Suppose that Erin spend her incomes on two goods, food (X) and clothing (Y), and that her utility function is given by U(X,Y)=.20X2Y2 (The marginal utility for X is .40XY2 and that for Y is .40X2Y ). The prices of food and clothing are $10 and $20 for each unit, respectively. Her income is $500 per week.
Find the level of her utility when she purchases 10 units of food and 20 units of clothing every week.
In (a), find her marginal rate of substitution.
Find her choice for X and Y when she maximizes her utility given her budget constraint.