Unit5_Feb2015.pdf

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5PROPERTY, CONTRACT AND POWER

HOW INSTITUTIONS INFLUENCE THE BALANCE OF POWER BETWEEN ECONOMIC ACTORS, AND HOW THIS AFFECTS THE FAIRNESS AND EFFICIENCY OF THE ALLOCATIONS THAT RESULT FROM INTERACTIONS AMONG THEM.You will learn:

How technology and biology limit what is economically feasible.

How interaction between economic actors can result in mutual gains, and also in conflicts over how the gains are distributed.

How institutions influence the relative power and other bargaining advantages of actors and can therefore shape the allocations that arise from interaction.

How the concept of Pareto efficiency can be applied to economic interactions

How we can evaluate outcomes using the concepts of fairness and Pareto efficiency.

February 2015 beta

See www.core-econ.org for the full interactive version of The Economy by The CORE Project. Guide yourself through key concepts with clickable figures, test your understanding with multiple choice

questions, look up key terms in the glossary, read full mathematical derivations in the Leibniz supplements, watch economists explain their work in Economists in Action and much more.

Mr and Mrs Andrews, Thomas Gainsborough, 1750, National Gallery

coreecon | Curriculum Open-access Resources in Economics 2

perhaps one of your distant ancestors considered shipping out with Blackbeard, or Captain Kidd, for an opportunity to earn income. If he had settled on Captain Bartholomew Roberts pirate ship The Rover, he and the other members of the crew would have been required to consent to the ships written constitution. This document (called The Rovers Articles) guaranteed, among other things, that:

Source: Leeson, P. 2007. An-Argh-Chy: The Law and Economics of Pirate Organization. Journal of Political Economy, 115, pp. 1050-94.

The Rover and its Articles were not unusual. During the heyday of European piracy in the late 17th and early 18th centuries most pirate ships had written constitutions that guaranteed even more powers to the crew members. Their captains were democratically elected, the Rank of Captain being obtained by the Suffrage of the

UNIT 5 | PROPERTY, CONTRACT AND POWER 3

Majority. Many captains were also voted out, at least one for cowardice in battle. Crews also elected the quartermaster who, when the ship was not in a battle, could countermand the captains orders.

If your ancestor had served as a lookout and had been the first to spot a ship that was later taken as a prize, he would have received as a reward the best Pair of Pistols on board, over and above his Dividend. Were he to have been seriously wounded in battle, the articles guaranteed him compensation for the injury (more for the loss of a right arm or leg than for the left). He would have worked as part of a multiracial, multiethnic crew of which probably about a quarter were of African origin, and the rest primarily of European descent, including Americans.

The result was that a pirate crew was often a close-knit group. A contemporary observer lamented that the pirates were wickedly united, and articled together. Sailors of captured merchant ships often happily joined the roguish Commonwealth of their pirate captors.

Nowhere else in the world during the late 17th and early 18th century did ordinary workers have the right to vote, or to compensation for occupational injuries, or to the protection of the kinds of checks on arbitrary authority that were taken for granted on The Rover.

Nor could workers in British textile mills and other industrial establishments claim such a large share of income. The prize-sharing system described in The Rovers articles, if faithfully implemented, would have resulted in a Gini coefficient (see Unit 1 to recall how it is calculated) for the Dividend of approximately 0.05. A Gini coefficient of 0 indicates perfect equality, and that a pie divided among two people with a Gini coefficient of 0.05 would imply that the smaller piece was 47.5%, and the larger only 52.5%. In contrast, when the Royal Navys ships Favourite and Active captured the Spanish treasure ship La Hermione, the division of the spoils among the captain, officers and crew of the two British men-of-war resulted in a Gini coefficient of 0.65: about the same as the Gini coefficient for income in some of the most unequal countries in the world today. By the standards of the day, pirates were unusually democratic and fair-minded in their dealings with each other.

Another unhappy commentator remarked: These Men whom we term the Scandal of human Nature, who were abandoned to all Vice were strictly just among themselves.


5.1 INSTITUTIONS: THE RULES OF THE GAME

the rovers articles were part of the pirate institutions that determined who did what aboard shipwhether your ancestor would serve as a lookout or as a helmsman, for exampleand who would get what as a result of what each did, for example the size of his dividend compared to that of the gunner. Other aspects of their institutions were the unwritten informal rules of appropriate behaviour that the pirates followed by custom, or to avoid condemnation by their crewmates.

In economics, institutions are the written and unwritten rules that govern both what people do when they interact in a joint project, and the distribution of the products of their joint effort. Using the terminology of game theory introduced in the previous unit, we could say that The Rovers articles were the rules of the game, much as the rules of the Ultimatum Game specify who can do what, when they can do it, and how this determines each players payoff. The institutions provided both the constraints (no drinking after 8pm unless on deck) and the incentives (the best pair of pistols for the lookout who spotted a ship that was later taken). In this unit we use the terms institutions and rules of the game interchangeably.

We have already seen that, in experiments, the rules of the game matter for how the game is played, for the size of the total available to those participating, and for how this total is divided. The institutionsthe rules of the Ultimatum Game for exampledetermine who gets to be the Proposer; how much money the Proposer has when the game starts; and the fact that the Responder can refuse any offer, resulting in no payoffs for either player. In the standard Ultimatum Game, with a Proposer and one Responder, recall that the total to be divided may be zero for both players if the Responder refuses the Proposers offer. Or, if the Proposers the offer is accepted, the Responders share is the amount that the Proposer offers to share, while the Proposer gets what remains.

