In an imaginary economy all individuals have the same utility function over consumption, c, and leisure, L, given by U = JEJE Denote labour by N. The total number of hours an individual can work is 12. Wage is indicated by w. The price of consumption is 1. Answer the following questions: (a) Set up the maximization problem of this individual and solve for the labour supply function. (b) Find the choice of labour, leisure and consumption when the wage is taxed at a marginal tax rate r. (c) Calculate the income and substitution effects on leisure for the change in wage from w to w(1 t). (d) There is no tax on w. The government introduces a reform: a transfer of B is given to all individuals who are not in the labor force. What is the effect of this reform on labor supply? (e) The government chooses to subsidize earnings. A marginal subsidy of s is added to the wage. New wage is w(1+s). What is the effect of the reform on labour supply? (f) The government adopts a different policy: all individuals are given B but their earnings are taxed at a marginal tax rate t. Find the effect of this policy on labour supply. Find the highest wage level of the person who chooses to stop working with this policy