Consider an economy with an unemployment insurance (UI) program that has the following policy parameters: Replacement rate: 40% (i.e., weekly benefit amount = 40% of weekly wages) A minimum of 14 weeks of employment required to qualify for unemployment benefits Maximum 20 weeks of UI benefits A unit of time is a week such that an individual's total time endowment is T=52 (i.e., 52 weeks in a year). For simplicity, assume that if an individual is not working, they can receive UI benefits as long as the conditions above are met. Furthermore, assume that there are no other sources of non-labor income. a) (4 points) Derive the budget constraint for an individual who faces a weekly wage rate of w in this economy. You must illustrate the budget constraint both mathematically and graphically. For the graphical illustration, set consumption on the vertical axis and leisure (in weeks) on the horizontal axis. Label slopes accordingly