91Ó°ÊÓ

The gross domestic product is used by economists as a measure of the nation's economic position. The gross domestic product \(P\) is calculated as the sum of personal consumption expenditures \(C\), gross private domestic investment \(I\), government consumption expenditures and gross investment \(G\), and net exports \(E\) of goods and services (exports minus imports). All of these are measured in billions of dollars. a. Find a formula that gives the gross domestic product \(P\) in terms of \(C, I, G\), and \(E\). b. In 2002, personal consumption expenditures was \(7303.7\) billion dollars, gross private domestic investment was \(1593.2\) billion dollars, government consumption expenditures and gross investment was \(1972.9\) billion dollars, and net exports of goods and services was \(-423.6\) billion dollars. i. Which was larger in 2002 , U.S. imports or exports? ii. Calculate the gross domestic product for \(2002 .\) c. Solve the equation in part a for \(E\). d. Suppose that in another year the values for \(C, I\), and \(G\) remain the same as the 2002 figures, but the gross domestic product is 10,886 billion dollars. What is the net export of goods and services for this year?

Step by step solution

01

Write the Formula for GDP

The gross domestic product \( P \) is calculated as the sum of personal consumption expenditures \( C \), gross private domestic investment \( I \), government consumption expenditures and gross investment \( G \), and net exports \( E \). The formula is given by: \[P = C + I + G + E\] This formula will be used in the subsequent parts of the exercise.

02

Analyze the 2002 Export and Import

The net export \( E \) is negative, specifically \( -423.6 \) billion dollars, implying that the value of imports exceeded the value of exports in 2002. This indicates that the U.S. imported more goods and services than it exported.

03

Calculate the GDP for 2002

Using the values provided, compute the GDP: \[P = 7303.7 + 1593.2 + 1972.9 - 423.6 = 10446.2 \,\text{billion dollars}.\] This gives the GDP for 2002.

04

Solve for Net Export \( E \)

Rearrange the formula from Step 1 to solve for \( E \). We have: \[E = P - C - I - G\] This will allow us to find the net export given the rest of the values.

05

Calculate Net Export for a Different Year

Given the GDP as 10,886 billion dollars and keeping \( C, I, G \) constant as in 2002, compute \( E \) using the rearranged equation: \[E = 10886 - 7303.7 - 1593.2 - 1972.9 = 16.2 \,\text{billion dollars}.\] This net export value indicates a surplus where exports exceed imports by 16.2 billion dollars.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Gross Domestic Product

Gross Domestic Product, commonly known as GDP, is a vital economic indicator that reflects the economic health of a country. It encompasses the total monetary value of all goods and services produced within a nation's borders in a specific time period, typically a year. GDP helps economists, policymakers, and analysts understand the economic performance of a country.
It is calculated using the formula:

• \[ P = C + I + G + E \]

here:

• \( C \) represents personal consumption expenditures.
• \( I \) stands for gross private domestic investment.
• \( G \) is government consumption expenditures and gross investment.
• \( E \) represents net exports (exports minus imports).

Each component captures a different aspect of the economy, making GDP a comprehensive measure of economic activity.
For example, in 2002, the GDP of the United States was calculated using specific values for each of these components, highlighting the country's economic position during that period.

Mathematical Modeling

Mathematical modeling involves translating a real-world situation into a mathematical framework to analyze and understand the dynamics of a system. In the given exercise, mathematical modeling is used to derive a formula for GDP.
This process begins by identifying the key variables that influence the phenomenon. In our case, these variables are personal consumption expenditures \( C \), gross private domestic investment \( I \), government expenditures \( G \), and net exports \( E \).
,By modeling GDP with an equation, economists can quantify the effect of changes in one component on overall economic performance. This method simplifies complex economic relations into manageable calculations, facilitating predictive analysis and decision-making.

• For example, if government investment increases, its impact on GDP can be directly calculated, providing insights into potential economic growth.

Economic Analysis

Economic analysis involves evaluating data to understand and predict economic trends and behaviors. It often includes examining GDP figures to determine past and current economic conditions, which can guide future economic policies.
In 2002, an economic analysis of the U.S. GDP, which totaled 10,446.2 billion dollars, revealed insights about national economic strength. By examining the components of GDP, analysts determined that net exports \( E \) were negative. This indicated the U.S. imported more than it exported, reflecting a trade deficit.
Such analyses have practical implications:

• Identifying key areas of spending and investment within the economy.
• Understanding trade dynamics and how they affect domestic industries.
• Developing strategies for increasing exports or reducing imports.

Assessing these components can highlight strengths and weaknesses, guiding decisions that aim to boost economic productivity and stability.

Equation Solving

Equation solving is a critical mathematical skill used to find unknown values in mathematical expressions. In the exercise, solving equations is key to determining the individual components of GDP.
For instance, to find net exports \( E \) for a given GDP, the equation:

• \[ E = P - C - I - G \]

is used. Rearranging the GDP formula effectively isolates \( E \), allowing for its calculation when the other variables are known.
In the exercise, solving this equation was necessary to determine the net export value of 16.2 billion dollars for a year with a GDP of 10,886 billion dollars, while keeping other components constant. This demonstrates how solving equations can be instrumental in analyzing economic data and making informed decisions.