Waec Model Questions Vol1 2017 Economics Question 39

The Human Development Index (HDI) of a country is calculated as the geometric mean of three dimension indices: Life‑expectancy index (LE), Education index (Edu) and Income index (Inc). Country A has LE = 85, Edu = 70, Inc = 60. Country B has LE = 78, Edu = 80, Inc = 55. (a) Compute the HDI of each country (round to one decimal place). (b) Which country has the higher HDI? (c) Using logarithmic decomposition, calculate the percentage contribution of each component (LE, Edu, Inc) to the difference in HDI between the two countries. Use the formula: \[\text{Contribution}_i = \frac{\ln(A_i)-\ln(B_i)}{3\,\bigl(\ln\text{HDI}_A-\ln\text{HDI}_B\bigr)}\times 100\%\] Present the contributions to one decimal place, indicating the sign (positive or negative).