Welfare in general equilibrium

Question 1

Go beyond pareto optimality and add more conditions we’d like society to adhere to.

Question 2

until now we had assumed if an allocation is pareto efficient (no change could make someone better off without making someone wrose of) it is good.

Question 3

Impartial spectator uses constrained optimisation to decide on the best allocation - what info is needed (2)

Answer 3

The set of all pareto efficient combinations of utility levels.

The value they place on each of these combinations of utility levels of the two.

Question 4

Then what does the impartial spectator do with these 2 pieces of info?

Answer 4

limits her choices to allocations only on the utility possibilities frontier (UPF)

Question 5

Pg 19 - demonstrate UPF graphically

Answer 5

Conceptually like budget constraint, feasible combinations under the line.

X axis A’s utility
Y axis B’s utility

Question 6

So what does the impartial spectator choose an allocation based on?

What do they use to make this decision?

Answer 6

Depending on how much she values A and B’s utility. How they feel about Ayanda and Biko.

Does this by using UPF to study cardinal utility of each person. (size of utility, not just order like ordinal utility!!!).

Question 7

Cardinal utility as an example

Answer 7

Assings number to a bundle
E.g
U(x,y) = 10u (x’,y’) means the first bundle (x,y) is preferred 10x more than bundle (x’,y’)

Question 8

Social welfare function

Answer 8

A representation of the common good based on some weighting of the utilities of the people in society

Question 9

Social welfare function expression

And when is the spectator impartial?

What property exists?

Answer 9

W(utility of A, utility of B) = (utility of A to the λ) (utility of B to the 1-λ)

I.e CD function and use λ
When λ=0.5 , impartial spectator weighs both players utility equally. (IMPARTIAL)

Diminishing marginal value - more goods consumed, greater utility, and thereofore less they add to the specator’s assessment of social welfare

Question 10

How can the impartial spectator’s values be represented graphically

Answer 10

Iso-social welfare curves

Shows constant welfare levels for different combinations of utility.

Question 11

Where is the spectators optimal allocation

Answer 11

MRS=MRT
(Slope of pareto efficient frontier=slope of iso-social welfare curve)

Bundle is best for society given the UPF

Question 12

Note; spectator is imaginary. A and B may have to consult their own values

Question 13

Other-regarding preferences: Let A have altruistic preferences.

How is altruism measured?

Answer 13

λ
0 to 0.5
0 is entirely self-regarding, 0.5 perfect altruist (value other just as much as myself)

Question 14

What does A’s utility function become (pg26)

Answer 14

Utility of A (πA, πB)= (πA) to the 1-λ (πB) to the λ

Just a CD function with π representing payoff

Question 15

How would A’s indifference curves look

Answer 15

Like contours on a hill - satiated preferences. Bliss point is the optimal.

Altruist ignores monotonicty, doesn’t always want the most.

Question 16

1) Pg 28 - A altruistic B self regarding diagram - where is pareto efficency, and what is the optimal point?

2) What if both altruistic (other-regarding)
Where is the pareto efficient curve? (Pg29)

Answer 16

1) Pareto efficiency is achieved where tangent (as normal) , and we reside at A’s bliss point.

2) Conflict of interest
Both want 6 and give other 4 coffees at their bliss points. Conflict of interest as both want more (6) than the other is prepared to give (4)

Pareto efficient point is the line connecting the 2 bliss points.

Question 17

The more altruistic (higher λ)……..

Answer 17

The shorter the PE curve (more they care about each other (other regarding)

Question 18

How to solve this conflict of interest (3)

Answer 18

Social norms e.g finders keepers

Procedural rule of justice - e.g flipping a coin

Or take midpoint of the pareto efficient curve

Question 19

Next topic: social welfare functions:

How to balance welfare of different members of society as policymakers

Answer 19

E.g people prefer micro to macro, others dont. Do we allocate extra hours for micro or macro .

Question 20

Generic social welfare function notation, and what does it look like grahically? (Pg35)

Answer 20

W(.) = f(u₁,u₂,…,un)

W. is the social welfare function. Ui is the utility of individual “i” in a society of “n” individiuals

Iso-welfare functions are the squigly lines, where different utility represent same social welfare.

Question 21

Now we look at specific ones…

Classic Utilitarian/Benthamite SWF:
Formula, explanation and example,

Graphically, and what is the slope of the isowelfare curve? (pg38)

Answer 21

ΣUi
Social welfare is the unweighted sum of utilities of each individual.

Implication: Consider £1 from person 1 to person 2.

Social welfare enhancing if the increase in person 2’s utility is greater than the fall in person 1’s utility.

Graphically, iso-welfare curve is downwardsloping linear with slope -1, as unweighted sum of utilities

Question 22

Second SWF: Weighted sum of utilities

Formula, explanation, example, and graphic and slope, given person 1’s utility is valued twice as important as person 2’s utility (pg40)

Answer 22

Σai ui
Sum of weighted utilities of each indiviudal. Weight reflects importance of each individual’s utility for society overall given by “a”. (ai is weight placed on individual i’s utility)

Implication - transferring £1 from person 1 to person 2. This is social welfare enhancing if the increase in person 2’s utility multiplied by 𝑎₂ is greater than the decrease in person 1’s utility mutlipled by 𝑎₁.

Graphically, in this example 1’s utility is twice as important, so W=2u₁+u₂

Slope is -a₁/a₂ so -2/1 = -2

Question 23

3rd SWF: Preference for equality of utility
Explanation and implication and grsaphically

Answer 23

u₁u₂

Social welfare depends on how equal final allocations are.

Implication
This is social welfare enhancing if the final utilities are closer together than the initial ones (i.e. if person 1 initially had higher utility than person 2).

Graphically, usual CD isowelfare curve
So if 2 has high utility, willing to reduce a lot to increase 1’s utility a little. If 2 has low utiltiy, willing to reduce a little to increase 1’s utility a little.

Question 24

4th SWF: Minimax / Rawlsian

Answer 24

Min (u₁…,un)

Social welfare is determined by the person with the lowest utility.

Implication: radical transfers of income can be social welfare enhacing.

Question 25

E.g of Minimax or Rawlsian (mathmatically correct but extreme!) (pg44)

Answer 25

Say person 1 has 1m, person 2 has 39,999.

It is welfare improving to reduce person 1’s wealth by 960k to improve person 2’s wealth by £1.

Question 26

What does minimax look like on diagram

Answer 26

L shaped isowelfare functions.

Question 27

Rawls veil of ignorance

Answer 27

Argued society’s allocations are optimal as long as they would be considered optimal by someone who didn’t know which position in society they would occupy.

Thus allowing for some inequality, which provides incentives for effort and innovation (there needs to be inequality and reward for people to be successful)

Question 28

Noszick equality of opportunity social welfare criteria.

Answer 28

Distribution is just if the initial distribution of goods was just movement into a new distribution if voluntary by all agents.

Question 29

Evaluation of Noszick

Answer 29

Redistribution through mandatory taxation is not “just”. Rich cannot keep what they have gained.