Consider an economy made up of / individuals. All individuals have the same preferences over consumption, c, and labour supply, L, represented by the utility function U(c, L) = c-.502 An individual's income is given by y = w/ where w is the individual's wage rate. There are No individuals who are unable to work, M individuals who earn w1, and N2 individuals who earn wy > w1, and where No + Mi + N2 = N. The government imposes a linear progressive income tax such that T(y) = ty - b where b > 0 is an income transfer received by all individuals regardless of income. (a) Solve for the optimal labour supply of each type of wage earner