Set up the Lagrangian, solve the consumers optimization problem and derive the labour supply curve.

5. (30 points) Consider a one-period closed economy model with government. The aggre- gate production is given by Y=2N where N represents the employment and z is the total factor productivity. The consumer's preferences are given by U(C,l) =nC+4+Inl subject to the following budget constraint C=wh-D+a-T where 7 denotes profits. The consumer has fh units of time to split between labour supply and leisure. The government spending is denoted by G and lump-sum taxes are denoted by T. The government's budget constraint is G = T