Suppose a child only cares about food (F) and toys (T) and that the child’s preferences can be represented by the utility function U(F,T) = F^0.5 + T^0 .5.

(a) Does the child’s preferences exhibit diminishing marginal utility for food and for
(b) Suppose further that the child has an allowance of $30. Find the child’s demand curve for food when the price of toys is $2.
(c) Find the equation of the child’s income-consumption curve when the price of toys is $2 and the price of food is $1?
(d) How will the child’s choice of food and toys change if the price of food rises to $4 but her allowance remains at $30?