1. **Problem Statement:** Calculate the Laspeyres, Paasche, and Fisher Price Indices for office equipment from 2022 to 2023 using given prices and quantities. 2. **Laspeyres Price Index (PL):** Measures price change using base year quantities. Formula: $$PL = \frac{\sum p_1 q_0}{\sum p_0 q_0} \times 100$$ Calculate numerator: $$\sum p_1 q_0 = (30,000 \times 20) + (18,000 \times 25) + (48,000 \times 10) = 600,000 + 450,000 + 480,000 = 1,530,000$$ Calculate denominator: $$\sum p_0 q_0 = (25,000 \times 20) + (15,000 \times 25) + (40,000 \times 10) = 500,000 + 375,000 + 400,000 = 1,275,000$$ Calculate index: $$PL = \frac{1,530,000}{1,275,000} \times 100 = \frac{1,530,000}{1,275,000} \times 100$$ Show cancellation: $$PL = \frac{\cancel{1,530,000}}{\cancel{1,275,000}} \times 100 = 120$$ Interpretation: Prices increased by 20% from 2022 to 2023 using base-year quantities. 3. **Paasche Price Index (PP):** Measures price change using current year quantities. Formula: $$PP = \frac{\sum p_1 q_1}{\sum p_0 q_1} \times 100$$ Calculate numerator: $$\sum p_1 q_1 = (30,000 \times 18) + (18,000 \times 22) + (48,000 \times 8) = 540,000 + 396,000 + 384,000 = 1,320,000$$ Calculate denominator: $$\sum p_0 q_1 = (25,000 \times 18) + (15,000 \times 22) + (40,000 \times 8) = 450,000 + 330,000 + 320,000 = 1,100,000$$ Calculate index: $$PP = \frac{1,320,000}{1,100,000} \times 100 = \frac{1,320,000}{1,100,000} \times 100$$ Show cancellation: $$PP = \frac{\cancel{1,320,000}}{\cancel{1,100,000}} \times 100 = 120$$ Interpretation: Prices increased by 20% from 2022 to 2023 using current-year quantities. 4. **Fisher’s Ideal Price Index (PF):** Geometric mean of Laspeyres and Paasche indices. Formula: $$PF = \sqrt{PL \times PP}$$ Calculate index: $$PF = \sqrt{120 \times 120} = \sqrt{14400} = 120$$ Interpretation: Balanced index showing a 20% increase in price level, reliable and satisfies time/factor reversal. **Final Summary:** - Laspeyres Index = 120 (20% increase) - Paasche Index = 120 (20% increase) - Fisher Index = 120 (20% increase)