Question

Consider an economy with only two goods, bread and wine. In 2020 a typical family bought 4 loaves of bread at R1.83 per loaf and 2 bottles of wine at R13 per bottle. In Year X, a loaf of bread cost R8.00 per loaf and one bottle of wine cost R21. The CPI for Year X using 2020 as he base year is:

Answer 1

To calculate the Consumer Price Index (CPI) for Year X using 2020 as the base year, we need to follow these steps:

1. **Calculate the cost of the basket in the base year (2020)**:
- **Bread**: 4 loaves * R1.83 per loaf = R7.32
- **Wine**: 2 bottles * R13 per bottle = R26.00
- **Total Cost in 2020**: R7.32 + R26.00 = R33.32

2. **Calculate the cost of the same basket in Year X**:
- **Bread**: 4 loaves * R8.00 per loaf = R32.00
- **Wine**: 2 bottles * R21 per bottle = R42.00
- **Total Cost in Year X**: R32.00 + R42.00 = R74.00

3. **Calculate the CPI for Year X**:
\[
\text{CPI} = \left( \frac{\text{Cost of basket in Year X}}{\text{Cost of basket in base year}} \right) \times 100
\]
\[
\text{CPI} = \left( \frac{R74.00}{R33.32} \right) \times 100 \approx 222.18
\]

So, the CPI for Year X using 2020 as the base year is approximately **222.18**.