All individuals have the same utility function over consumption, C, and leisure, L, given by U = C 1/3 L 2/3 , Denote the wage rate by w. The total time available for labour and leisure is equal to...

All individuals have the same utility function over consumption, C, and leisure, L, given by U = C^1/3L^2/3, Denote the wage rate by w. The total time available for labour and leisure is equal to 12. The price of consumption is P_C=1. Denote the amount of labour supplied as N.

1)Find the Labour supply function.

2)The government introduces a tax t=0.2 on wage, such that the after-tax wage is (1-t)w. How much tax revenue does the government collect on everyone? What is the effect on labour supply?

3)The government chooses instead to collect a fixed lump-sum T from everyone. What is the effect on labour supply?