Welfare in general equilibrium Flashcards
Go beyond pareto optimality and add more conditions we’d like society to adhere to.
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.
Impartial spectator uses constrained optimisation to decide on the best allocation - what info is needed (2)
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.
Then what does the impartial spectator do with these 2 pieces of info?
limits her choices to allocations only on the utility possibilities frontier (UPF)
Pg 19 - demonstrate UPF graphically
Conceptually like budget constraint, feasible combinations under the line.
X axis A’s utility
Y axis B’s utility
So what does the impartial spectator choose an allocation based on?
What do they use to make this decision?
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!!!).
Cardinal utility as an example
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’)
Social welfare function
A representation of the common good based on some weighting of the utilities of the people in society
Social welfare function expression
And when is the spectator impartial?
What property exists?
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
How can the impartial spectator’s values be represented graphically
Iso-social welfare curves
Shows constant welfare levels for different combinations of utility.
Where is the spectators optimal allocation
MRS=MRT
(Slope of pareto efficient frontier=slope of iso-social welfare curve)
Bundle is best for society given the UPF
Note; spectator is imaginary. A and B may have to consult their own values
Other-regarding preferences: Let A have altruistic preferences.
How is altruism measured?
λ
0 to 0.5
0 is entirely self-regarding, 0.5 perfect altruist (value other just as much as myself)
What does A’s utility function become (pg26)
Utility of A (πA, πB)= (πA) to the 1-λ (πB) to the λ
Just a CD function with π representing payoff
How would A’s indifference curves look
Like contours on a hill - satiated preferences. Bliss point is the optimal.
Altruist ignores monotonicty, doesn’t always want the most.
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)
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.
The more altruistic (higher λ)……..
The shorter the PE curve (more they care about each other (other regarding)
How to solve this conflict of interest (3)
Social norms e.g finders keepers
Procedural rule of justice - e.g flipping a coin
Or take midpoint of the pareto efficient curve
Next topic: social welfare functions:
How to balance welfare of different members of society as policymakers
E.g people prefer micro to macro, others dont. Do we allocate extra hours for micro or macro .
Generic social welfare function notation, and what does it look like grahically? (Pg35)
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.
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)
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
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)
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
3rd SWF: Preference for equality of utility
Explanation and implication and grsaphically
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.
4th SWF: Minimax / Rawlsian
Min (u₁…,un)
Social welfare is determined by the person with the lowest utility.
Implication: radical transfers of income can be social welfare enhacing.
E.g of Minimax or Rawlsian (mathmatically correct but extreme!) (pg44)
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.
What does minimax look like on diagram
L shaped isowelfare functions.
Rawls veil of ignorance
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)
Noszick equality of opportunity social welfare criteria.
Distribution is just if the initial distribution of goods was just movement into a new distribution if voluntary by all agents.
Evaluation of Noszick
Redistribution through mandatory taxation is not “just”. Rich cannot keep what they have gained.