We also saw that changing the rules changes the outcome: if there are two Responders in the Ultimatum Game rather than just one, the Proposer knows that at least one of the Responders is likely to accept a low offer. Each Responder knows this too. And because they cannot be sure that their rejecting a low offer will result in the proposer will be punished (the other Responder may accept) Responders tend to accept low offers they would have rejected as unfair had they been a sole Responder.This means the Proposer has more bargaining power, and gets a larger payoff as a result. We discover in Unit 7 that, when people must purchase goods from a single business organisation, they have less bargaining power than when there are many sellers.


In the Ultimatum Game (and in the economy) the division of the payoffs depends on what is called bargaining power. A partys bargaining power is the extent of their advantage when dividing the pie. The Proposer in the Ultimatum Game has the fortunate position of making the offer, and so is likely to get at least half of the pie, while the most the Responder is likely to get is half. Being the Proposer means having more bargaining power; but the power is limited. The Proposers bargaining power is limited by the need to get the Responder to accept the offer.

The Proposer could have even more than this take-it-or-leave-it power: the rules might allow a Proposer simply to divide up the pie in any way, without any role for the Responder other than to take whatever he gets (if anything). In this case the Proposer has all of the bargaining power and the Responder none. There is an experimental game like this, and it is called (you guessed it) the Dictator Game. The past, and even the present, provide many examples of economic institutions that are like the Dictator Game, in which there is no option to say no. Examples include slavery as it existed in the US prior to the end of the American Civil War in 1864, or todays remaining political dictatorships such as North Korea. Criminal organisations involved in sex trafficking and drugs would be another modern example.

Units 1 and 2 showed that the pay people receive for their work depends on the rules of the game as well as technology, and we will explore this further in subsequent units. Remember from Unit 1 that, even though the amount that people produced started to increase in Britain around the middle of the 17th century, it was not until the middle of the 19th century that a combination of labour scarcity and new institutions, such as trade unions and the extension of the vote to workers, gave wage earners the bargaining power to raise wages substantially.

Rather than the isolated student or farmer studied in Unit 3, in this unit we continue the studyintroduced in Unit 4of how people interact. But, instead of experiments or history, we will explore a model of situations describing who produces what, who gains from the process, and what they gain. Like the experiments we will see that both cooperation and conflict occur: cooperation leading to a larger pie, and conflict over how it is divided. As in the experiments, and in history, we will find that the rules matter.

To do this we will return to the model in Unit 3 of the farmer who produces a crop. Here we introduce a second person who would also like some of the harvest: the owner of the land on which the farmer works.


5.2 MUTUAL GAINS AND CONFLICT: FEASIBLE OUTCOMES

recall that the farmer in Unit 3 cultivated land; and the harvest depended on the amount of labour devoted to farming according to the production function. The farmer now has a name: meet Angela. Angela has company. The farmer in Unit 3 had no economic dealings with anyone else; Unit 3s farmer worked the land, enjoyed the remainder of the day as free time, and consumed the grain that this activity produced. In the real world few individuals work on their own and can claim everything they produce, because few people own the tools, land, or other capital goods that they require in their work.

To study what happens in a more realistic case, meet Bart. Bart, not Angela, owns the land. Bart has many parcels of land and is not interested in working the land himself. If Angela works for Bart as an employee for a wage, or by paying a fixed rent, or giving Bart a share of the crop, they will divide whatever Angela produces.

How many hours Angela works, how much she produces, and how much of this output that she and Bart each get is (using the terms introduced in Unit 4) an economic outcome, or an allocation resulting from their interaction. Recall from Unit 4 that there are two aspects to every allocation: the extent to which the possibility of mutual gains are realised (is the allocation Pareto efficient?) and the distribution of the gains from exchange (is the allocation fair?). Figure 1 shows Angela and Barts combined feasible consumption frontier. The frontier indicates how many bushels of grain Angela can produce given how much free time she takes. If Angela takes 12 hours free time and works for 12 hours then she produces ten bushels of grain. Point E is a possible outcome of the interaction between Angela and Bart. The distribution of grain at point E is such that five bushels go to Bart, and Angela retains the other five for her own consumption.

DISCUSS 1: USING INDIFFERENCE CURVES

In Figure 1, point F shows an allocation in which Angela works more and gets less, and point G shows the case in which she works more and gets more. Show how you could use Angelas indifference curves (from Unit 3) to determine which of these three points she prefers.


Total grainproduced

WhatBart gets

WhatAngela gets

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Feasible consumption frontier: Angela and Bart combined

Angelas free time Angelas work

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Figure 1. Mutual gains and conflicts over distribution.

INTERACT

Follow figures click-by-click in the full interactive version at www.core-econ.org.

To see how every economic interaction, and the distribution of the gains, among people can be analysed from two standpoints, consider an example. When you sign on to Amazon Mechanical Turk (LINK), the online marketplace for work, you may select one of more than 400,000 human intelligence tasks, or HITs. The HITs are offered by requesters, businesses and individuals looking for individuals to complete tasks such as listing product preferences, writing product descriptions, choosing preferred images, or even naming places that they honeymooned. Each HIT is described, along with the qualifications required and the payment per selected task. As a Mechanical Turk worker (a turker), you complete the HIT you have selected and are then paid.

The allocation in this case is the time you spent, your product transferred to the requester (the completion of the HIT), and your pay. Figure 2 compares the farming model with Mechanical Turk.


FARMER

EXTENT OF MUTUAL GAINS REALISED

DISTRIBUTION OF MUTUAL GAINS

TURKER

Could both Angela and Bart be better off if she worked fewer or more hours?

