differences and explain the results

Finally, we will compare the total changes in real GDP for both scenarios and explain the results. The multiplier for changes in government purchases is greater than the multiplier for government transfers, which means the decrease in government purchases has a larger effect on real GDP.

Key concepts

Marginal Propensity to Consume (MPC)

The Marginal Propensity to Consume, or MPC, is a crucial concept in economics. It measures how much people consume when they receive additional income. For example, if the MPC is 0.6, it means that for every extra dollar received, people will spend 60 cents and save the remaining 40 cents.

Understanding the MPC is essential as it indicates consumer behavior and spending patterns. It helps economists predict how changes in income levels, like wages or government transfers, will affect overall consumption in the economy.

When governments decide on fiscal policies, knowing the MPC allows them to estimate the potential impact on national consumption and economic output. High MPC means more spending could lead to increased demand for goods and services, while a lower MPC means more savings, potentially slowing down economic growth.

Multiplier Effect

The multiplier effect is a fascinating concept that describes how initial changes in spending can lead to larger overall changes in the economy. It occurs due to the repeated rounds of spending that follow an initial expenditure injection.

The fundamental principle behind the multiplier effect is that one person's spending becomes another person's income. This initiates a chain reaction of further spending. For government purchases, the multiplier formula is given by \[\text{Multiplier} = \frac{1}{1 - \text{MPC}}\] Each dollar the government spends is magnified as it circulates through the economy.

Conversely, the effect of government transfers is less pronounced. Transfers rely on the MPC: only a portion of the transfer is spent, and the multiplier here is \[\text{Multiplier for Transfers} = \frac{\text{MPC}}{1 - \text{MPC}}\]This smaller multiplier means a reduced impact on overall economic output.

Government Spending

Government spending is a key component of fiscal policy and plays a vital role in the economy. It includes expenditures on goods, services, infrastructure projects, and public programs. Such spending directly introduces money into the economy, influencing both overall output and employment.

When the government increases its spending, this action can spur economic activity and growth. For instance, building a new highway creates jobs not only for construction workers but also for suppliers of materials and services. The increase in demand generates a ripple effect across different sectors.

• Government purchases affect real GDP more significantly because every dollar spent enters the GDP count directly.
• In contrast, reductions in government spending can slow down the economy since they reduce overall demand for goods and services.

Real GDP

Real GDP, or Gross Domestic Product, represents the total value of all goods and services produced within a country over a specific time period, adjusted for inflation. This adjustment allows for a more accurate comparison of an economy's productivity across different time periods.

Real GDP is a crucial metric, as it provides insights into the health and growth of an economy. Higher real GDP indicates a prosperous economy with more production and higher income levels. Conversely, a drop in real GDP signifies an economic slowdown, with reduced production and consumption.

• Fiscal policies, such as changes in government spending, can significantly affect real GDP.
• Understanding these effects helps governments and policymakers make informed decisions to stabilize or boost economic growth.