2. Consider a one period model, where the period is a week and a population of individuals (with possibly different reservation wages) choose whether...

2. Consider a one period model, where the period is a week and a population of individuals (with possibly different reservation wages) choose whether to participate and how many hours to work in the week. Let the offered hourly wage be $10. Now suppose that a progressive tax is imposed on labour earnings with a rate of zero on weekly earnings up to $300, and a rate of 20% on earnings above $300. Use a labour-leisure diagram to help guide you in answering the questions below. Note this is different from our standard problem of a simple linear full income constraint, so be careful. 

a. What effect would this have on the total labour supply for the week from this population if most of the existing participants were originally working 30 hours a week? Explain. 

b. Suppose now that, in addition to the progressive tax system, an overtime law is introduced so that hours supplied above 30 hours per week are paid a pre-tax wage of $12. How will your answer to (a) change? Explain.