Math Problem Statement

In an economy, the price index in 2006 was 100 and the real gross domestic product (GDP) was $1,000. In 2010, the price index was 110 and the nominal GDP was $2,200. Based on that information, which of the following can be inferred about the economy’s nominal GDP in 2006 and real GDP in 2010?

Solution

Let's break down the given data from the image and analyze the problem:

Given Data:

  • In 2006:

    • Price index = 100
    • Real GDP = $1,000
  • In 2010:

    • Price index = 110
    • Nominal GDP = $2,200

To Determine:

  • Nominal GDP in 2006
  • Real GDP in 2010

Key Concept:

The relationship between Nominal GDP, Real GDP, and the Price Index can be expressed as:

Nominal GDP=Real GDP×Price Index100\text{Nominal GDP} = \frac{\text{Real GDP} \times \text{Price Index}}{100}

Thus, if we know the Real GDP and the Price Index, we can calculate the Nominal GDP, and vice versa.

Step 1: Nominal GDP in 2006

We already know the Real GDP in 2006 is $1,000 and the price index is 100. Using the formula:

Nominal GDP2006=1,000×100100=1,000\text{Nominal GDP}_{2006} = \frac{1,000 \times 100}{100} = 1,000

So, the Nominal GDP in 2006 is $1,000.

Step 2: Real GDP in 2010

For 2010, we know the nominal GDP ($2,200) and the price index (110). We can rearrange the formula to find the real GDP:

Real GDP2010=Nominal GDP2010×100Price Index2010\text{Real GDP}_{2010} = \frac{\text{Nominal GDP}_{2010} \times 100}{\text{Price Index}_{2010}} Real GDP2010=2,200×100110=2,000\text{Real GDP}_{2010} = \frac{2,200 \times 100}{110} = 2,000

So, the Real GDP in 2010 is $2,000.

Conclusion:

The correct option based on the analysis is B:

  • Nominal GDP in 2006 = $1,000
  • Real GDP in 2010 = $2,000

Would you like further clarification on any part of this solution?

Here are 5 related questions to expand your understanding:

  1. How do changes in the price index affect the real GDP over time?
  2. What is the significance of nominal vs. real GDP in economic analysis?
  3. How do economists adjust for inflation when comparing GDP across years?
  4. Can the price index ever decrease, and what does that imply for GDP calculations?
  5. How is the GDP deflator different from the Consumer Price Index (CPI)?

Tip: Always remember that nominal GDP is measured at current market prices, while real GDP is adjusted for inflation using a base-year price level.

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Math Problem Analysis

Mathematical Concepts

Macroeconomics
GDP calculation
Price Index

Formulas

Nominal GDP = (Real GDP × Price Index) / 100
Real GDP = (Nominal GDP × 100) / Price Index

Theorems

GDP relationship with inflation

Suitable Grade Level

Grades 10-12 or Introductory College Economics