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Suppose that a physician has the hallo-wing utility function: TIL-r} E B [2]\" shelf\"? where a: is the quantity of health care, 3&1 is patient's benet and x] is physician's prot. i} For arbitrary functions of B and 1r that are increasing and concave in an, characteze the quantity that maximizes the physician's utility. Next, assume that 3(a) = m, and x] = F + fa: mg. ii} Find the value of a: that maximizes the physician's utility. Suppose that social welfare is dened by 3(a) (3(a), so socially optimal quantity or\" is where 313:\") = UTE\"); iii} For Bfm) = on, and {3(a) = mg, calculate z\". iv} Is there a set of F and f such that the physician ptimlly chooses zabanrl obtains a zero prot