Unit 5 The rules of the game: Who gets what and why
5.7 Case 2: A take-it-or-leave-it contract
Consider a different situation for Angela and Bruno. As in Case 1, Bruno owns the land that Angela works on to produce grain. But in Case 2, the government—through laws administered by courts and enforced by police—protects Angela from being forced to work, as well as Bruno’s property rights as a landowner. Furthermore, the legal system will enforce contracts between Bruno and Angela. Angela’s rights improve her alternative options: she has greater structural power in her relationship with Bruno.
We will consider two kinds of contracts that Bruno could offer to Angela: an employment contract, and a tenancy contract. In both cases, it is a take-it-or-leave-it offer: Angela can accept or reject it. She has the right to say no, and Bruno would be punished by the government if he used violence, or threats of violence, to make Angela accept his offer. Their situation is similar to the self-interested players in the ultimatum game, with Bruno as the Proposer and Angela as the Responder.
Contracts and related institutions
Contracts are written or spoken agreements that are intended to be enforced by law. For a contract to be valid, both parties have to agree voluntarily, and both are required to provide something. For example, if a homeowner makes a contract with a painter, the painter will be required to paint the home, and the homeowner will be required to pay the agreed fee in a reasonable time period (as specified in the contract).
Contracts play a central role in the economy. One of the key factors in explaining historical differences in economic growth between countries is the variation in the ability of their institutions to secure property rights and enforce contracts at a low cost. Effective contract enforcement requires a well-functioning judiciary (that is, a system of courts) that resolves cases in a reasonable time and is predictable and accessible to the public.
Units 6 and 9 discuss employment contracts, and contracts between lenders and borrowers, in more detail. They examine the important cases where contracts are incomplete: that is, the contract does not cover everything that matters to the parties involved: for example, how hard the employee works, or the risks taken by the borrower with the funds they have borrowed. Here we simplify by assuming that Angela cannot vary how hard she works in an hour.
An employment contract
In an employment contract, Bruno can specify Angela’s hours of work, and the wage (in bushels of grain) that she will be paid. This is a take-it-or-leave-it offer, so she does not have the option to ask for different terms of employment. If she rejects, she would leave Bruno’s land and find other work. Her reservation option is the utility she would receive in this alternative. Angela’s reservation option in Case 2 is much better than in Case 1: her utility from finding work elsewhere is higher than the utility she could expect if she attempted to revolt or escape.
Figure 5.13 shows Angela’s reservation indifference curve in Case 2. It is IC2, above IC1, which represents her alternative as a forced labourer.
The decisions Bruno has to make are similar to those in Case 1: how many hours Angela should work, and how much grain she should receive (as a wage, this time). The difference is that her alternative option is better. Unless he offers a contract that gives Angela at least as much utility as that indicated by IC2, she will say no.
Again, Bruno will choose an allocation on Angela’s reservation indifference curve in which Angela’s MRS on her reservation is equal to the MRT for grain production. He offers a contract that pays 23 bushels for eight hours of work. She produces 46 bushels of grain, so Bruno also gets 23 bushels—less than in Case 1, because Angela’s alternative option is better.
Bruno’s choice of hours is the same in Case 1 and Case 2, and the same as Angela’s choice as an independent farmer. This happens because, in our model, Angela’s MRS at a given level of hours is the same on every indifference curve. It would not happen if she had different preferences. But it always happens that—whether Angela or Bruno chooses the hours—they do best at a point where MRS = MRT.
The joint surplus
- gains from trade, gains from exchange
- The benefits that each party gains from a transaction compared to how they would have fared without the transaction.
- joint surplus
- The sum of the economic rents of all involved in an economic interaction.
People engage voluntarily in economic interactions when there are potential benefits for both parties, compared with their reservation options: in other words, economic rents or gains from exchange. There are rents available from an interaction between Angela and Bruno: his reservation option is zero bushels of grain, and the amount of grain she can produce by farming his land is greater than the amount that would give her reservation utility. The total amount of rent available in Figure 5.13 is the vertical distance between the feasible frontier and Angela’s reservation indifference curve. This additional grain is the potential joint surplus from the interaction.
When he offers Angela an employment contract, Bruno sets her working hours so that MRS = MRT. This is where the joint surplus (the vertical distance) is maximized: it is 23 bushels.
By setting the wage, he chooses how the joint surplus of 23 bushels will be shared between himself and Angela: that is, how much rent each will get. For example, he could choose to share it equally, taking 11.5 bushels for himself, and giving her a wage of 34.5 bushels (23 for her reservation utility, plus a rent of 11.5).
