Topic 2 Preferences Flashcards
Define preferences
Preferences represent the taste of the consumer
What do the following signs represent in terms of preferences?
> = (greater than sign with horizontal line underneath it)
<= (less than sign with horizontal line underneath it)
Squiggly line<
The greater than sign with the horizontal line underneath it (=>) denotes a consumers weak preferences for one bundle over another
Note the same sign above but in the opposite direction does not exist as you would simply prefer the bundle you weakly prefer more first and then have the greater than or equals to sign (remember even the great than sign is 2 curved lines joined together rather than a straight one)
The squiggly horizontal line denotes that one is indifferent to the 2 bundles being compared
The greater than sign (again joined by 2 curved lines) means that one strictly prefers one bundle to another
Again the same sign in the opposite director (less than) doesn’t really exist as you put the bundle you strongly prefer first
How many main preference signs are there and what are they?
There are 3 main preference signs and they are:
1) > (curved lines)
2) >= (curved lines with straight horizontal line underneath)
3) - (squiggly)
How are the 3 main preference signs related?
If one bundle is strictly preferred to another then that same bundle is also weakly preferred to the other - BUT it is not true to say that the second bundle is weakly preferred to the first
If we are indifferent between one bundle and another, it means that we weakly prefer the first bundle to the second AND we weakly prefer the second bundle to the first
What assumptions regarding preferences are assumed to always hold (for preferences to be rational) and what are they?
1) Complete - everything can be compared - given any preference comparison either one bundle will be weakly preferred to another or both bundles will be weakly preferred to each other (if one is indifferent between 2 bundles then both will apply and if one strongly prefers one bundle then one bundle will be weakly preferred to the other and not the other way round)
2) Transitive - if bundle x is preferred to bundle y and bundle y is preferred to z then it can be assumed that bundle x is preferred to bundle z
What do complete and transitive preference assumptions allow preference relations to be and what do they also allow you to do?
Complete and transitive preference assumptions are considered necessary to consider a preference to be rational
It allows bundles to be ranked in terms of preferences up until you become indifferent between bundles
How many other preference assumptions are there and what are they?
About 3 more
3) Monotonic - more is always better - if x1 is greater than y1 and x2 is greater than y2, then the bundle of x1 and x2 is strictly preferred to the bundle of y1 and y2
4) Convex - basically means that mixtures are preferred if you indifferent between 2 bundles - you prefer having a combination
5) Continuous - a preference relation is continuous of all weakly better sets and all weakly worse sets are closed - a set is closed if it includes its boundary e.g. for the set (x1,x2), x1 + x2 is less than or equal to say 2 is closed where is x1 + x2 was less than 2 this would not be closed - preferences are usually assume to be continuous and hence sets closed
How would you graphically represent preferences?
Using an indifference curve:
You are indifferent to the bundles that occur on the indifference curve and weakly prefer the bundles which exist above the indifference curve
What are the properties of indifference curves given the assumptions we have looked at?
If preferences are monotonic then indifference curves need to be thin and be curves (include straight lines and NOT areas) - areas would imply that you are indifferent between one bundle and another bundle in which you have more x1 and x2 which cannot be possible if monotonicity holds
Indifference curves also cannot intersect - if you indifference curve intersect then the intersection point is indifferent to 2 bundles (one of one indifference curve and one on the other) - by transitivity you can the say that you are indifferent between the 2 points on each of the respective indifference curves - this however cannot hold is one of the indifference curves will lay above the other and therefore you can be indifferent between two bundles when one yields you more x1 and x2 (if monotonicity holds) - can be shown using a diagram and choosing good points on each indifference curve
How can convex preferences be seen graphically?
They can be seen with a convex indifference curve (remember a convex curve is u shaped)
If you take 2 points on either end of the indifference curves (you are indifferent between these 2 points) - if you draw a straight line between these 2 points and take a point in the middle of this straight line you fall in the weakly preferred set) - this mid point is a mixture of both x1 (x-axis) and x2 (y-axis) … as it falls in the weakly preferred set it proves that mixtures are preferred and hence convexity holds
If you were to attempt the same process but this time with a concave curve (n shaped), you would find the mid point between the 2 indifference curves would not fall in the weakly better set and hence mixtures are not preferred
What are lexicographic preferences?
Where the consumer only cares in the first place about good 1 - here good 2 is used only for tie breaking (good 1 has primary importance and good 2 has secondary importance)
For example: if bundle x is strictly preferred to bundle y (x1,x2) > (y1,y2) then this is probably because there is greater quantity of x1 than y1 OR x1 and y1 are equal but there is greater quantity of x2 than y2 … it would be unlikely for there to be less x1 than y1 but much greater x2 than y2 for bundle x to be strictly preferred to bundle y
Are lexicographic preferences continuous?
No, as the weakly better set is not a closed set
(Don’t really understand why at the minute - don’t know if it’s necessary to understand)
What is the marginal rate of substitution?
The MRS at (x1,x2) is the slope of the indifference curve at (x1,x2)
Interpret the meaning of the marginal rate of substitution (MRS)
If I gain a small quantity of good 1 (change in x1 is positive), how many units of good 2 can I give up (change is x2 is negative) without being worse off (and … reside on the same indifference curve - maintain the same utility)
If the change in x1 and the change in x2 are small, what is the marginal rate of substitution approximately equal to?
MRS is approximately equal to change in x2 over change in x1 (change in y over change in x) - basically saying that you can treat an indifference curve as a straight line when the change in x1 and x2 are small
