Answer :
Final answer:
By using the Laspeyres price index formula, comparing the fixed basket of goods prices between 2018 and 2022, we calculate a price index of approximately 159 for 2022. The closest given answer option is 160 (option a).
Explanation:
To calculate the price index in 2022, we can use the Laspeyres price index formula which compares the cost of a fixed basket of goods at different points in time. According to the information provided, the price index in 2018 was 150 when the cost of the basket was $500. Using the year 2018 as the base year, this means that:
Price Index 2018 = ($500 / $500) × 100 = 150
To find the price index for 2022, we use the price of the fixed basket in 2022, which is $530, and compare it to the base year price:
Price Index 2022 = ($530 / $500) × 100
Calculating this gives us:
Price Index 2022 = 1.06 × 100 = 106
Now, to align this with the 2018 index, we adjust it to the same scale as used in 2018:
Price Index 2022 (Scaled) = 106 × (150 / 100) = 159
So, we have a price index of approximately 159 for 2022. However, this does not precisely match any of the options provided (160, 170, 175, or 180). Since this is a high school level approximation problem, we'd select the closest value, which is option a) 160.
