Question

Given the following figures: $$ \begin{array}{ll} \text { Total income } & \frac{\text { Year } 1}{\$ 400 \text { billion }} & \frac{\text { Year } 6}{\$ 550 \text { billion }} \\ \text { Price index } & 1.00 & 1.00 \end{array} $$ find the increase in real income from Year 1 to Year \(6 .\)

Short answer

The increase in real income from Year 1 to Year 6 is \(150\) billion.

Step-by-step solution

Calculate real income for Year 1

For Year 1, we already have the total income (nominal income) as \(400\) billion, and the price index is \(1.00\). To find the real income for Year 1, we'll divide the total income by the price index: $$\text{Real Income}_{\text{Year 1}} = \frac{\text{Total Income}_{\text{Year 1}}}{\text{Price Index}_{\text{Year 1}}}= \frac{\$400 \text{ billion}}{1.00}$$

Calculate real income for Year 6

Similar to step 1, for Year 6, we have the total income (nominal income) as \(550\) billion, and the price index is \(1.00\). To find the real income for Year 6, we'll divide the total income by the price index: $$\text{Real Income}_{\text{Year 6}} = \frac{\text{Total Income}_{\text{Year 6}}}{\text{Price Index}_{\text{Year 6}}}= \frac{\$550 \text{ billion}}{1.00}$$

Calculate the increase in real income

Now that we have calculated the real income for both Year 1 and Year 6, we'll find the difference between them to calculate the increase in real income. Subtract the real income in Year 1 from the real income in Year 6: $$\text{Increase in Real Income} = \text{Real Income}_{\text{Year 6}} - \text{Real Income}_{\text{Year 1}} = \frac{\$550 \text{ billion}}{1.00} - \frac{\$400 \text{ billion}}{1.00}$$

Simplify and find the answer

Simplify the expression to find the increase in real income: $$\text{Increase in Real Income} = \$550 \text{ billion} - \$400 \text{ billion} = \$150 \text{ billion}$$ So, the increase in real income from Year 1 to Year 6 is \(150\) billion.

Key concepts

Nominal Income

Nominal income refers to the total amount of money earned in a particular period without any adjustments for inflation. In simple terms, it's the income amount in its original value. For instance, if you're given a salary, that's your nominal income, as it shows your earnings in current dollars. Think of it like the price tag on a product; it tells you how much you pay without considering if that amount can buy you as much over time.

In the context of the problem, the nominal income was provided as $400 billion for Year 1 and $550 billion for Year 6. These figures represent what was made in those years, not reflecting any price changes over time. This is important because knowing the nominal income alone without understanding how prices are changing gives an incomplete picture of financial growth.

Price Index

The price index is a tool used to measure the average change in prices over time for a basket of goods and services. It serves as an indicator of inflation or deflation within an economy. In its simplest form, a price index of 1.00 means no change in the level of prices from a base year.

For this exercise, the price index remained at 1.00 for both Year 1 and Year 6. This suggests that there are no adjustments needed for inflation when calculating real income. If the price index had changed, say to 1.10, it would mean prices increased by 10%. However, with the index being 1.00 in this example, the nominal and real incomes remain the same because prices haven't risen.

Income Growth

Income growth refers to the change in income over a period of time. It can be analyzed in terms of nominal income or real income. Nominal income growth looks purely at the change in dollar amounts, while real income growth considers the purchasing power by adjusting for inflation using the price index.

In this problem, the real income growth from Year 1 to Year 6 was calculated by finding the difference between the real incomes of these years. With a price index of 1.00, both the nominal and real incomes were identical. Thus, the nominal increase of $150 billion also represents the real increase, showcasing genuine income growth over these years without the complication of inflation. This step is essential to understand how much more was actually gained over time in terms of purchasing power.