Given her hours of work and his ownership rights in the land is the distribution of grain and her working time fair?

Is his ownership of the land fair?

Is the pay a fair compensation for the effort and skills of the turker, given the benefit to the requester and their economic situation.

Is there a redesign of the HIT, the pay and other aspects so that both the requester and the turker could be better off?

Figure 2. Mutual gains and conflict in farming and turking.

DISCUSS 2: ALLOCATIONS YOU HAVE KNOWN

Consider a job that you, or someone you know has done and identify the allocation associated with this job and whether it was Pareto efficient and fair.

We study two aspects of the allocation resulting from Angelas interaction with Bart, in two steps. First, we will determine the set of technically feasible combinations of Angelas hours of work and the amount of grain she produces, and Angela and Barts share of grain. By technically feasible we mean outcomes that are possible if technology (the production function) and biology (Angelas need to get at least enough nutrition to carry out the work tasks of the allocation and survive) impose the only limits on what can occur. Then, in the next section, we ask how the institutions governing their interaction determine which technically feasible allocations actually occur.

How do we determine what is technically feasible? We know from the feasible consumption frontier in Unit 3 that the total amount consumed by Bart and Angela combined cannot exceed the amount produced and, as determined by the production function, this depends on the hours that Angela works. Figure 1 shows the feasible consumption frontier from Unit 3.


But, as we have just seen, there is another limit on what can happen. There are some combinations of consumption of grain and free time that would leave Angela so undernourished or overworked that she would not survive. So, for example, an outcome in which Angela works 12 hours, Bart consumes the entire amount produced and Angela consumes nothing (point H in Figure 1) is biologically infeasible.

Angelas minimum nutrition requirements depend on how much she works. In Figure 3 we show the minimum consumption that would allow Angela to survive for each amount of work that she does. If she does not work at all, then she needs two bushels to survive. If she expends energy working she needs more food; thats why the curve is higher when she has fewer hours of free time. This is the biological feasibility frontier. Points below it are biologically infeasible, while points above the feasible consumption frontier are technically infeasible.

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Angelas biological feasibility frontier

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Technically infeasible

Technically feasible set

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Figure 3. Technically feasible allocations.

Note that in the figure there is a minimum amount of work that Angela must do to survive even if she can consume the entire crop. And, given the feasible consumption frontier, there also is a maximum amount of work that would allow her barely to survive, even if she could consume everything she produced.

As we saw in Unit 2, throughout human history people crossed the survival threshold when the population outran the food supply. This is the logic of the Malthusian population trap. The productivity of labour placed a limit on how large the population could be.

In Angelas case, however, it is not only the limited productivity of her labour that might jeopardise her survival, but rather how much of what she produces is successfully claimed by Bart. To see the difference note in Figure 3 that, if Angela could consume all of what she produced, (the height of the feasible consumption


frontier) and if she could choose her hours of work, her survival would not be in jeopardy. The reason is that the biological feasibility frontier is below the feasible consumption frontier for a great many hours of work and free time that she might choose. The question of biological feasibility arises because of Barts claims on her product.

In Figure 3, the feasible solutions to the allocation problem are bounded by the feasible consumption frontier and the biological feasibility frontier (including points on the frontier). This lens-shaped shaded area gives the technically possible outcomes. We can now ask what actually happenswhich allocation occurs, and how does this depend on the institutions governing how Bart and Angela interact?

DISCUSS 3: MORE ON THE MALTHUSIAN TRAP

Go back to Unit 2 and use the two frontiers in Figure 3 in this unit to explain how the Malthusian Trap worked. Why was the feasible consumption frontier different in Unit 2, compared to Figure 3 in this unit? Hint: youll have to shift the feasible consumption frontier up and down as the amount of population per unit of land changes.

5.3 INSTITUTIONS: PROPERTY, CONTRACT AND POWER

the second step in determining the allocation when Bart and Angela interact depends on institutions. To understand how this works, we need to introduce four terms: ownership, property, contract, and power.

Ownership means the right to use and exclude others from the use of something, and the right to sell it (or to transfer these rights to others). A sign that tells you No trespassing is an expression of ownership; another expression of ownership is a copyright, which, among other things, excludes a musician from recording a tune for the purpose of selling it without compensation to the songwriter. Property is what is owned (the land, or the right to perform the song).

A contract is a legal document or understanding that specifies a set of actions that the parties to the contract are to undertake. For example, a sale contract for a car transfers ownership, meaning that the new owner can now use the car and exclude


others (including the former owner) from its use. A rental contract on an apartment does not transfer ownership (which would include the right to sell the apartment); instead it allows the tenant to engage in a limited set of uses of it including right to exclude others (including the landlord) from its use.

Under a wage labour contract, an employee transfers to the employer the right to direct him to be at work at specific times, and during those times to accept the authority of the employer over the use of his time. The employer does not own the employee as a result of this contract, unless the employee is a slave: we can say that the employer has rented the employee for particular times of the day.

Power is the ability to do and get the things we want in opposition to the intentions of others. The Proposers bargaining advantage in the Ultimatum Game is a form of power. The Responder could instead have been the lucky one, having the power associated with being Proposer, and going home with a half or more of the pie. In experiments, the assignment of the role of Proposer or Responder, and hence the distribution of bargaining power, is typically assigned by chance. But in real economies the assignment of power is definitely not random.

Those who own a factory or other business are the ones proposing the wage and the hours of work. Those seeking employment are like Responders, but with a difference: typically more than one person is seeking to land a job, so if one of them rejects the employers proposal the employer can move to the next potential worker, just as in the Ultimatum Game when there are two Responders. We will see in the next unit how the labour market, along with other institutions, gives power to employers. In Unit 7 we explain how firms selling goods sometimes have the power to propose take-it-or-leave-it offers to consumers, and in Unit 11 how the credit market gives power to banks and other lenders over people seeking mortgages and loans.