Since Angela’s rent is zero, you may wonder whether she would actually be willing to participate after all. But we know she would participate if she got very slightly more. Rather than repeatedly saying, ‘Angela’s wage is 23 bushels of grain plus a little bit more,’ we assume that she is willing to participate if she gets her reservation utility. This is a common assumption in economic models.
But Bruno is self-interested and wants to maximize his own economic rent. And he can make a take-it-or-leave-it offer—so he has all of the bargaining power. He sets the wage as low as possible, at allocation L, where Angela gets only her reservation utility. Her rent is zero, and he gets the whole of the joint surplus: a rent for himself of 23 bushels.
A tenancy contract
What happens if, rather than employing her, Bruno offers Angela a tenancy: he specifies the rent that she must pay him to use the land, and leaves it to her to decide how to use it?
In this situation, it appears that Bruno has less power over Angela. The contract does not allow him to determine how much she works. But he can still make a take-it-or-leave-it offer, and as before he will do best if he can ensure that Angela gets no more than her reservation utility.
We know from Figure 5.13 that, of all the allocations on the reservation indifference curve, Bruno gets the most grain when Angela works for eight hours. So he would like the allocation to be point L where—under an employment contract—he could receive 23 bushels of grain.
Perhaps surprisingly, he can achieve exactly the same outcome with a tenancy contract, by setting the rent payment for the land at 23 bushels. Figure 5.14 shows the situation that then faces Angela. She is free to choose her hours of work. The dotted line shows how much grain she can consume—23 bushels less than she produces, depending on the hours she chooses. The highest indifference curve she can reach is IC2, which just touches her frontier for grain consumption at point L.
Figure 5.14 Angela’s choice of hours under the tenancy contract.
The best Angela can do if she has to pay a land rent of 23 bushels is to work for eight hours, and consume 23 bushels of grain (point L). This gives her the reservation level of utility, so she will be willing to accept Bruno’s offer. (Any other choice of hours would give her less than reservation utility.) Bruno has achieved exactly the same outcome for himself, and Angela, as under the employment contract.
Rents and efficiency in Case 2
The allocation from a take-it-or-leave-it contract is L, where Angela gets 16 hours of free time and she and Bruno both get 23 bushels of grain. Angela has better outside options than in Case 1, and she is better off as a result: her working hours are the same, but her income is higher.
Bruno’s rent is lower than in Case 1, where the rules of the game allow him to use force. Although the outcome is better for Angela because she has more structural power, she still gets zero economic rent because the ability to make a take-it-or-leave-it offer gives Bruno all the bargaining power.
The Pareto criterion does not rank the outcomes in the two cases: Angela is better off at allocation L, while Bruno is better off in Case 1 at D. Both allocations are Pareto efficient. At allocation L, there is no change that could make either Bruno or Angela better off without making the other worse off. To understand why, we can use exactly the same argument that we used in the previous section for allocation D.
But if you regarded the outcome at D as unfair, you may think allocation L, with an equal distribution of grain between the two, should be preferred.
Given the institutions governing the interaction, and the Pareto efficiency of the outcome, Angela cannot negotiate to improve her situation beyond allocation L. Any alternative contract she suggested would make Bruno worse off.
Angela’s hours of free time | 16 | |
Angela’s bushels of grain | 23 | |
Bruno’s bushels of grain | 23 | |
Angela’s economic rent (bushels) | 0 | She gets the same level of utility as in the best alternative of working elsewhere |
Bruno’s economic rent (bushels) | 23 | His best alternative is 0 (if she refuses his offer) |
Figure 5.15 The outcome of Case 2.
Question 5.4 Choose the correct answer(s)
Figure 5.13 shows the outcomes when Angela is forced to work for Bruno (Case 1) and when Angela has the choice to accept or reject Bruno’s contract (Case 2). Based on this information, read the following statements and choose the correct option(s).
- Bruno’s reservation option is to receive nothing. Under the contract, Bruno receives the whole of the surplus: the amount in excess of what Angela needs to be willing to work. So this is his economic rent.
- Bruno is better off in Case 1, while Angela is better off in Case 2.
- Under the contract, Bruno offers an allocation Angela is only just willing to accept. She is indifferent between D and her reservation option, so her economic rent is zero.
- Angela’s working hours remain the same in both cases.
The rules of the game illustrated by Case 2 make Angela better off and Bruno worse off than under the forced labour rules of the game of Case 1. Of course, Angela was better off in the baseline case than in either of Case 1 or 2 because she owned the land and could consume all of the grain she produced.