Lecture 3 - More Preferences & Utility Function

Question 1

What is meant by monotonic preferences?

Answer 1

preferences are monotonic if: (x1, x2) ≻ (y1, y2) whenever x1 ≽ y1, and x2 ≽ y2, and at least one of these inequalities is strict

Question 2

What will the indifference curve look like for monotonic preferences?

Answer 2

indifference curves are downwards sloping

Question 3

What is meant by a satiation/bliss point?

Answer 3

an overall best bundle for for the consumer, and the closer that that are to that bundle, the better off they are in terms of their own preferences

Question 4

If preferences are experiencing satiation, are the preferences monotonic?

Answer 4

no

Question 5

What are the conditions for preferences to be classed as convex?

Answer 5

• if for any two equivalent bundles,
• (x1, x2) ∼ (y1, y2), and any weight t between 0 and 1,
• (tx1 + (1 − t)y1, tx2 + (1 − t)y2) ≽ (x1, x2)

Question 6

Give an example of what non-convex preferences may be?

Answer 6

2 things that do not go well together, e.g. beer and milk

Question 7

What are the conditions for preferences to be classed as strictly convex?

Answer 7

• if for any two equivalent bundles,
• (x1, x2) ∼ (y1, y2), and any weight t between 0 and 1,
• (tx1 + (1 − t)y1, tx2 + (1 − t)y2) ≻ (x1, x2)

Question 8

In terms of the indifference curves, what is the difference between convex preferences and strictly convex preferences?

Answer 8

convex preferences may have flat spots in their indifference curves, strictly convex preferences cannot have flat spots

Question 9

Are perfect complements convex, strictly convex, both, or neither?

Answer 9

convex but not strictly convex

Question 10

What are the 5 criteria that need to be satisfied in order to say preferences are well-behaved?

Answer 10

• if they are
• complete
• transitive
• continuous
• monotone
• strictly convex

Question 11

If a preference relation ≽ over a finite set A of alternatives is _____ and _____, then it has a _____ _____?

Answer 11

• complete and transitive
• utility representation

Question 12

If a preference relation ≽ over a finite set A of alternatives is _____, _____ and _____, then it has a _____ _____?

Answer 12

• complete, continuous and transitive
• utility representation