Power can be used in less subtle ways too. Perhaps the reason that Bart owns the land rather than Angela is that Angelas family was displaced from the land by force. In this case Bart gained his power to make take-it-or-leave-it offers due to his ownership of the land, because he exercised a more overt form of power: physical coercion. But, in a capitalist economy in a democratic society, most economic interactions are not conducted at the point of a gun. They are usually the result of individuals pursuing their objectives as best as they can (as in Unit 3) given the property and contracts available to them, and given the power they exercise under the institutions of that economy.


5.4 WHY PROPERTY, CONTRACT AND POWER MATTER

to see why institutions matter, we consider two extreme cases. In the first, Bart allows Angela to work the land without payment (or perhaps the land is simply free for the taking, as it was in many land abundant regions in the past, and Bart has not yet arrived to claim ownership of it). What is the resulting allocation?

Recalling the analysis from Unit 3, Angela values both the grain produced and her free time. The value that she places on free time and on grain depend on how much of each she has, because of diminishing marginal utility. We represent these values, as we did in Unit 3, as indifference curves, giving all of the combinations of grain and free time for which she does not prefer one to the other. The feasible consumption frontier is just the mirror of the production function, showing how much free time and grain are jointly feasible given the productivity of an hour of her labour.

Angela is free to choose her typical hours of work, and the decision that gives her the most preferred combination of free time and grain is point C in Figure 4 (which is similar to Figure 9 in Unit 3). Recall that the slope of the indifference curve is called the marginal rate of substitution between grain and free time and the slope of the feasible consumption frontier is the marginal rate of transformation of free time into grain. Figure 4 shows that the best Angela can do, given the limits set by the feasible consumption frontier, is to work for six hours, giving her 18 hours of free time and producing eight bushels of grain. This is the number of hours of work at which the marginal rate of substitution is equal to the marginal rate of transformation. She cannot do better than this! (If youre not sure why, go back to Unit 3 and check.)

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Angelas best feasible indifference curve

Angelas feasible consumption frontier


Slope of feasible consumption frontier

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Slope of indifference curve

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Figure 4. Farmer-owner Angelas feasible consumption frontier, best feasible indifference curve and choice of hours of work.


The resulting allocation is:

6 hours of work 18 hours of free time

8 bushels of total output

Angela consumes 8 bushels Bart consumes 0 bushels

Bart has plenty of other parcels of land, so we dont need to worry about his survival.

Now consider the other extreme. Bart has arrived heavily armed, and there is no one to protect Angela from his threats of violence. It doesnt matter whether he owns the land or not; he has the power to implement any allocation that he chooses. He is the dictator in the Dictator Game. Unlike the experimental subjects in Unit 4 he is entirely selfish. He wants only to maximise the amount of grain he can get from Angela.

But because Bart thinks about the future, he will not take so much that Angela will die. He has to impose some allocation that is biologically feasible. He has to choose some point in the purple lens-shaped technically feasible set of allocations. But which one?

Bart reasons like this:

For any number of hours that I order Angela to work, she will produce the amount determined by the feasible consumption frontier of the production function (Figure 3). But for that amount of work Ill have to give her at least the amount shown by the biological feasibility frontier. I get to keep the difference between what she produces and what I need to give her, so that I can continue to exploit her. Therefore I should find the hours of Angelas work for which the vertical distance between the feasible consumption frontier and the biological feasibility frontier is the greatest.

The amount that Bart will get if he implements this strategy is called his economic rent or his surplus, in this case meaning the amount he gets over what he would get if Angela did no work at all, which in this case is zero. Economic rent here also means the amount of the harvest that Bart requires Angela to give him, so it corresponds to the everyday meaning of rent. But remember from Unit 2 that an economic rent is any payment or other benefit that exceeds the next best option that the individual has (in this case letting the land go fallow).


Bart first considers letting Angela continue working six hours a day, as she did when she had free access to the land. At that time she produced eight bushels, as shown by Figure 5. The distance between the feasible consumption frontier and the biological feasibility frontier indicates that Bart could now take five of them without jeopardising his future opportunities to benefit from Angelas labour.

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Angelas biologicalfeasibility frontier

Feasible consumption frontier: Angela andBart combined


Figure 5. Power and plunder. The maximum technically feasible transfer from Angela to Bart.

Bart is studying Figure 5 and asks your help. You say:

Bart, your plan cannot be right. If you forced her to work a little more, you wouldnt have to let her have much more grain because the biological feasibility frontier is relatively flat at six hours of work. But the feasible consumption frontier is steep, so while youd have to let her have a little more, shed produce a lot more if you imposed longer hours.

You add:

You have to work out, for any length of working day that you impose, how much grain you will get while making sure that Angela survives to be exploited next year.


You would present him with an updated version of Figure 5, which indicates that the vertical distance between the feasible consumption frontier and the biological feasibility frontier is the greatest when Angela works for 11 hours. If Bart commands Angela to work for 11 hours then she will produce 10 bushels and Bart will get to keep six of them for himself. We can use Figure 5 to find out how many bushels of grain Bart will get for any technically feasible allocation. The grey arrows in the figure show that the amount Bart gets falls as when Angela works for more or less than 11 hours. If we join up the points then we can see that the amount Bart gets is hump-shaped, and peaks at 11 hours of work and 13 hours of free time.

