Deck 4: Tastes and Indifference Curves

Question 1

You like bundle A better than bundle B,and bundle C is an average between A and B.If your tastes satisfy convexity,then C is at least as good as A and as B.

Answer 1

False
Convexity implies that you will prefer average bundles to extremes that you are indifferent between.

Question 2

Prove formally that the rationality axioms alone rule out the possibility of indifference curves crossing.

Answer 2

Suppose A is strictly preferred to B and thus lies on a different indifference curve.Suppose further that the two indifference curves cross at some point C,a point that therefore lies on both indifference curves.This implies that
and
.But we know that
.Transitivity implies that
and
implies --- which contradicts A and C lying on the same indifference curve.Thus,it can't be that indifference curves cross and the indifference map satisfies transitivity.

Question 3

The number of units of the good on the horizontal axis that we are willing to give up to get one more unit of the good on the vertical axis is equal to the absolute value of the slope of the indifference curve.

Answer 3

False
The slope of the indifference curve gives us the number of units of the good on the vertical axis that we are willing to give up to get one more unit of the good on the horizontal axis.

Question 4

Explain the following statement: Individuals with different tastes might have the same tastes at the margin at their current consumption bundles.

Question 5

Bundle A is worse than bundle B,and bundle C is an average of bundles A and B.Then our usual assumptions about tastes imply that bundle B is at least as good as bundle C.

Question 6

Complete tastes are tastes that make people desire at least some of every good.

Question 7

If you observe me choosing bundle A over bundle B on Monday,bundle B over bundle C on Tuesday and bundle C over bundle A on Wednesday,it must be that my tastes violate transitivity.

Question 8

Suppose tastes are NOT monotonic anywhere.Then diminishing MRS is not consistent with convexity of tastes.

Question 9

Suppose bundle A is better than bundle B for a consumer,and bundle C is an average of bundles A and B.
a.Use the continuity,convexity and monotonicity assumptions to formally prove that this implies that bundle C is better than bundle B.
b.Did you also -- implicitly or explicitly -- use the rationality axioms?

Question 10

If the marginal rate of substitution is not diminishing,it must mean that tastes violate convexity (assuming that our other assumptions about tastes hold).

Question 11

You like bundle A better than bundle B,and bundle C is an average of bundles A and B.Which of the following is correct if your tastes satisfy our usual assumptions?
a.
Bundle C is at least as good as bundle B.
b.
Bundle A is at least as good as bundle C.
c.
Both (a)and (b).
d.
None of the above.
e.
There is not enough information to tell.

Question 12

Consider the utility function .(Explain all your answers.)
a.Derive the function for the marginal rate of substitution.
b.Do the tastes represented by this utility function satisfy diminishing MRS?
c.The marginal utility of a good is defined as the change in utility from additional consumption of that good (holding all else constant).Derive the marginal utility of
and
.
d.Why does an ordinal approach to utility theory not any attention to what you derived in (c)?
e.Why does an ordinal approach to utility not treat the marginal rate of substitution the way it treats the marginal utility concept?

Question 13

Consider a worker who dislikes working end enjoys consuming a composite good.With labor hours on the horizontal and the composite consumption good on the vertical axis,which of the following statements are true.
a.
If the worker's tastes are convex,the slope of indifference curves increases as we move to the right in the graph.
b.
The worker becomes better off as we move to the northwest in the graph.
c.
A tax on wage income does not change this worker's indifference map.
d.
All of the above.
e.
None of the above.

Question 14

When the price of beer goes up,our model of tastes would typically require tastes to change.

Question 15

Explain the following statement: For the same individual,tastes over goods may vary at the margin as we move from one bundle to another.