Suppose that Tang and Wilson must split a fixed 400 pounds of food between them. Tang’s utility function is U T = sqrt ( F 1 ) and Wilson’s utility function is U W = ½ sqrt ( F 2 ), where F 1 and F 2 are pounds of food to Tang and Wilson, respectively.

a. How much utility will Tang and Wilson receive if the food is distributed evenly between them?

b. If the social welfare function is U T + U w , then what distribution of food between Tang and Wilson maximizes social welfare?

c. If social welfare is maximized if they each obtain the same level of utility, then what is the distribution of food between Tang and Wilson that maximizes social welfare?