William and Charlotte Collins divorced in November of Year 1. William moved out and Charlotte remained in their house with their 10-month-old daughter, Autumn. Diana, Charlotte's mother, lived in the home and acted as Autumn's nanny for all of Year 1. William provided 70 percent of Autumn's support, Diana provided 20 percent, and Charlotte provided 10 percent. When the time came to file their tax returns for Year 1, William, Charlotte, and Diana each wanted to claim Autumn as a dependent. Their respective adjusted gross incomes for Year 1 were $50,000, $35,000, and $52,000. Who has priority to claim Autumn as a dependent

Suppose life expectancy in years (l) is a function of two inputs, health expenditures (h) and nutrition expenditures (n) in hundreds of dollars per year. the production function is upper l equals ch superscript 0.40 baseline upper n superscript 0.60l=ch0.40n0.60. beginning with c = 1, a health input of $400400 per year (hequals=44) and a nutrition input of $400400 per year (nequals=44), show that the marginal product of health expenditures and the marginal product of nutrition expenditures are both decreasing. the marginal product of health expenditures when h goes from 44 to 55 is nothing, and the marginal product of health when h goes from 66 to 77 is nothing. (round your answers to three decimal places.)