How can you calculate Angelas hours of work to give Bart the greatest amount of grain, consistent with Angela surviving? Find out how to do this mathematically in EINSTEIN 1.

EINSTEIN 1

How can you figure out Angelas hours of work that gave Bart the greatest amount of grain, consistent with Angela surviving? To the right of 13 hours (more free time for Angela), the biological feasibility frontier is flatter than the feasible consumption frontier. That means the marginal rate of transformation of hours of labour into output is greater than the marginal rate of substitution of hours of labour into subsistence nutrition requirements. So moving to the left (Angela working more) results in an increase in production (her marginal product) that is greater than the increase in her subsistence needs. So Angela working more increases Barts surplus, which you recall is his economic rent. To the left of 13 hours of free time (Angela working more), the reverse is true. Barts surplus is greatest at the hours of work where the slopes of the two frontiers are equal. That is:

Marginal rate of transformation of work hours into grain output

=Marginal rate of substitution of work hours into subsistence requirements


5.5 VOLUNTARY EXCHANGE: HOW THE MUTUAL GAINS ARE DIVIDED

we check back on Angela and Bart much later, and immediately notice that Bart is no longer armed. He explains that this is no longer needed, as there now is a government with laws administered by courts, and professional enforcers called police. Bart now owns the land, and Angela must have permission to use his property. He can offer a contract in which she can farm the land. In return she gives him part of the harvest. Alternatively, she can refuse the offer.

It used to be a matter of power, Bart says, but now both Angela and I have property rights: I own the land, and she owns her labour.

The new rules of the game, he adds, mean that I can no longer force Angela to work. She has to agree to the allocation that I propose.

And if she doesnt?

There is no deal. She doesnt work on my land, I get nothing, and she gets barely enough to survive from the government.

Just like the Ultimatum Game, you think.

So you and Angela have the same amount of power? you ask.

Certainly not! Bart replies, surprised, I am the one who gets to make a take-it-or-leave-it offer. I am like the Proposer in the Ultimatum Game; except that this is no game. If she refuses she goes hungry, and I have a plenty of grain from other farmers.

But you get zero if she refuses?

That never happens, Bart assures you. Bart knows that if he makes an offer that is just a tiny bit better for Angela than not working at all and getting subsistence rations from the government, she will accept. So now he asks you a question similar to the one he had asked earlier, and which you had answered by showing him the biological feasibility frontier. Now the limitation is not that the offer is such that Angela survives, but rather that she agrees.

Over years of interacting with Angela and people like her he knows that she values her free time, so the more hours he offers her to work, the more he is going to have to pay. Bart turns to you again, and you explain:


Why dont you just look at Angelas indifference curve that passes through the point where she does not work at all and barely survives? That will tell you how much is the least you can pay her for each of the hours of free time she would give up to work for you.

Figure 6 shows this curve. Point O, the allocation in which Angela does no work and gets only survival rations from the government (or from her family) is called her reservation option: if she refuses Barts offer she has this option in reserve. The curve giving all of the allocations that are just as highly valued by Angela as the reservation option is called her reservation indifference curve: below or to the left of the reservation indifference curve she is worse off than in her reservation option. Above and to the right she is better off.

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O: Angelas reservation option

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Economically feasible set


Figure 6. Economically feasible allocations when exchange is voluntary.

The points in the area bounded by the reservation indifference curve and the feasible consumption frontier (including the points on the frontiers) is the set of all economically feasible allocations, once the principle has been accepted that in order for it to be implemented, Angela has to agree to the proposal that Bart makes. Bart thanks you for this handy new tool for figuring out the most he can get from Angela. You remind him that what you showed him is exactly the same as the reservation indifference curve of the farmer in Unit 3.

The biological feasibility frontier and the reservation indifference curve have a common point (point O): Angela does no work and gets subsistence rations from the government. Other than that the two curves differ: the reservation indifference curve is uniformly above the biological feasibility frontier. The reason, you explain to Bart, is that however hard she works along that frontier, she barely survives; and the more she works the less free time she has, so the unhappier she is. Along the reservation


indifference curve, by contrast, she is just as well off as at her reservation option, meaning that being able to keep more of the grain that she produces compensates exactly for her lost free time.

DISCUSS 4: BIOLOGICAL FEASIBILITY

Explain why a point on the biological feasibility frontier is higher (more grain is required) when Angela has fewer hours of free time. Why does it also get steeper as she works more? Why is the shape of the two frontiers different for all except one amount of Angelas free time?

We can see that both Angela and Bart may benefit if a deal can be made. The reason is that their exchangeallowing her to use his land (that is, not using his property right to exclude her) in return for her sharing some of what she producesmakes it possible for both to be better off than if no deal had been struck. As long as Bart gets some of the crop he will do better than if there is no deal. If there is no deal his land lies fallow and he gets nothing, making his reservation option zero (as we have seen). As long as Angelas share makes her better off than she would have been if she took her reservation option, taking account of her work hours, she will be also benefit. This potential for mutual gain is why their exchange need not take place at the point of a gun, but can be motivated by the desire of both to be better off. All of the economically feasible allocations that represent mutual gains are shaded dark purple in Figure 6.

Of course the fact that mutual gains are possible does not mean that both Angela and Bart will benefit. It all depends on the institutions in force. If Bart has the power to make a take-it-or-leave-it offer, subject only to Angelas agreement, then he can capture the entire surplus, leaving none for Angela. Bart knows this already.

