Consumer Choice: Preferences Flashcards
Preference notations (3)
A>B A is strictly preferred
A~B indifferent to B
A>=B weakly preferred (equally good)
4 assumptions to give CONSISTENT PREFERENCES
Completeness - Bundles can be compared.
Reflectivity - Any bundle is at least as good as itself
Transitivity- if A>B and B>C then A>C
Consumer makes rational choices
Why is consistency needed?
Difficult to build model.
What additional assumption is often made?
Monotonicity/Nonsatiation - more is always better
Self regarding vs other-regarding preferences
Self regarding - only concerned with outcomes we experience
Other-regarding - also concerned with outcomes of others.
Indifference curve
Shows all combinations of bundles between which the consumer is indifferent. (Provide same level utility)
Can indifference curves cross?
No, as we assume Transitivity. If they intersect it is wrong as that would infer same utility, and they are not on the same indifference curve!
3 properties of well-behaved indifference curves
Monotonicity/nonsatiation
Convexity - diversity is preferred (e.g 5 apples 5 bananas vs 10 apples)
Continuity - a small change in consumption results in small change in utility
Key concept for convexity - diversity is preferred: pg 47 hard.
Equation.
Averages are preferred to extremes.
(tx₁+(1-t)y₁, tx₂+(1-t)y₂ >= (x₁,x₂)
t is the weight assinged to the good between 0-1.
If expression is true, then it is convex, needed for well behaved preferences.
Nonconvex and concave preferences don’t accept convexity, since the averaged bundle is always under the original curve (less utility)
Example
2 bundles A and B
A= (100;10) B=(10:100) A~B
- Will consumer prefer bundle X (120,10) to bundle B?
- Will consumer prefer bundle Y with Y=10,90 to bundle A?
- What about Z=55:55?
- Yes, monotonicity (130>110)
- No, by transitivity and monotonicity. It is not better than B (monotonicity 100>90) , and B is indifferent (~) to A, so bundle Y cannot be preferred to A.
- Same amount as A and B, so need to check convexity. We need a t between 0-1.
Look at both goods separately. Good 1 first….
Use formula tA + (1-t)B , if = Z, Z preferred to A&B.
Quantity of good 1 in A=100, and B=10… so
t x 100 + (1-t)10 =55
100t + 10 - 10t=55
t=0.5
Now do for 2nd good to see if same coefficient (t=0.5 is valid - done workings on goodnotes)
Quantity of good 2 in A=10 B=100
0.5(10) + (1-0.5)100=55 which is Z!!!
So it is preferred!!!
Well behaved preferences may not be realistic due to the assumption of continuity. Evaluation of continuity
If goods only come in whole units there cannot be continuity. E.g buying a car.
What does a perfect substitute look like on indifference curve
Constant rate of substitution, so slope is constant.
What do perfect complements look like on indifference curve?
L SHAPE - consumed together in a fixed proportion. E.g left and right shoes. (Just like fixed proportion isoquant)
What do bads look like on indifference curves (assume good Y to be the bad good)
A bad is a good consumers doesn’t like (negative utility)
ASSUMING Y IS A BAD GOOD AND X IS STANDARD,
What assumption is violated by bads
Monotonicity - as we don’t want more BADS
What do neutrals look like on indifference curve
Give 0 utility. So vertical lines as utility only increases when the consumption of the standard good increases.
What does satiated preferences look like (pg53)
There is an overall best bundle for the consumer.
The further away, the worse off they are.
Shown by a point on the graph. (Bliss point)
What assumption does satiated preferences violate
Monotonicity.
E.g don’t want music tooo loud, we want it at a certain level. More is not always better than less in this model.
Thus satiated preferences are more realistic
What do discrete goods look like (pg54)
Good X only consumed in integers, has to be a linear line for indifference curves. (Dotted lines in between the discrete values - acts as a hypothetical indifference curve since we cannot consume non-discrete values in reality)
MRS definition and formula.
Rate willing to trade good Y for good X. Essentially WTP!!
Eg X=20 Y=10
MRS = -2 (2Ys to replace X)
Change in Y/Change in X
MRS for perfect subs, neutrals, perfect complements, and strictly convex curves
Perfect subs -Constant (e.g if one for one, slope -1)
Neutrals - infinite
Perfect complements - 0 or infinity.
Strictly convex indifference curves - MRS is diminishing.
What happens as your move down an indifference curve
Experience a diminishing MRS (Slope gets flatter)
When u have a lot, more willing to give it up for an additional unit of the other one. When u have limited, less willing to give up.
MRS as exchange rate
If she gives up ∆x of good 1 then she can obtain E∆x units of good 2.
Slope is -E
