Welfare In General Equilibrium - Fairness

Question 1

SWF helps us find the utility maximising option.

However what is a fair outcome

Question 2

Consider 2 cases

Answer 2

Giving all good to a single person

Giving 1/n of allocation to each of the n people

Question 3

Giving all of good to a single person - is it fair, and/or pareto efficient?

Answer 3

May be Pareto efficient, but not fair morally.

Question 4

Giving 1/n of the allocation to each of the n people - is it fair, and/or pareto efficient?

Answer 4

Fair as distribution is symmetric.
But it may not be pareto efficient.

Question 5

It may not be pareto efficient - upon what assumption is this true

Answer 5

If agents have different tastes, and so want to trade from the symmetric allocation. (E.g prefer bananas>apples, due to preference or allergies etc)

So they reach a PE allocation, but may no longer be symmetric.

Question 6

So agents with different tastes will reach Pareto efficiency by trading away from the symmetrical allocation (1/n).

Is this still considered fair now? Explain why

Answer 6

Yes, if we define fairness as equality of opportunity.

I.e starting with fair allocations (1/n), and everyone has equal opportunity to trade.

No, if only some get the chance to trade.

Question 7

If some people get chance to trade and others do not.

What may the non-traders experience?

Answer 7

Envy

Question 8

Equity definition

Answer 8

No agent prefers another bundle to his own, so no envy

Question 9

Envy

Answer 9

Preferring another agent’s bundle to their own.

Question 10

Fairness definition (2 components)

Answer 10

Pareto efficient (no one can be better off without making someone worse off)

Equitable - (no agent prefers another bundle to their own)

Question 11

How does fair allocation look like on Edgeworth box (pg52)

Answer 11

Endowment is in the middle. Both agents get equal split since fair.

Trade is at exchange 1:1 so budget constraint slope -1. (Fairness of opportunity)

Tastes differ indicated by their ICs, and trade at point X (where both IC’s and budget line meet i.e slope -1)

(Diagram is essentially market clearing diagram for Edgeworth box with prices)

Question 12

How to check if point X fair i.e would A or B want to swap?

Answer 12

Swap point is reflection of point X.

Look at annotated diagram for better understanding

But basically swap point is at a lower IC for both people, thus lower utility, and so both would rather keep their bundle, so no envy, so equitable

So the pareto efficient point X is equitable too, thus passing the criteria for FAIRNESS!

Question 13

What efficiency is always in competitive markets

Answer 13

Competitive markets are always pareto-efficient. Since consumers always choose the best affordable bundle.

But we need to show it is always equitable…

Question 14

If not equitable… A would envy B. How can this be expressed?

And how can we use this to show that competitive markets are fair?

Answer 14

(X¹a,X²a) < (X¹b,X²b)

And since A has got their best affordable bundle (since in a competitive market) , this means A could not have afforded (X¹b,X²b).

But…. It also implies B could not also afford B’s bundle (since we assume A and B have equal endowments)

Therefore a competitive equilibrium with an equal division of goods must be fair.