. Last year, a welfare-eligible mother with one child living in County X could receive a daily living allowance from the welfare department of $40, which was reduced dollar-for-dollar by any earnings she might have had. In algebraic terms, where E = daily earnings, the welfare subsidy was calculated as follows: Daily subsidy = 40 E. Assuming she could earn $5 per hour, draw her daily budget constraint assuming she had 16 hours per day of available time. . Are there any circumstances in which a welfare-eligible mother in County X would have chosen to work? (That is, can any mothers work and receive welfare payments at the same time?) Explain. Suppose that County Y has the same $40 subsidy for welfare-eligible mothers who do not work, but that it reduces the subsidy for those who have earnings by 80 cents for every dollar earned. That is, its daily subsidy is as follows: Daily subsidy = 40 0.8E. Draw the budget constraint facing welfare-eligible mothers in County Y, again assuming a mother who can earn $5 per hour. At what level of earnings does the subsidy become zero? . Do you expect the labor force participation rate among low-income mothers in County Y to be above that in County X? Why? . Now focus on a group of low-income mothers in County X who choose to work 10 hours a day (at $5 per hour). Would they work more, less, or the same number of hours if they faced a constraint like that in County Y