Once you have explained the reservation indifference curve, Bart knows the take-it-or-leave-it offer that he should make. For every possible level of work hours he might require, he looks at the vertical distance between the reservation indifference curve and the feasible consumption frontier, and finds the hours for which this distance is the greatest. He uses a modified version of Figure 5, taking into account that Angela has to agree to any proposal. In the economically feasible case Angela gets just enough grain to compensate for the value of her foregone free time due to working. Only Bart benefits from the exchange.



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Figure 7. Barts take-it-or-leave-it proposal when exchange is voluntary.

Figure 7 shows that Bart should make an offer where Angela works for nine hours and is allowed to keep whatever is left after Bart has taken five-and-a-half bushels of grain. We can see that the amount of grain Bart gets falls as Angela works more or less than nine hours. Again, if we join up the points we can see that the amount Bart gets is hump-shaped. The peak is lower than when Bart has the power to order Angela to work, because he needs Angela to agree to the proposal.


DISCUSS 5: TAKE IT OR LEAVE IT

Why is it Bart, and not Angela who is in a position to make a take-it-or-leave-it offer? Are there conditions under which the farmer, not the landowner, might have this power?

Suppose that Bart could not force Angela to work a particular number of hours (because, for example, he lives far away, and cannot observe what she is doing). But he can charge rent of a number of bushels for her use of the land. What rent will he charge?

TEST YOUR UNDERSTANDING

Test yourself using multiple choice questions in the full interactive version at www.core-econ.org.

Bart will choose the rent that maximises the amount of grain he gets, while taking into account the fact that Angela will not accept any offer below her reservation indifference curve. The maximum feasible rent is therefore five-and-a-half bushels of grain, which is equal to the maximum amount of grain Bart can get when exchange is voluntary (see Figure 7). The imposition of maximum rent by Bart is shown by the downward shift of the feasible consumption frontier in Figure 8. Point A, where Angela is working for nine hours, is the best that she can do when Bart is charging maximum rent. At this point she is on her reservation indifference curve, so is indifferent between accepting the offer and refusing the offer and living on government rations.We will suppose that Bart charges a tiny bit less rent than this, so she accepts.



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Angelas feasible consumption frontieraer paying maximum rent

Barts maximumeconomically

feasible rent = 5.5

Point A is the best that Angela can do when Bart charges the maximum rent

O: Angelas reservation option

150 24

Figure 8. Barts maximum feasible rent, and the best Angela can do when he charges it.

DISCUSS 6: ANGELAS HOURS OF WORK

In Figure 8, we show that the best Angela can do when Bart imposes maximum rent is to work for nine hours. Would she be willing to work any other number of hours when maximum rent is charged?

5.6 SHARING THE MUTUAL GAINS FROM EXCHANGE

bart thinks that the new rules, requiring him to make an offer that Angela will not refuse, are not so bad after all. Angela too is better off than she had been when she had barely enough to survive. The reason is that, under the old rules, she had no choice but to accept whatever allocation proposal Bart imposed, even if he made her worse off than when she did no work at all.


But she is not pleased, because Bart is capturing all of the gains from exchange. She would like to benefit too. Although it stretches the meaning of mutual in this case, as a matter of definition we say that there are mutual gains from exchange, because Bart benefits and Angela is no worse off.

It does not feel very mutual to her. She and her fellow farm workers agitate for a new law that limits the work time that can be imposed to four hours a day, while requiring that total pay is at least three bushels. They threaten to not work at all unless the law is passed.

Bart says that they are bluffing. Angela makes it clear they are not.

Bart, we would be no worse off at our reservation option than under your contract, working the hours and receiving the small fraction of the harvest that you impose!

They campaign, inspired by the slogan of the early American labour movement: Eight hours for sleep, eight hours for play, eight hours for work, eight dollars a day! They win, and the new law imposes even more leisure time, and limits her working day to four hours.

How did things work out?

Angela was working for nine hours and getting 3.75 bushels of grain before the new law (when Bart was charging maximum rent); see point A in Figure 9. The new law implements the allocation at point D: Angela and her friends now work four hours, getting 20 hours of free time as a result and three bushels. Although they receive less grain, they have five more hours of free time, which, given their preferences, more than compensates for the lower amount of grain. You can see that Angela is better off at D than at A (Angelas indifference curve through point D is above and to the right of her indifference curve through point A).

Point B is the Pareto efficient outcome (better than D for Angela; not worse than D for Bart)

Point D is a Pareto inefficient outcome (resulting from the new legislation)

Vertical distance between IC1 and IC2 is a measure of how much better off Angela is, measured in grain, under the new legislation

3 = whatBart gets

3 = whatAngela gets

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IC3IC2IC1

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Figure 9. Angelas revenge. The effect of legislation.


What did the law change? Angela and her friends are now benefitting from the exchange. They are better off under the new rules of the game than they had been before. More important: they are better off than they would be if they could not work for Bart. They are better off than they would be with their reservation option , which means they are now receiving an economic rent. Note that we are using the term rent in the way we defined it above, and in Unit 2. Unlike when we used the term to refer to Bart, its use here is quite different from the everyday use of the word. Bart is not paying Angela a rent in the usual sense of the word (or any other sense).The size of Angelas rent is how much better off she is at the new situation than at her reservation option. One measure of how much better off she is, measured in grain, is the vertical distance between her reservation indifference curve and the indifference curve she is able to achieve under the new legislation. In Figure 9, this is the vertical distance between indifference curves IC1 and IC2.

Another way to describe Angelas part of the gains from exchange is that its the maximum amount of grain per year that Angela would give up to live under the new law rather than in the situation before the law was passed. Or, because Angela is obviously political, it is the amount she would be willing to pay (lobbying the legislature, contributing to election campaigns and the like) so that the law passed.

