**Unit 5** The rules of the game: Who gets what and why

## 5.9 Case 3 continued: Negotiating to a Pareto-efficient sharing of the surplus

Under the new law that changes workers’ rights, Angela’s reservation position has improved, and Bruno offers her contract N on her new reservation indifference curve IC_{N} (Figure 5.18 below). But Angela has an opportunity to do better still, because allocation N is not Pareto efficient. This doesn’t mean it would be better to go back to the Pareto efficient contract L—that would make her worse off. It means that there are other allocations that both parties would prefer to N. Both Angela and Bruno could be better off if they could negotiate successfully.

- Pareto improvement
- A change that benefits at least one person without making anyone else worse off.
*See also: Pareto dominant, Pareto criterion.*

Figure 5.18 shows that in contract N, where Angela has more free time than in Cases 1 and 2, her indifference curve is flatter and the feasible frontier is steeper: MRS at N < MRT at M. Her marginal rate of substitution between grain and free time is lower than the rate at which she can transform free time into grain. And whenever MRS and MRT are unequal, there is the potential for a **Pareto improvement**. In particular, when MRS < MRT, Angela could transform some of her free time into grain, producing more grain than she would need to compensate her for the loss of free time (in other words, to keep her on IC_{N}). So if her free time were reduced, the extra grain could make both Angela and Bruno better off.

Within the lens-shaped area between IC_{N} and the feasible frontier, the surplus is maximized where Angela has 16 hours of free time. Angela’s indifference curves are parallel, so at 16 hours the MRS on every indifference curve is equal to the MRT.

Just as before in Cases 1 and 2, an allocation where MRS = MRT is Pareto efficient.

### Negotiation

We will suppose that the new law allows a longer work day if both parties voluntarily agree, provided that the fallback position is a four and a half hour day if no agreement is reached.

Bruno has offered contract N. Angela could respond with a counter-offer: she could suggest a contract with eight hours of work (16 hours of free time) to increase the surplus, and a way of splitting the surplus that makes them better off than at N.

Figure 5.19 shows what might happen.

Through negotiation, Angela and Bruno agree to an allocation between points P and R, with a wage of 32 bushels for eight hours of work. Compared with N, they are both better off. This is the outcome in Case 3.

Since there is scope to go back and forth in the negotiation, it is not the only possible outcome. But we can say that they are likely to reach an agreement on PR with a wage above 30 and below 34.

The change from the outcome in Case 2 to the final one in Case 3 is summarized in Figure 5.20. It consists of two distinct steps:

- From L to N, the outcome is imposed by new legislation. This is definitely not win-win: Bruno loses because he gets less grain at N than at L. Angela benefits from greater structural power, raising her reservation position.
- But once at the legislated outcome N, they both have bargaining power because N is not Pareto efficient. They voluntarily agree to a Pareto-efficient contract with longer working hours. This change is win-win. They share the gains from the negotiation.

Case 2: Contract L | Case 3: Contract N | Case 3: Outcome | |
---|---|---|---|

Angela’s free time | 16 hours | 19.5 hours | 16 hours |

Angela’s income | 23 bushels | 23 bushels | 32 bushels |

Bruno’s income | 23 bushels | 12 bushels | 14 bushels |

Angela’s change in utility | +7 bushels | +2 bushels | |

Bruno’s change in utility | –11 bushels | +2 bushels |

### Pareto efficiency, and the Pareto efficiency curve

We now know that there are many Pareto-efficient allocations that could result from the interaction between Angela and Bruno, including all the outcomes from Cases 1, 2, and 3.

To be Pareto efficient, an allocation must have two important properties:

- The MRT on the feasible frontier is equal to the MRS on Angela’s indifference curve.
- No grain is wasted: all the grain produced is consumed by Angela or Bruno.

We have demonstrated the first property by arguing that if MRS is not equal to MRT, a Pareto improvement is possible if Angela’s hours of work are changed, while if MRS = MRT, no Pareto improvement is available. The diagrams show that when MRS ≠ MRT, the surplus can be increased; if MRS = MRT, it cannot.

The second property, which holds at all the allocations we have considered, means that no Pareto improvement can be achieved simply by changing the amounts of grain they each consume. If it holds, then if one consumed more, the other would get less. If it doesn’t hold, some grain is not being consumed, and consuming it would make at least one of them better off.

You may also hear it called the contract curve, even in situations where there is no contract, which is why we prefer the more descriptive term Pareto efficiency curve.

- Pareto efficiency curve
- The set of all allocations that are Pareto efficient. The Pareto efficiency curve is sometimes called the ‘contract curve’, even though it is not necessary for any contract to be involved.
*See also: Pareto efficiency.*

The set of all Pareto-efficient allocations is called the **Pareto efficiency curve**. In our model, it is the set of allocations with 16 hours of free time, shown in Figure 5.21. It is a vertical straight line, because of our assumption that Angela’s indifference curves are parallel; if we had made a different assumption about her preferences, the Pareto efficiency curve would have had a different shape.

At any allocation on this line, such as allocation S, the MRS (the slope of IC_{S}) is equal to the MRS at R. At S, Angela gets 38 bushels and Bruno gets eight bushels; different allocations on the line correspond to different ways of splitting the grain between them.

**Question 5.6** Choose the correct answer(s)

Figure 5.19 shows the outcome from the interaction between Angela and Bruno.

Read the following statements and choose the correct option(s).

- All points on the Pareto efficiency curve (allocations at 16 hours of free time) are Pareto efficient, so none of them is Pareto-dominated. (Comparing A and L, Bruno prefers L and Angela prefers A.)
- The Pareto efficiency curve, by definition, joins all the points where MRS = MRT (all allocations at 16 hours of free time).
- All the points on AL are Pareto efficient. It does not make any sense to say that one point on AL is more efficient than another.
- All the points on the Pareto efficiency curve are Pareto efficient, but Bruno and Angela are not indifferent. Some points (like A) are better for Angela, while others (like L) are better for Bruno.

**Question 5.7** Choose the correct answer(s)

In Figure 5.19, suppose that Angela and Bruno are at allocation N, where she receives 23 bushels of grain for four and a half hours of work.

From the figure, we can conclude that:

- Along MN, MRS < MRT. So MN is not Pareto efficient—there are other allocations where both would be better off.
- In area RPN, Angela is on a higher indifference curve than IC
_{N}, and Bruno has more grain than MN, so both are better off. - Points on PL are Pareto efficient, but below P, Angela is on a lower indifference curve than at N, so she would be worse off.
- Points on RP are all Pareto efficient, but Bruno and Angela are not indifferent. He prefers points nearer to P, and she prefers points nearer to R.