This economics question tests your understanding of economic models and analysis. The step-by-step answer below applies the relevant framework and explains the reasoning.
ScanSolve AI Answer
Here's the solution for question 13. To construct the index numbers, we first need to calculate the necessary sums. Let P_0 and Q_0 be the price and quantity in the base year (2010), and P_1 and Q_1 be the price and quantity in the current year (2012). Step 1: Create a table to calculate the required products. |c|c|c|c|c|c|c|c|c| Items & P_0 & Q_0 & P_1 & Q_1 & P_0 Q_0 & P_1 Q_0 & P_0 Q_1 & P_1 Q_1 \\ A & 6 & 50 & 10 & 56 & 300 & 500 & 336 & 560 \\ B & 2 & 100 & 2 & 120 & 200 & 200 & 240 & 240 \\ C & 4 & 60 & 6 & 60 & 240 & 360 & 240 & 360 \\ D & 10 & 30 & 12 & 24 & 300 & 360 & 240 & 288 \\ E & 8 & 40 & 12 & 36 & 320 & 480 & 288 & 432 \\ Total & & & & & 1360 & 1900 & 1344 & 1880 \\ From the table, we have: P_0 Q_0 = 1360 P_1 Q_0 = 1900 P_0 Q_1 = 1344 P_1 Q_1 = 1880 a) Laspeyre's Method: The formula for Laspeyre's Price Index (P_01^L) is: P_01^L = ( P_1 Q_0)/( P_0 Q_0) × 100 Substitute the values: P_01^L = (1900)/(1360) × 100 P_01^L = 1.3970588 × 100 P_01^L = 139.71 b) Paasche's Method: The formula for Paasche's Price Index (P_01^P) is: P_01^P = ( P_1 Q_1)/( P_0 Q_1) × 100 Substitute the values: P_01^P = (1880)/(1344) × 100 P_01^P = 1.3988095 × 100 P_01^P = 139.88 c) Fisher's Method: The formula for Fisher's Ideal Price Index (P_01^F) is the geometric mean of Laspeyre's and Paasche's indices: P_01^F = sqrt(P_01)^L × P_01^P Alternatively: P_01^F = sqrt(( P_1 Q_0)/( P_0 Q_0) × ( P_1 Q_1)/( P_0 Q_1)) × 100 Using the calculated Laspeyre's and Paasche's indices: P_01^F = sqrt(139.70588 × 139.88095) P_01^F = sqrt(19542.06) P_01^F = 139.79 Last free one today — make it count tomorrow, or type /upgrade for unlimited.