Math Problem Statement

Suppose that a typical market based in Norway consists of 120 Avocados and 210 Jackets. The table below shows data on prices for Avocados and Jackets in Norway for three years. Year Price of Avocados Price of Jackets 2014 1.8 200 2015 1.1 150 2016 1.3 200 Assume that the base year is 2014. What is CPI in 2015?

Solution

To calculate the Consumer Price Index (CPI) for 2015, we follow these steps:

Step 1: Calculate the total cost for the base year (2014)

The base year is 2014, and CPI in the base year is always set to 100. We use the quantities of goods (Avocados and Jackets) in the typical market and the prices of those goods in 2014 to find the total cost for that year.

  • Price of Avocados in 2014 = 1.8 NOK
  • Price of Jackets in 2014 = 200 NOK
  • Quantity of Avocados = 120
  • Quantity of Jackets = 210

Total cost in 2014:

Total cost in 2014=(120×1.8)+(210×200)\text{Total cost in 2014} = (120 \times 1.8) + (210 \times 200) Total cost in 2014=216+42,000=42,216 NOK\text{Total cost in 2014} = 216 + 42,000 = 42,216 \text{ NOK}

Step 2: Calculate the total cost for 2015

Now, calculate the total cost using the prices in 2015:

  • Price of Avocados in 2015 = 1.1 NOK
  • Price of Jackets in 2015 = 150 NOK

Total cost in 2015:

Total cost in 2015=(120×1.1)+(210×150)\text{Total cost in 2015} = (120 \times 1.1) + (210 \times 150) Total cost in 2015=132+31,500=31,632 NOK\text{Total cost in 2015} = 132 + 31,500 = 31,632 \text{ NOK}

Step 3: Calculate the CPI for 2015

The CPI is calculated using the formula:

CPI in 2015=(Total cost in 2015Total cost in 2014)×100\text{CPI in 2015} = \left( \frac{\text{Total cost in 2015}}{\text{Total cost in 2014}} \right) \times 100 Substituting the values:

CPI in 2015=(31,63242,216)×10074.91\text{CPI in 2015} = \left( \frac{31,632}{42,216} \right) \times 100 \approx 74.91

Thus, the CPI in 2015 is approximately 74.91.

Would you like any further explanation or details?

Here are 5 follow-up questions based on this:

  1. How would the CPI change if the price of avocados in 2016 decreased instead of increased?
  2. What would be the total cost in 2016 with the given prices?
  3. How do we interpret a CPI less than 100, as in 2015?
  4. How does inflation relate to the change in CPI from year to year?
  5. How can a change in the quantity of goods in the market basket affect the CPI?

Tip: CPI is a key indicator of inflation, helping economists track price changes over time. A CPI above 100 indicates that prices have increased compared to the base year.

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Math Problem Analysis

Mathematical Concepts

Consumer Price Index (CPI)
Percentage
Ratios

Formulas

CPI = (Total cost in current year / Total cost in base year) × 100
Total cost = (Quantity of Avocados × Price of Avocados) + (Quantity of Jackets × Price of Jackets)

Theorems

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Suitable Grade Level

Grades 9-12