(a) Suppose we have preferences U(X,Y)=min[X,3Y]. Graph/sketch the indifference curve through the bundle (X=30,Y=30). What is the utility of (30,30) and explain why the indifference curves look the way they do. (b) What does the Marginal Rate of Substitution tell us about preferences? (c) Why is the Marginal Rate of Substitution not applicable in this example? (d) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain. (e) State the consumer's maximization problem and express this in words. (f) Now let Px=10,Py=20 and income M=2000. Find optimal X,Y, and the resulting Utility (U). Show your work. (g) Now let Py=15. How does optimal consumption (X3,Y) and utility (U) change relative to (e)? Explain in simple terms and show in a diagram. (a) Suppose we have preferences U(X,Y)=min[X,3Y]. Graph/sketch the indifference curve through the bundle (X=30,Y=30). What is the utility of (30,30) and explain why the indifference curves look the way they do. (b) What does the Marginal Rate of Substitution tell us about preferences? (c) Why is the Marginal Rate of Substitution not applicable in this example? (d) What do we mean by a composite good? What does this composite good look like with these preferences? Show and explain. (e) State the consumer's maximization problem and express this in words. (f) Now let Px=10,Py=20 and income M=2000. Find optimal X,Y, and the resulting Utility (U). Show your work. (g) Now let Py=15. How does optimal consumption (X3,Y) and utility (U) change relative to (e)? Explain in simple terms and show in a diagram