Chapter 22: Problem 8

Use the following data to work Problems 8 and 9 The people on Coral Island buy only juice and cloth. The CPI basket contains the quantities bought in $2013 .$ The average household spent $\$ 60$ on juice and $\$ 30$ on cloth in 2013 when juice was $\$ 2$ a bottle and cloth was $\$ 5$ a yard. In 2014 , juice is $\$ 4$ a bottle and cloth is $\$ 6$ a yard. Calculate the CPI basket and the percentage of the household's budget spent on juice in 2013

Short Answer

Expert verified

The CPI basket contains 30 bottles of juice and 6 yards of cloth. In 2013, 66.67% of the household's budget was spent on juice.

Step by step solution

- Determine the quantities

Calculate how many bottles of juice and yards of cloth were bought in 2013. Use the total expenditure and the price per item to find the quantities. For juice, use the formula: \[ \text{Quantity of juice} = \frac{\text{Total expenditure on juice in 2013}}{\text{Price per bottle in 2013}} = \frac{60}{2} = 30 \text{ bottles} \] For cloth, use the formula: \[ \text{Quantity of cloth} = \frac{\text{Total expenditure on cloth in 2013}}{\text{Price per yard in 2013}} = \frac{30}{5} = 6 \text{ yards} \]

- Calculate the total household budget

Sum the expenditures on juice and cloth to find the total household budget in 2013: \[ \text{Total budget in 2013} = 60 + 30 = 90 \text{ dollars} \]

- Calculate the percentage of the household's budget spent on juice

Use the formula for percentage to find how much of the budget was spent on juice: \[ \text{Percentage spent on juice} = \left( \frac{60}{90} \right) \times 100\% = 66.67\% \]

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Key Concepts

These are the key concepts you need to understand to accurately answer the question.

basket of goods

Imagine you have a shopping list that includes the items you buy frequently, like juice and cloth for the people on Coral Island. This list is called a 'basket of goods.' For our example, the basket of goods includes:

30 bottles of juice
6 yards of cloth.

These items are what make up the CPI basket because they are what an average household buys regularly. The quantities of these items are crucial because they represent the consumption patterns.
To calculate the quantities:

For juice: Total expenditure on juice / Price per bottle in 2013 = 30 bottles
For cloth: Total expenditure on cloth / Price per yard in 2013 = 6 yards

These quantities are then used to understand how price changes over time affect the total cost of the basket of goods.

budget calculation

Calculating a household's budget involves adding up all the money spent on different items. In 2013, the total budget includes spending on both juice and cloth.
First, we look at individual expenditures:

Juice expenditure: \(60
Cloth expenditure: \)30

Next, we sum these amounts to get the total household budget:

Total Budget = Juice expenditure + Cloth expenditure = 60 + 30 = 90 dollars.

This total allows households to know how much they are spending overall. Understanding your budget helps in managing finances and planning for future expenses.

percentage expenditure

To know how much of the budget is used on a specific item, we calculate the percentage expenditure. For example, the percentage of the budget spent on juice can be found using a simple formula:

Percentage spent on juice = (Total expenditure on juice / Total budget) × 100% = (60 / 90) × 100 = 66.67%

This means 66.67% of the household's budget was spent on juice in 2013. By calculating percentage expenditures, households can see which items take up more of their budget. This helps in making informed decisions about where they might want to cut costs or allocate funds differently.