Question 12 (8 points) 4)) Listen b ' Consider an economy with two sectors, a traditional one labeled Twith many producers but all added up in one representative firm for the sector, and an industrial one labeled lcomposed of a price limiting monopolist. There is only one factor of production in the economy, namely (unskilled) labour, where there are one hundred individuals. The traditional sector produces rice ( QT) in a competitive market with linear (constant returns) production function QT : LT where LT denotes the amount of labour used in that sector. The price limiting monopolist on the other hand produces rice with a production function that has increasing returns, which is defined as _ 0 ifL1 0 represents the cost of migrating from the traditional sector to the industrial sector, a switching cost that can be say transportation. Suppose the demand for rice from the traditional sector is defined as 01', where a E (0.1), while the complement (1 , 003' is the demand for rice from the monopolist where Ydenotes total labour income in the economy, i.e. Y = WTLT + WILL The distribution of labour among the two sectors determines if the monopolist enters since that would only happen if L: is sufficiently large, otherwise it would not, in which case the demand for rice is satisfied only by the traditional sector and a\": 1. In what follows we study the conditions under which industrialization through a Big Push would arise or not. Note that the profit function for the traditional sector is Hr = PQT * WrLr = (1 * WT)LT while that for the industrial sector is _{W1Lf if L]