Question

Assume our economy produces only one good, product \(\mathrm{X}\), and that its quantities and prices over time are given in the following table: $$ \begin{array}{lcc} \text { Year } & \text { Units of Output } & \text { Price of } \mathrm{X} \\ 1 & 5 & \$ 10 \\ 2 & 7 & 20 \\ 3 & 8 & 25 \\ 4 & 10 & 30 \\ 5 & 11 & 28 \end{array} $$ a) Compute the price index in percent using Year 1 as the base year; i.e., (Year \(1=100\) ). b) Compute the unadjusted, or money GNP. c) Compute the adjusted, or real GNP.

Short answer

a) Price index: Year 1: 100, Year 2: 200, Year 3: 250, Year 4: 300, Year 5: 280 b) Unadjusted GNP: \$998 c) Adjusted GNP: \$410

Step-by-step solution

a) Compute the price index

To compute the price index for each year using Year 1 as the base year, we will follow this formula: \( Price \ Index \) = \( \frac{Price \ of \ X \ in \ Current \ Year}{Price \ of \ X \ in \ Base \ Year} \times 100 \) Use the given data to compute the price index for each year: Year 1: \( \frac{10}{10} \times 100 = 100 \) Year 2: \( \frac{20}{10} \times 100 = 200 \) Year 3: \( \frac{25}{10} \times 100 = 250 \) Year 4: \( \frac{30}{10} \times 100 = 300 \) Year 5: \( \frac{28}{10} \times 100 = 280 \) The price index for each year is shown below: Year 1: 100 Year 2: 200 Year 3: 250 Year 4: 300 Year 5: 280

b) Compute the unadjusted, or money GNP

To compute the money GNP for each year, use the following formula: Money GNP = Units of Output × Price of X Year 1: \( 5 \times 10 = \$ 50 \) Year 2: \( 7 \times 20 = \$ 140 \) Year 3: \( 8 \times 25 = \$ 200 \) Year 4: \( 10 \times 30 = \$ 300 \) Year 5: \( 11 \times 28 = \$ 308 \) Sum up the values of the money GNP for all years: \( \$50 + \$140 + \$200 + \$300 + \$308 = \$998 \) Therefore, the unadjusted or money GNP is \$998.

c) Compute the adjusted, or real GNP

To compute the real GNP for each year, use the following formula: Real GNP = Units of Output × Price of X in Base Year (Year 1) Year 1: \( 5 \times 10 = \$ 50 \) Year 2: \( 7 \times 10 = \$ 70 \) Year 3: \( 8 \times 10 = \$ 80 \) Year 4: \( 10 \times 10 = \$ 100 \) Year 5: \( 11 \times 10 = \$ 110 \) Sum up the values of the real GNP for all years: \( \$50 + \$70 + \$80 + \$100 + \$110 = \$410 \) Therefore, the adjusted or real GNP is \$410.

Key concepts

Price Index

The price index is a way to measure how prices change over time, relative to a base year. It's expressed in percentage terms. In simple terms, the price index reflects how the cost of a good, or basket of goods, evolves from one period to another.

To calculate the price index using Year 1 as the base year, we use the formula:

• Price Index = \( \frac{\text{Price of X in Current Year}}{\text{Price of X in Base Year}} \times 100 \)

For example, for Year 2, with the price of product X at \(20 and the base year price at \)10, the price index is:

• \( \frac{20}{10} \times 100 = 200\% \)

This means that in Year 2, the price of X has doubled compared to Year 1. Continuing this calculation for the subsequent years helps us understand how the relative price of the product X changes compared to the base year. An increasing price index indicates inflation, while a decreasing one can signal deflation.

Real GNP

Real Gross National Product (Real GNP) serves as a crucial measure that adjusts for inflation. It represents the true productivity of an economy by calculating the total values of goods and services produced, adjusted to exclude the distortions of inflation. This measure helps depict the real growth of the economy over time.

Calculating real GNP requires using the base year's price to eliminate the effects of price changes:

• Real GNP = Units of Output × Price of X in Base Year

For example, in Year 3, the economy produced 8 units of product X. Using the base year's price of \(10, the real GNP is:

• \( 8 \times 10 = \\) 80 \)

By maintaining the base year's prices across all years, we can see how the actual volume of production is changing, providing a clearer view of economic growth without the influence of inflation.

Money GNP

Money GNP, sometimes referred to as unadjusted GNP, measures the total market value of all finished goods and services produced within a year. Unlike Real GNP, Money GNP doesn't adjust for price changes or inflation, reflecting the nominal values based on current prices.

To compute Money GNP, we multiply the actual production output by the current year's price:

• Money GNP = Units of Output × Price of X

For example, in Year 4, with 10 units produced at a price of \(30 each, the Money GNP is:

• \( 10 \times 30 = \\) 300 \)

This nominal measure indicates the economic activity based purely on current conditions. While it shows the current value of production, it does not account for how much price changes might have affected these values.