Bart is not happy. You try to cheer him up:

Next time they threaten to quit working, saying they have nothing to lose, they really will be bluffing. They have their economic rent to lose. Remember, Bart, Angelas economic rent is for her the opportunity cost of telling you to get lost: now she will not be tempted to walk away.

Bart can see that this rent will be useful later. We will return to it in the next unit, and later in the course.

5.7 EFFICIENT AND FAIR ALLOCATIONS

angela and her friends are pleased with their success. She asks what you think of the new policy. This time, you say:

Congratulations, but your policy is far from the best you could do.

You lay out Plan B.

Under your new law, Bart is getting three bushels and cannot make you work more than four hours.


Why dont you offer to pay him the three bushels that he is now getting, in exchange for agreeing to let you keep anything you produce above the three bushels you have given to him? Then you get to choose how many hours you work.

You can now redraw Figure 9, explaining that, after paying Bart three bushels in rent, Angelas feasible consumption frontier is just like the earlier feasible consumption frontier for the two togetherexcept that it is shifted down by the amount of the rent, which in this case is equal to three bushels. Now, because she has already paid Bart, it refers to her feasible consumption only.

You show her the new figure with the downshifted feasible consumption frontier passing through point D. Under Plan B, you can have any point on the frontier, you explain.

Although Angela values having more free time, she can see that, because the feasible consumption frontier is steeper than her indifference curve at point D, it would not make sense to work less; the increase in free time would be more than offset by the reduction in grain she would get. But if she works longer hours she can get to a higher indifference curve and be better off.

What is the best you can do, given what is now feasible, as indicated by the feasible consumption frontier after paying rent to Bart? you ask Angela. She now understands how the figure works and puts her finger on point B in Figure 9.

Seeing that Bart will otherwise have to learn to live with point D, changing to B would be no worse for Bart, and if she conceded just a little more rent than three bushels, then it would be better for both of them.

Before the legislation to limit working hours Angela considered the distribution to be unfair, but this outcome did have a desirable property: there was no feasible alternative allocation in which both parties would have been better off. Recall from Unit 4 that an allocation that has this property is termed Pareto efficient. The outcome was Pareto efficient because Bart alone was benefitting from the exchange and, as a result, he made sure to benefit as much as he could.

Making Angela better off (if she worked a different number of hours, or Bart allowed her more of the harvest) would make Bart worse off.

Is the new law Pareto efficient? No, because Angela could be made better off without making Bart worse off: point D is Pareto inefficient. Point B, on the other hand, like point A is a Pareto efficient outcome. Any change from point B that makes Bart better offAngela working the same hours and keeping less of the grain, or keeping the same amount and working more hours, for examplewould make Angela worse off. And correspondingly, anything that would make Angela better off would make Bart worse off.


DISCUSS 7: PARETO EFFICIENCY

Test Pareto efficiency: indicate two points in Figure 9 at which Bart would be better off than at point B, and using Angelas indifference curves show why Angela would be worse off as a result. Do the same for two changes that would make Angela better off and show that they would make Bart worse off.

We have already seen another Pareto efficient outcome. It was the initial allocation that resulted when Angela had free use of the land. Go back to Figure 4. When Angela worked six hours, and received the whole harvest of eight bushels she was doing the best she could under the constraints of the technology available (and the free use of the land). Bart, however, got nothing. Is there an allocation that could have made both Bart and Angela better off than under this outcome (or made one of them better off and the other not less well off)? The answer is no, because Angela had already chosen the allocation that she preferred, so any change (including giving Bart some of the harvest) would make her worse off. So the outcome was Pareto efficient. This is of course just the mirror image of the Pareto efficient outcome that resulted when Bart had enough bargaining power to choose the allocation, subject only to the limitation that Angela had to agree to it.

You can see that Pareto efficiency is only distantly related to the usual way that the term efficiency is used. When we talk of a way of doing something as efficient it means a reasonable or sensible means to some end. Something can be Pareto efficient, however, and seem far from reasonable or sensible. If Angela and Bart were dividing the pie discussed in Unit 1, then any way the pie was divided would be Pareto efficient, including Angela getting none of it, or all of it. The only thing that Pareto efficiency requires is that they not simply throw away some of the pie.

Figure 10 shows the three Pareto efficient points that we have discussed so far. What they have in common is that at each allocation one of Angelas indifference curves is tangent to her feasible consumption frontier, meaning that her marginal rate of substitution (the slope of her indifference curve) is equal to her marginal rate of transformation of free time into grain (the slope of her feasible consumption frontier after the payment of rent to Bart). They differ, of course, in how well-off each of them are. At point A, Bart alone experiences gains from exchange (compared to the reservation option in which Angela does not work his land at all). At point C the opposite is true and Angela is experiencing all the gains from trade. At point B, both Angela and Bart experience gains from exchange. LEIBNIZ 7 shows you how to find Pareto efficient allocations using calculus, when the utility function and the feasible consumption frontier are expressed algebraically.



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At point C, Angela experiencesall the gains from trade

Angelas best feasible indifference curve when she pays no rent

AO: Angelas reservation option

Angelas reservationindifference curve

8

Figure 10. Pareto efficient allocations with differing distributions of the gains from exchange.

LEIBNIZ

For mathematical derivations of key concepts, download the Leibniz boxes from www.core-econ.org.

