Question

As in the TV series ‘Lost’, your airplane crashes over the Pacific Ocean. You land on a desert island with one other passenger. A box containing 100 little bags of peanuts also washes up on the island. The peanuts are the only thing to eat.

In this economy with two people, one commodity and no production, represent the possible allocations in a diagram, and explain why every allocation is Pareto efficient. Is every allocation fair?

Answer 1

Given that the only eatable item are 100 peanuts, they can be divided between the two individuals as:

(100,0)(99,1) (98,2).......(0,100)

In this case, clearly all the allocations are Pareto optimal allocations. This is because we cannot improve the utility of one individual without decreasing the utility of another (due to a fall in the number of peanuts for another).

Such an allocation can be represented as a straight line cutting the y-axis on (0,100) and the x-axis on (100,0).

However, every allocation is not fair. The only fair allocation is where both the individuals recieve equal amounts of peanuts i.e. (50,50)