Microeconomics: true or false? explain?

Question

True or false? **EXPLAIN**

(i)If X is at least as good as Y and Y is at least as good as Z, then X is strictly preferred to Z.

(ii)For three commodity bundles X, Y and Z if X is at least as good as Y, Y is at least as good as X, and X is strictly preferred to Z, then , then Y is strictly preferred to Z.

(iii)We know the value of two of Jill’s indifference curves, U1 and U2. U1 = 5 and U2 = 7. These two indifference curves must cross

Answer 1

(i) This is false.  The counterexample is that X, Y, and Z are all equally valued.  X is then at least as good as Y, and Y is at least as good as Z, but X is not strictly preferred to Z.

(ii) False.  The counterexample is that X is better than Y, while Y and Z are equally valued.  Thus, X is at least as good as Y, and Y is at least as good as Z, but Y is not strictly preferred to Z.

(iii) Also false.  An indifference curve with utility = U is the set of bundles of goods that are worth U.  If two utility curves cross, then there must be a bundle of goods that is worth both the utility of the first curve and the utility of the second curve.  If two curves are dissimilar, then they cannot cross for a single bundle of goods cannot have multiple worths.

Hope that helps!

Answer 2

i false  look at the strictly part

ii this is true    X=Y given the info so if X>Z then Y>Z

iii false   ICs never ever ever ever cross