This exercise challenges students to recalculate the revenue deviation using the Logarithmic Method. By utilizing natural logarithms, students will see how the mathematical residual (the joint effect) is distributed perfectly proportionally. This method eliminates the sequence bias found in chain substitution, ensuring a flawlessly objective and fair performance evaluation for department managers.
Roadmap to Solution:
Step 1: Calculate the Total Revenue Index (P₁ / P₀) and take its natural logarithm: ln(P₁ / P₀). This will be your denominator.
Step 2: Calculate the Volume Index (Q₁ / Q₀) and the Price Index (C₁ / C₀), and take the natural logarithm of both.
Step 3 (Volume Impact): Multiply the Total Deviation (ΔP, from Exercise 1) by the fraction: ln(Volume Index) / ln(Total Revenue Index).
Step 4 (Price Impact): Multiply the Total Deviation by the fraction: ln(Price Index) / ln(Total Revenue Index).