Suppose you are studying the rate of growth of income in a country as a function of the rate of growth of capital in that country and of the per capita income of that country. You are using a cross-sectional data set that includes both developed and developing countries. Suppose further that the underlying theory suggests that income growth rates will increase as per capita income increases and then start decreasing past a particular point. Describe how you would model this relationship with each of the following functional forms:
a-A quadratic function
b-A semi log function
c-A slope dummy equation