Helen has a utility function given byU=[x^0.5+y^0.5 ]^2, where x is the amount of product X consumed per month and y is the amount of product Y consumed per month. The government has instituted rationing. Everyone receives 200 ration points per month. To purchase products X and Y, Helen must pay with ration coupons as well as money prices. Each unit of product X requires 2 coupons and $4. Each unit of product Y requires 4 coupons and $2. Helen has a monthly income of $280.

For parts (a)-(b) assume that coupons cannot be sold for money. Find Helen's utility maximizing output?

b) Redo part (a) assuming her monthly allocation of coupons is 280.

c) How would your answers to (a) and (b) change if there were a market where coupons could be bought or sold for $2 each?