Suppose two neighbouring countries, call them country A and country B, have (roughly) the same population sizes, the same size of real gross domestic product (RGDP) per capita, and are growing at the same rate of 2% per year. Then country A discovers reserves of a natural resource and begins mining to extract that, which raises country A's growth rate to 3% per year, while country B continues at 2% per year. a) If those new growth rates continue indenitely, calculate the time taken for country A's output to double, and the time taken for country B's output to double, using the rule of 70. (2 marks) b) Discuss the advantages and disadvantages of the higher economic growth rate for country A, given the discovery of this natural resource. (6 marks) c) Now suppose there is a third neighbouring country, Country C, which is similar to country B in terms of population size and natural resource endowment, but starts out with a smaller RGDP per capita than country B. If both countries B and C invest similar amounts in physical capital, explain why we might expect country C to grow faster than country B. (6 marks) d) Analyse how the institutional structure of country C could affect its ability to grow faster than country B. (4 marks)