Utility

Question 1

In ordinal utility how are utility functions represented?

Answer 1

We can assign numbers to the goods to establish their order of preference, however the numbers are arbitrary and only the order matters so the size of the difference between the bundles is meaningless

Question 2

How does a positive monotonic transformation effect preferences in ordinal utility?

Answer 2

It has no effect

Question 3

What does it mean for utility to be cardinal?

Answer 3

Differences in utility have meaning and we can make interpersonal comparisons, i.e. add individuals utility together to make welfare comparisons about different groups welfare

Question 4

Describe a Positive Affine Transformation (PAT)

Answer 4

It is a type of transformation that will preserve
preferences under uncertainty even when utility function is ordinal and generally takes the form: g(u) = au(·) + b where a and b equal 1

Question 5

What is the indifference curve like for perfect substitutes?

Answer 5

A straight line of gradient -1 intersecting each axis at the same value

Question 6

What is the indifference curve like for perfect complements and why?

Answer 6

The indifference curves are a series of perpendicular lines with the adjoining points all passing through the ray of a line with gradient a/b. This is because one good is needed for the other so even an infinite increase in one of the goods has no effect on utility.