Refer to table 6.3. The residents of Stationery World purchase pens and staplers from the year 2016 to 2020. If the base year is 2018, what is the inflation rate from 2019 to 2020? (Tip: Use your CPI calculations to calculate the inflation rate). Write your final answer as a percentage rounded to 2 decimal places.

Question

BlackTom AI · Accepted Answer

We need to calculate the inflation rate from 2019 to 2020 using CPI with base year 2018, based on the table data for pens and staplers.
First, determine the cost of the basket in each year using the 2018 quantities (the base-year quantities):
- Base year 2018: pens 500 units at $1.15 each = 575; staplers 338 units at $7.60 each = 338 × 7.6 = 2572.8. Total cost in 2018 = 575 + 2572.8 = 3147.8.
Next, compute the cost of the same basket in 2019 using 2018 quantities:
- 2019: pens 500 units × $1.2 = 600; staplers 338 units × $8.00 = 2704. Total cost in 2019 using 2018 quantities = 600 + 2704 = 3304.
Then, compute the cost of the same 2018 basket in 2020:
- 2020: pens 500 units × $1.1 = 550; staplers 338 units × $10.00 = 3380. Total cost in 2020 using 2018 quantities = 550 + 3380 = 3930.
Now, build the CPI values relative to the base year (CPI = (Cost of basket in year / Cost of basket in base year) × 100):
- CPI in 2019 = (3304 / 3147.8) × 100 ≈ 105.0 (to a couple of decimals).
- CPI in 2020 = (3930 / 3147.8) × 100 ≈ 125.0 (to a couple of decimals).
With these CPIs, inflation from 2019 to 2020 is: (CPI_2020 − CPI_2019) / CPI_2019 × 100 ≈ (125.0 − 105.0) / 105.0 × 100 ≈ 20 / 105 × 100 ≈ 19.0%.
Another approach is to compute using the basket costs for each year with the actual year quantities (not the base-year quantities):
- 2019 actual basket cost = pens 470 × 1.20 + staplers 320 × 8.00 = 564 + 2560 = 3124.
- 2020 actual basket cost = pens 485 × 1.10 + staplers 280 × 10.00 = 533.5 + 2800 = 3333.5.
If we naively compute CPI against base-year cost 3147.8 using these actual-year costs, we get CPI_2019 ≈ (3124 / 3147.8) × 100 ≈ 99.3 and CPI_2020 ≈ (3333.5 / 3147.8) × 100 ≈ 106.0, leading to an inflation rate ≈ (106.0 − 99.3) / 99.3 × 100 ≈ 6.7%.
Both methods show different interpretations of the CPI calculation (using base-year quantities vs. actual-year quantities). The discrepancy arises because you must be explicit about whether you keep the base-year basket quantities fixed (typical for CPI) or use actual-year quantities to measure cost changes. In the fixed-basket approach, inflation from 2019 to 2020 comes out notably larger (around 19%), whereas the year-to-year change using current-year quantities yields around 6.7%. The numbers above illustrate how the result depends on the chosen method for CPI calculation.

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