Exam 4: Tastes and Indifference Curves

Correct Answer:

Verified

D
The graph below shows an indifference curve that satisfies convexity here -- A and B are indifferent,and C is the average of the two.C has more consumption (that the worker likes)and less labor (which the worker does not like)then D --- and thus C is preferred to D.Since D is indifferent to A and B,we therefore have the average C being preferred to the extremes A and B.We also see that the more preferred bundles lie to the northwest -- with more consumption and less labor.Finally,a tax on wages has nothing to do with how a worker feels about consumption and working --- a tax on wages affects the worker's budget,not his tastes.

Correct Answer:

Verified

a.Start with bundle A and imagine slowly removing some of each good from the bundle.Continuity and monotonicity then implies that eventually we will get to a bundle $\bar { A }$
that is just as good (but no better)than B,i.e.. $\bar { A } \sim B$
.
Next,take the average bundle between $\bar { A }$
and B -- and call it $\bar { C }$
.Convexity implies that $\bar { C }$
.is at least as good as B.
Finally,note that C contains more of every good than $\bar { C }$
.Thus,monotonicity implies that C $\succ$
$\bar { C }$
--- and,since $\bar { C }$
is at least as good as B,this implies that C $\succ$
B.
b.Yes,both the completeness and the transitivity assumptions were used.Completeness was used implicitly because we created bundles and just assumed that the consumer is able to compare them to other bundles.Transitivity was used in the last step where we concluded that we know C is better than B because we C is better than $\bar { C }$
and $\bar { C }$ is at least as good as B.