Exercise 3 (Poverty Trap). The countries South Growana (SG), Central Growana (CG), and North Growana (N G) have the same Cobb-Douglas production function Y; 2 K31\". U)HtLt)1a, where Y: denotes output, K t denotes the capital stock, n denotes the fraction of time devoted to the accumulation of human capital (e.g., education and onthejob training), Ht denotes the stock of human capital, Lt denotes population, and o: is a parameter. The three countries have dierent levels of human capital. In period 1, H1 takes the value 50 in SC, 75 in CG, and 100 in NC. In all three countries the depreciation rate, 5, equals 0.1, the savings rate, 0, equals 0.25, the capital share, 0:, equals 0.3, and the growth rate of the stock of human capital, 9(a), is given by 1.5/5. Households in all countries face the following quantity-versus-quality-of-children tradeoff, relating the population growth rate, 71, and the fraction of time allocated to the accumulation of knowledge, u, to the level of output per capita: If K/Lt