Answer this question using calculus.

Consider a standard consumer with preferences over consumption and leisure. The utility function is CES (Constant Elasticity of Substitution):

u(c, l) = (ac+ (1a)l)1/,

where 0< a <1, and >0. This is a quasi-concave utility function.

The consumer faces the usual constraints, with the following modifica- tions. First, let= 0. Second, suppose there is a proportional tax on labour income. That is, for every unit of income earned, the consumer pays a tax of.

1. (a)Carefully write out the consumer's budget constraint. Explain why the tax enters the way that it does.
2. (b)Formally write down the consumer's optimization problem. Include the non-negativity constraints forcandl(but you can ignore them for the remainder of the assignment).
3. (c)Write down the Lagrangian function. Give the interpretation of the Lagrange multiplier.
4. (d)Derive the necessary conditions.
5. (e)Interpret the necessary conditions.
6. (f)Explain how you know that the necessary conditions are also sufficient in this case. Why is this important to know?
7. (g)Calculate the effect of a change in the tax on the optimal choice of leisure.

Please help. I'm struggling with understanding this question.