Neco Model Questions Vol1 2024 Economics Question 48

Country X has the following development indicators: life expectancy 68 years, mean years of schooling 6, expected years of schooling 10, and GNI per capita (PPP) = \$4,500. The Human Development Index (HDI) is calculated as the geometric mean of three dimension indices: \[\text{LEI}= \frac{\text{LE}-20}{85-20},\quad \text{EduI}= \frac{\frac{\text{MYS}}{15}+\frac{\text{EYS}}{18}}{2},\quad \text{IncI}= \frac{\ln(\text{GNI})-\ln(100)}{\ln(75{,}000)-\ln(100)}.\] Overall HDI = \((\text{LEI}\times\text{EduI}\times\text{IncI})^{1/3}\). The government plans to increase mean years of schooling by 2 years and raise GNI per capita by 20 % while life expectancy remains unchanged. Compute the new HDI (rounded to three decimal places) and state whether the increase is greater than 0.02.