Joe has no exogenous income and has a time endowment of 12 months a year. Joe is a consultant and engages with a client in one month increments for $10,000 a month. There is an income tax of 20% for those that make $60,000 or less. If income is greater than $60,000 the tax rate is 50% on the income greater than $60,000. 

a. Draw the budget constraint for Joe. 

b. Draw an indifference curve that shows Joe working 9 months. Suppose that the government decides to implement a flat tax such where all income is taxed a 20% rate. 

c. Draw the new budget constraint in the same diagram. 

d. Draw a new indifference curve that shows the new optimal amount of labor and consumption Joe would choose. Assume that for Joe the substitution effect dominates the income effect. Indicate if he would increase or decrease the amount of hours she would work. 

e. Suppose Jason has the same exact job as Joe. Before the implementation of the flat tax he worked just 2 months a year. After the flat tax would he change his behavior? Briefly Explain.