1. An island country is a closed, no government, and no storage economy. There is a fixed amount of land in this island. The aggregate production function requires land and labor inputs as following: Y = =F(L, N), where Y is the total output, z is the total factor productivity, L denotes total size of land, and N denotes labor size for the current period. F(L, N) is a diminishing return to scale production function. Let C denote aggregate consumption and N' denote the labor size. Assuming the population growth rate depend on living standards & as the following: N' N = 9 where g is an increasing function. Suppose the technology improves, analyze the short-run and long-run effect on output, consumption, output per worker, consumption per worker, and population. (10 marks) 2. Suppose there are two countries. In the rich country, the representative consumer has Hr units of human capital, and total factor productivity is z,. In the poor country, the represen- tative consumer has Ho units of human capital, and total factor productivity is &p. Assume that b and / are the same in both countries, Hr > Hp, and 2, > 2p. How do the levels of per capita income, the growth rates of per capita income, and real wages compare between the rich and poor countries? (10 marks)