Two people, John and April, got stranded on an island. They can collect fruits (X) or catch fish (Y) for food. Over one day, John (person 1) can produce either X=4 or Y=6, while April (person 2) can produce X=5 or Y=2.

a. Are there reasons for John and April to specialize? How much X and Y would each person produce then? Preferences of John and April are summarized by the following utility functions: U1=X+4Y^0.5, U2=X(Y+1). John and April decide to make fruits their currency, so we can say that the price of one fruit is PX=1. Denote the price of one fish as simply P (so PY=P).

b. Find John's demand for fish - Y1 as a function of P.

c. If John and April specialize and trade using P=1, how much of each good would they consume?

d. John loses his fishing rod, so now John gathers fruits, while April can become a fish monopolist. In this situation, what is good for April? What is bad? Note: no additional math is required here.