Dave's utility function for leisure (R) and consumption (C) is given by U(C, R) = In C + In R. Denote the wage rate, his total time endowment, and his unearned income respectively by w, T, and M. 

(i) Derive his ordinary labor supply function 

(ii) Derive his Slutsky compensated labor supply function L*(w; 7, ) given his initial consumption-labor supply bundle (©, 7) Show that allow > 0. (iii) Derive his Slutsky equation for the labor supply then show that the substitution effect will always dominate the income effect.