You are given total debt for the second quarter of 2003 and the second quarter of 2004 for the overall population and four age groups. The four age groups collectively account for the entire population and their debt holdings account for overall total debt.
Quarter, Age_Group, Population, Total_Debt, Per_Capita_Debt Q2 2003,0,1000,10000,10 Q2 2003,1,250,3000,12 Q2 2003,2,400,5000,12.5 Q2 2003,3,250,1500,6 Q2 2003,4,100,500,5 Q2 2004,0,1300,15000,11.5 Q2 2004,1,380,4000,10.5 Q2 2004,2,450,7000,15.6 Q2 2004,3,270,2500,9.3 Q2 2004,4,200,1500,7.5
The per capita growth rate for age group 0, representative of the total per capita growth rate is 15 percent. But how does one convert the individual per capita growth rates to the contribution to the total rate? Perhaps weight by the population shares? Taking a weighted average of the per capita growth rates yields approximately 6 percent. Dividing the change in per capita debt for each of the groups over the per capita debt level for the population doesn't work as it would when using total debt. The result should be r1 + r2 +r3 + r4 = r0 Where rn is the growth rate for age group n.