Neco Model Questions Vol1 2023 Economics Question 30

A developing country aims to raise its real GDP per capita from $2 500 to $3 200 over a 5‑year horizon. The average annual growth rate of GDP per capita is modelled by\n\[\ng = \alpha I - \delta,\n\]\nwhere \(I\) is the average annual gross capital formation expressed as a percentage of GDP, \(\alpha = 0.30\) and \(\delta = 0.02\). Currently \(I = 22\%\).\n\nIncreasing \(I\) by one percentage point reduces consumption per capita by $30 in the first year, with the reduction falling by 10 % each subsequent year (i.e., second year reduction is $27, third year $24.3, etc.).\n\nDetermine the minimum increase in \(I\) (in percentage points) required to achieve the target GDP per capita exactly after 5 years, assuming the new growth rate \(g\) remains constant each year. Also compute the total cumulative consumption loss per capita over the 5‑year period caused by this increase in investment.