Question

Consider an economy with only two goods: bread and wine. In the base year, the typical family bought four loaves of bread at \(\$ 2\) per loaf and two bottles of wine for \(\$ 9\) per bottle. In a given year, bread cost \(\$ 3\) per loaf, and wine cost \(\$ 10\) per bottle. The CPI for the given year is a. 100 b. 123 c. 126 d. 130

Short answer

The CPI for the given year is around 123, which corresponds to option b. 123.

Step-by-step solution

Calculate the cost of the basket in the base year.

In the base year, the family bought 4 loaves of bread at \(\$ 2\) per loaf and 2 bottles of wine at \(\$ 9\) per bottle. We'll compute the total cost of the basket in the base year as follows: Base year cost of the basket = (Number of bread loaves × Price per loaf) + (Number of wine bottles × Price per bottle) Base year cost of the basket = (4 × \(2) + (2 × \)9)

Calculate the cost of the basket in the given year.

In the given year, the bread costs \(\$ 3\) per loaf and the wine costs \(\$ 10\) per bottle. We'll compute the total cost of the basket in the given year as follows: Given year cost of the basket = (Number of bread loaves × Price per loaf) + (Number of wine bottles × Price per bottle) Given year cost of the basket = (4 × \(3) + (2 × \)10)

Calculate the CPI.

Now we can calculate the CPI by dividing the cost of the basket in the given year by the cost of the basket in the base year and then multiply by 100: CPI = (Given year cost of the basket / Base year cost of the basket) × 100 CPI = ([(4 × \(3) + (2 × \)10)] / [(4 × \(2) + (2 × \)9)]) × 100 Calculate the values in the brackets and substitute into the equation: CPI = ([\(12 + \)20] / [\(8 + \)18]) × 100 CPI = (\(32 / \)26) × 100 Now, divide and multiply: CPI ≈ 1.23 × 100 CPI ≈ 123 The CPI for the given year is around 123, which corresponds to option b. 123.

Key concepts

Inflation

Inflation refers to the rate at which the general level of prices for goods and services rises, resulting in a decrease in purchasing power. Simply put, when inflation occurs, you pay more money to buy the same goods and services compared to before.

Imagine buying a candy bar for $1. If a year later, the same candy bar costs $1.10, inflation has taken place. This means your money buys you less than it did before. Over time, inflation can significantly affect the economy.

• People may demand higher wages if goods and services cost more.
• Businesses might adjust their prices to keep up with cost changes.
• Your savings might lose value if the interest rate on savings is lower than the inflation rate.

Using the Consumer Price Index (CPI) is a common way to measure inflation. The CPI indicates how much prices have increased by comparing the cost of a fixed basket of goods and services over time.

Basket of Goods

The term 'basket of goods' represents a fixed selection of items used to track price changes in an economy. This basket acts as a sample that reflects the spending habits of a typical consumer or household over time.

For example, in our exercise, the basket includes bread and wine, reflecting what a typical family might purchase. The quantities are fixed, but the prices can change from year to year, illustrating how price rises or falls affect the overall cost of the basket.

• Basket composition may include things like food, clothing, housing, and transportation.
• It aims to be comprehensive yet selective to facilitate easy tracking and comparison.

Economic authorities like government agencies regularly update these baskets to ensure they reflect current consumption patterns, ensuring this method stays relevant and accurate.

Economic Indicators

Economic indicators like the Consumer Price Index (CPI) play a crucial role in understanding the health of an economy. These indicators give insights into trends and help in making decisions.

The CPI is particularly useful for:

• Measuring inflation, as seen in the exercise by comparing costs between the base year and the current year.
• Adjusting salaries and pensions to maintain purchasing power.
• Informing government policies on economic stability and growth.

Other economic indicators include unemployment rates, Gross Domestic Product (GDP), and more. Together, they provide a comprehensive view of economic performance. Knowing how to interpret these metrics can help individuals, businesses, and policymakers make informed decisions.