Question

Suppose that this year's nominal GDP is 16 trillion dollars . To account for the effects of inflation, we construct a price-level index in which an index value of 100 represents the price level 5 years ago. Using that index, we find that this year's real GDP is 15 trillion dollars . Given those numbers, we can conclude that the current value of the index is: \(L O 27.5\) a. Higher than \(100 .\) b. Lower than \(100 .\) c. Still 100

Short answer

The current value of the index is higher than 100.

Step-by-step solution

Understand the Problem Statement

We have two GDPs: nominal and real. The nominal GDP is 16 trillion dollars for this year, and the real GDP is 15 trillion dollars for this year. There's a price-level index to account for inflation, with 100 as the base index value 5 years ago. We need to find whether the current index is higher, lower, or equal to 100.

Define the Relationship Between Nominal GDP, Real GDP, and Price-Level Index

Use the relation between nominal GDP, real GDP, and the price-level index: \[ \text{Nominal GDP} = \text{Real GDP} \times \frac{\text{Price-Level Index}}{100} \] where the price-level index is expressed as a percentage of the base year, which is 100.

Solve for the Price-Level Index

We have Nominal GDP = 16 trillion dollars and Real GDP = 15 trillion dollars. Rearrange the equation to solve for the price-level index: \[ \text{Price-Level Index} = \frac{\text{Nominal GDP}}{\text{Real GDP}} \times 100 \] Substitute the given values: \[ \text{Price-Level Index} = \frac{16}{15} \times 100 \] Calculate the price-level index: \[ \text{Price-Level Index} = 106.67 \]

Interpret the Result

The price-level index we calculated is 106.67, which is higher than 100. This indicates that, compared to 5 years ago, the price level has increased due to inflation.

Key concepts

Nominal GDP

Nominal GDP refers to the total market value of all goods and services produced in a country during a specific period, without adjusting for inflation. It's expressed in current prices, which means it reflects the current year's currency value.

• Nominal GDP includes changes in prices and quantities produced in the economy.
• Because it does not account for inflation, comparisons of nominal GDP over different years can be misleading.

For instance, if the nominal GDP of a country in a particular year is $16 trillion, it signifies the value of its production measured using the prices prevalent in that year. However, this figure does not tell us about the economy's true growth because it includes inflation's effects. That's why economists also consider Real GDP, which adjusts for price changes and provides a clearer picture of economic performance.

Price-Level Index

A price-level index is a measure that compares the current price level of goods and services to a base year price level. It helps in understanding how much prices have increased or decreased over time relative to that base year.

• It is often indexed to 100, representing the base year.
• If the price-level index is above 100, prices have risen compared to the base year, indicating inflation.
• If it is below 100, prices have fallen, suggesting deflation.

The exercise shows that the price-level index is 106.67, derived from the relationship between nominal and real GDP:\[ \text{Price-Level Index} = \frac{\text{Nominal GDP}}{\text{Real GDP}} \times 100 \]This calculation demonstrates an increase in the price level, signifying inflation since the base year, as the index value exceeds the 100 benchmark.

Inflation

Inflation is the rate at which the general level of prices for goods and services rises, consequently eroding purchasing power. It signifies that, over time, money buys fewer goods and services, suggesting that each unit of currency is worth less.

• Inflation can significantly impact economic decisions, influencing everything from consumer spending to interest rates and wage demands.
• A moderate inflation rate is generally considered healthy for an economy, as it encourages spending and investment.
• However, high inflation can be harmful, causing economic instability and uncertainty.

In the given exercise, the calculated price-level index of 106.67 indicates an increase in prices over the past five years, marking a period of inflation. Economists use this kind of data to assess economic health and guide monetary policies aimed at managing inflationary pressures.