MICRO DOUBT

[bhavya jain]

what will be the answer to this question-
Suppose that Paul and David have utility functions U = 2AP + OP and U = AD + 2OD;
respectively, where AP and OP are Paul's consumptions of apples and oranges and AD and OD are
David's consumptions of apples and oranges. The total supply of apples and oranges to be divided
between them is 14 apples and 18 oranges. The "fair" allocations consist of all allocations satisfying
the following conditions.
(a) AD = AP and OD = OP .
(b) 4AP + 2OP is at least 46 and 2AD + 4OD is at least 50.
(c) 2AP + OP is at least 46 and 2AD + 2OD is at least 50.
(d) AD + OD is at least 16 and AS + OS is at least 16.
(e) 2AP + OP is at least AD + 2OD and AD + 2OD is at least 2AP + OP .

[bhavya jain]

Here the pareto optimal pts would lie on the boundary of the edgeworth box. Than how do we choose for fair allocations among the options? Is there any mathematical way to solve this one?

[RajEco]

I think the answer is b.

You can do it like this-

U1 = 2x1 + y1
U2 = x2 + 2y2


The set of fair allocations must be that each should prefer their own bundles as compared to the other person.-

For 1:  2x1 + y1 => 2x2 + y2               .....(i)
For 2:  x2 + 2y2 => x1 + 2y2

We also know that x1 + x2 = 14 and y1 +y2 = 18
Put x2 = 14- x1  and y2= 18-y2  in (i)

You will get 4x1 + 2y1 => 46
similarly you can the 2nd inequality.

[bhavya jain]

Thank you Raj,i got it.