Question

Use the following table to answer question. The table shows the prices and the quanti­ties consumed in Carnivore Country. Suppose the base year is 2017. Also, suppose that 2017 is the year the typical consumption basket was determined, so the quantities consumed in 2017 are the only quantities needed to calculate the CPI in each year.

Year Price of Beef Quantity of Beef Price of Pork Quantity of Pork
2017 $2.00 100 $1.00 100
2018 2.50 90 0.90 120
2019 2.75 105 1.00 130

Suppose the base year is changed in the table from 2017 to 2019. Also, suppose that the typical consumption basket was now determined in 2019 (now use the 2019 consumption basket). What is the new value of the CPI in 2018?
a. 90.6
b. 100.0
c. 114.7
d. 134.3
e. none of the above

Answer 1

To calculate the Consumer Price Index (CPI) using the new base year (2019) and the quantities consumed in 2019, we first need to calculate the cost of the basket in both the base year (2019) and the year we are calculating (2018).

1. **Calculate the cost of the basket in the base year (2019):**

- Using the prices and quantities in 2019:
- Price of Beef: $2.75
- Quantity of Beef: 105
- Price of Pork: $1.00
- Quantity of Pork: 130

Cost of the basket in 2019 = (Price of Beef * Quantity of Beef) + (Price of Pork * Quantity of Pork)
\[
= (2.75 \times 105) + (1.00 \times 130)
= 288.75 + 130
= 418.75
\]

2. **Calculate the cost of the basket in 2018:**

- Using the prices and quantities in 2018:
- Price of Beef: $2.50
- Quantity of Beef: 105 (from 2019)
- Price of Pork: $0.90
- Quantity of Pork: 130 (from 2019)

Cost of the basket in 2018 = (Price of Beef * Quantity of Beef) + (Price of Pork * Quantity of Pork)
\[
= (2.50 \times 105) + (0.90 \times 130)
= 262.5 + 117
= 379.5
\]

3. **Calculate the CPI for 2018 using the base year (2019):**
\[
CPI = \left( \frac{\text{Cost of basket in 2018}}{\text{Cost of basket in 2019}} \right) \times 100
\]
\[
CPI = \left( \frac{379.5}{418.75} \right) \times 100 \approx 90.6
\]

Thus, the new value of the CPI in 2018 is approximately **90.6**, which corresponds to option **a. 90.6**.