Consider a hypothetical economy with only two goods: T-shirts and milk. Assume that a typical household purchases four litres of milk and two T-shirts. for the year. The following data relates to prices of these products in 2001 and 2017. 2001 is to be used as the base year. [table]
Product | Price in 2001 | Price in 2017 T-shirt | $9 | $14 Milk | $1.50 | $3.50
[/table] What is CPI for 2017?

Question

BlackTom AI · Accepted Answer

CPI uses a fixed basket priced in the base year; here the basket is 2 T‑shirts and 4 litres of milk and 2001 is the base year (index = 100).

1) Relevant knowledge points and concepts
- The Consumer Price Index (CPI) compares the cost of a fixed basket of goods in a given year to the cost of that same basket in the base year.
- CPI(base year) = 100 by definition.
- CPI(year t) = (Cost of basket in year t / Cost of basket in base year) × 100.

2) Complete reasoning process step by step
- Identify quantities in the basket: 2 T‑shirts and 4 litres of milk.
- Compute the basket cost in the base year (2001).
- Compute the basket cost in the target year (2017).
- Form the CPI ratio and multiply by 100.

3) Calculations with intermediate steps
- Cost in 2001:
  - T‑shirts: 2 × $9 = $18
  - Milk: 4 × $1.50 = $6.00
  - Total 2001 cost = $18 + $6 = $24.00
- Cost in 2017:
  - T‑shirts: 2 × $14 = $28
  - Milk: 4 × $3.50 = $14.00
  - Total 2017 cost = $28 + $14 = $42.00
- CPI for 2017 = (42 / 24) × 100 = 1.75 × 100 = 175

4) Why the correct answer is correct
- The CPI formula directly yields 175 because the fixed basket that cost $24 in 2001 costs $42 in 2017; prices increased by a factor of 1.75, so the index rises from 100 to 175 (a 75% increase).

5) Why the other options are incorrect
- 100 would imply no price change (cost still $24) — incorrect because basket cost rose to $42.
- 130 and 118 do not match the actual weighted change in the fixed basket; they arise from incorrect weighting or arithmetic mistakes (they do not equal 42/24 × 100).

6) Conclusion
- The correct CPI for 2017 is 175, matching answer d.

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