Question

Jane has 3 liters of soft drinks and 9 sandwiches. Bob, on the other hand, has 8 liters of soft drinks and 4 sandwiches. With these endowments, Jane’s marginal rate of substitution (MRS) of soft drinks for sandwiches is 4 and Bob’s MRS is equal to 2. Draw an Edgeworth box diagram to show whether this allocation of resources is efficient. If it is, explain why. If it is not, what exchanges will make both parties better off?

Short answer

The Edgeworth box diagram is as given below:

The current allocation is not efficient since Jane’s MRS is not equal to Bob’s MRS. They both can make it efficient through trading so that one is made better off without making the other worse off.

Step-by-step solution

Reason for inefficient allocation 

Since, therefore, the allocation is inefficient. One can derive the indifference curve of Jane and bob through their MRS given as 4 and 2, respectively. Based on these, one can plot an Edgeworth box diagram.

The initial allocation is at point A, where Jane is willing to trade 4 sandwiches for 1 drink, and Bob is willing to trade 2 sandwiches for 1 drink.

Step 2. Exchange that makes both parties better off

In the diagram given above, any trade between Jane and Bob that stays inside the area formed by the ICs will make Jane and Bob better off. For example, suppose at point C that if Jane gives Bob 3 sandwiches, she will be better off since she was willing to trade 4 sandwiches, and Bob will be better off since he expected 2 sandwiches but received 3. Therefore both are better off.