Final answer:
The question asks for the calculation of a price index and inflation rate based on the provided costs of a market basket in different years. By calculating the total cost for both current and base years and then determining the price indices, one can calculate the inflation rate. The inflation rate remains consistent, regardless of the chosen base year.
Step-by-step explanation:
The subject of the student's question pertains to the calculation of the total cost of a market basket in the current year as compared to the base year. It involves understanding of concepts such as price indices and inflation rate from the field of economics, which are applied within the mathematical framework for calculation purposes.
Firstly, we must calculate the total cost of the market basket for the current year using the current-year prices. For goods X, Y, and Z, this would mean multiplying the quantities of each good by their respective current-year prices and summing these products:
- (10 units of X * $1) + (20 units of Y * $4) + (45 units of Z * $6) = $10 + $80 + $270 = $360
Secondly, we would calculate the total cost of the market basket for the base year using the base-year prices:
- (10 units of X * $1) + (20 units of Y * $3) + (45 units of Z * $5) = $10 + $60 + $225 = $295
Now that we have the total costs for the current and base years, we can calculate the price indices using the base year as a reference:
- Current year price index = (Current year cost / Base year cost) * 100
- Base year price index = 100 (since it's the reference year)
Finally, the inflation rate would be the percentage increase in the price index from the base year to the current year. It is crucial to note that regardless of which year is chosen as the base year, the inflation rate remains the same because it is the rate of change that is measured, not the absolute price index values.