Consider two different countries, A and B. They are very similar, given that they share lots of characteristics, as: - the growth rate of GDP between t and t+1, equal to 2%, - the interest rate in t and t+1, constant and equal to 2% - the tax-to-GDP ratio, constant and equal to 0.1. Moreover, they display also the same: - initial GDP, i.e. YAt = Yst = 100 - previous level of debt, Bat-1 = BBt-1 = 50. They differ only regarding the composition of their population: - in year t, both countries have an old population-to-total population ratio equals to At = Bt = 0.2 - in year t+1 these ratios are At+1 = 0.8 for country A and ast+1 = 0.2 for country B. Some studies have shown that the total public expenditure depends positively on the portion of old people living in a country; assume for simplicity that Git = it Yit and it is valid in any country I in any period. Find the level of public debt at t and t+1 for both country A and country B, and then compare their growth rates.