Consider abled Australians aged 18 to 59, who can earn $40 / hour and have 60 hours available per week for work and leisure. They have no other source of income. Income tax is on every dollar of wage income over $400 at a rate of 25%. In addition, consider that if they can not find work they can receive $380 per week from JobSeeker Payments that are not taxed, but these are clawed back by $0.50 for every $1 in wage income earned. Once wage income exceeds $760 per week, no Job Seeker payments are received and there is no clawback. For example, if they earn $240 in a week, they will lose 0.50 x $240= $120 of their $380 JobSeeker payment and be left with $260. If they earn $760 in a week they will lose all their JobSeeker payment and also pay ($760 - $400) x 25% = $90 in income tax. Assume that individuals who do not want to work can also receive the JohSeeker Payment even if they could find work, but choose not to take it. This diagram may be useful in answering the following questions. Consider four types of individuals with the following utility functions, for consumption(C) and leisure (L) per week i Ui = LC2 ii Uii = LC iii Uii = L2C iv Uiv = L4C Budget Constraint for wage = $40, 25% income tax after income over $400, Job Seeker $380, clawback rate 50%. $40x60 =52400 Wages: C= 2400 40L BC: C= 1900~ 30L $30x50+$400= $1900 (5 of consumption expenditure per week) o= Liours o esure perweek] gy oo o a. Calculate the reservation wage for each of the four worker types and compare it to the wage (after clawback) to explain which type(s) of workers want to work. b. Verify that the mathematical expression for the budget constraint of consumption C for leisure L for an individual that pays tax and is not receiving any JobSeeker Payments (and so not having wages clawed back) is = 1900 - 30L. c. Demonstrate that the optimal choice of leisure hours for a type i individual is L* = 21.11hours per week and consumption C* = $1,266.67 per week. How much income tax does a type i individual pay per week? {First assume they pay tax and are not receiving any JobSeeker. Payments and use that BC from part b to calculate L* and check if w H*>$760. If w H*>$760 then are not receiving JohSeeker. Payments (they are paying income tax since w H*>$400) and you have used the correct BC If $400>w H*>$760 use the blue BC: 1080-10L. If w H*$760. If w H*>$760 then are not receiving JobSeeker Payments (they are paying income tax since w H*>$400) and you have used the correct BC. If $400> w H*>$760 use the blue BC: 1080-10L. If w H*