9

Suppose a family orders one pizza to be shared exclusively by their two children.

Child 1 gets a fraction S1 of the pizza, while Child 2 gets a fraction S2.

The utility of child 1 for a fraction S1 of the pizza is given by U1 (S1) = S1

The utility of child 2 for a fraction S2 of the pizza is given by U2 (S2) = 3S2

9.1 Suppose the family wants to maximize the sum of the utilities of the two

children, that is:

Ufamily = U1(S1) + U2(S2)

Write the family maximization problem. What fraction of the pizza should be

allocated to child 1?

____________

9.2 Suppose now that the family utility is the lowest utility of the two children,

that is:

Ufamily = Min[U1(S1), U2(S2)]

Write the family maximization problem. What fraction of the pizza should be

allocated to child 1?

_____________

9.3 Define a pizza sharing as fight-proof if neither child prefers the fraction of

pizza allocated to the other one.

What share of the pizza should child 1 get if the pizza sharing is fight-proof?