Question

7. Pareto efficiency (Graphs or math optional with your answer)
a. Consider the following parameters for an allocation problem:
• Two goods: Apples and oranges
• Two individuals: Bob and John
Each person’s preferences are as follows:
• Bob does not have a preference for apples or oranges
• John has a preference for apples over oranges
Consider the following allocation:
• Bob owns all the apples
• John owns all the oranges
Is this allocation Pareto efficient? Explain!
b. Consider the following parameters for an allocation problem:
• One type of good: A chocolate bar
Two individuals: Bob and John
Consider their preferences:
• Bob prefers as much of the chocolate bar as possible
• John prefers as much of the chocolate bar as possible
Consider three possible allocations:
• A chocolate bar is all allocated to Bob.
• A chocolate bar is all allocated to John.
• A chocolate bar is half allocated to Bob and half
allocated to John.
Is each one of these allocations Pareto efficient? Explain!

Answer 1

A. The given allocation is not Pareto efficient. This is explained by the above graph, John prefers apples over the oranges. Bob is indifference, so his indifference curve will take the shape of well behave preferences. Since, John utility will fall when he will be given less of apples and more of oranges. As there is a point of improvement needed, so it is not the Pareto Efficient point.

B. The pareto efficient point is when chocolate bar is distributed equally among John and Bob.

When the chocolate bar is given to only one individual, then the utility of other individual is affected, so these are not the Pareto efficient point. Equal distribution leads to equal welfare for both the individuals .