(a) Write down the consumer's maximization problem. You can use whichever formulation (Lagrangean or brute-force) you are most comfortable with. (b) Derive the first-order condition that characterizes the consumer's optimal choice of hours worked. (c) Derive the consumer's optimal labor supply (hours) choice as a function of the parameters of the tax function and the wage. (d) Suppose W increases. What happens to the labor supply curve? Why? (e) Suppose increases. What happens to the labor supply curve? Why? (f) Suppose increases. What happens to the labor supply curve? Why