Outcomes in which gains from exchange are shared rather than monopolised by one or the other party seem fairer; and being win-win they are easier to implement, either by agreements of the kind that Angela has proposed to Bart, or by government policy. The move from point A (at which Bart had all the bargaining power and alone experienced gains from exchange) to point B, with shared gains, consists of two distinct steps. The first is from A to D, the outcome imposed by Angelas legislation. This was definitely not win-win: Bart lost because his rent at D is less than the maximum feasible rent that he got at A. Angela benefitted.

Once at the legislated outcome, there were many win-win possibilities open to them. They are shown in the purple shaded area in Figure 9. Win-win alternatives to the allocation at D are possible by definition, because D was not Pareto efficient.

Bart is open to a deal, but is not happy with Angelas proposal.


I am no better off under your proposed Plan B than I would be just living under that legislation that you passed, he says.

You can help if you persuade Bart to accept the fact that, as a result of the legislation, Angela now has bargaining power, too.

What has happened because of the legislation is that Angelas reservation option is no longer 24 hours of free time at survival rations. Her reservation option is the legislated allocation at point D.

Bart already knows he has to learn to live with Angelas new bargaining power. He makes a counter offer. Ill let you work the land for as many hours as you choose if you pay me four and a half bushels. They shake hands.

Because Angela is free to choose her work hours, subject only to paying Bart the rent of four and a half bushels, she will seek to find the highest indifference curve that she can attain, resulting in an allocation, point B in Figure 9, that is Pareto efficient.

DISCUSS 8: NEGOTIATING A PARETO EFFICIENT ALLOCATION

Explain, using Figure 9, why point B is better for both Bart and Angela than point D. Explain how you know that B is Pareto efficient.

There are many other such Pareto efficient outcomes with shared gains compared to the initial reservation options prior to the legislation; some favour Angela, some favour Bart. In Figure 11 we compare the allocations A, B, C, and D in Figures 9 and 10.


POINT B

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GAINS SHARED (COMPARED TO POINT O)

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POINT D

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Angela passes a labour law

Figure 11. Pareto efficiency and shared gains from exchange as aspects of economic outcomes, and the institutions that support them.

There are three lessons here, to which we will return when we discuss policies to try to implement Pareto efficient outcomes with distributions that are considered to be fair by most people. The first is that when one person or group has power to dictate the allocation, subject only to not making the other party worse off than in their reservation option, the powerful party will capture all of the gains from exchange. They will implement an allocation that makes their gains as large as possible, subject only to the other party not being worse off than with no exchange at all. If they have done this, then there cannot be any way to make either of them better off without making the other worse off. So the result must be Pareto efficient.

The second lesson is that those who consider their treatment unfair often have some power to influence the outcome through legislation and other political means, and the result may be a more fair distribution, but one that is not necessarily Pareto efficient. So societies may face trade-offs between Pareto efficient but unfair outcomes, and fair but Pareto inefficient outcomes.

Finally, if we have institutions under which people can jointly deliberate, agree on, and enforce alternative allocations then there may be outcomes that make both parties better off, and that are also more fair than the status quo. Angela and Bart managed this. Starting from a very uneven distribution of the benefits of exchange (only Bart benefitted) legislation was passed increasing Angelas bargaining power, and then the two agreed on a win-win outcome that was Pareto efficient. In this case a society need not accept the trade-off between Pareto efficiency and fairness.


DISCUSS 9: LOVE CONQUERS ALL

Suppose (improbably) that Angela and Bart fall in love and marry; but as a thoroughly modern couple they decide to keep their economic matters separate, at least as far as bookkeeping is concerned. As before, Bart cannot work on the land.

1. Which allocation do you think they would implement?

2. Does evidence from the economic experiments in the previous unit give you any clues?

5.8 CONCLUSION

when the pirates on Captain Roberts The Rover agreed unanimously to a constitution, they accepted a set of rules of the gamethat is institutionsthat would determine who did what on the ship and how the spoils were to be divided. The same is true of the terms proposed by requesters, and agreed to by the turkers, who proofread texts or evaluate the attractiveness of images in the online marketplace for work.

When two or more people voluntarily come together to undertake a common project, whether pirates, turkers, or Angela farming Barts land when Barts proposed terms were at least minimally acceptable to Angela, their cooperation results in the possibility of mutual gains from exchange. They are potentially both better off having engaged in a common project than they would have been otherwise, when they gain only their reservation utility.

The same is true when people directly exchange, or buy and sell, goods for money. If you have more apples than you can consume, and your neighbour has an abundance of pears, the same logic applies. The apples are worth less to you than they are to your neighbour, and the pears are worth more to you. So there must be some rate of exchange under which you are happy to exchange some apples for some pears.

The same logic applies to apples and pears, land and labour, or the requesters need for a human intelligence task to be completed by would-be turkers with time on their hands. When people with differing needs, property and capacities meet, there is an opportunity to generate mutual gains, so that all parties can potentially benefit. That


is why people often like to come together in markets, online exchanges and pirate ships. The mutual gains are the pie. For the most part, however, people engage in these projects not for the pie, but for their slice.

Whether they are able to mutually benefit depends on technology and biology. If Barts land had been so unproductive that no amount of labour would have produced enough to compensate Angela for her time, then there would have been no deal that they could strike. Mechanical Turk is possible because people around the world (many of them with abundant free time and little income) can work on the projects of comparatively rich, but busy, requesters in the US.

Among the set of allocations that are technically feasible, the ones that we observe through history are largely the result of the institutions, including property rights and bargaining power, that were (or are) present in the economy. The institutions answer two questions. The first is: who does what, so that mutual gains are possible? The second is about distribution: who gets what, or how are the mutual gains distributed among the parties to the exchange? A summary of these points appears in Figure 12.

Allocation (outcome): who does what & who gets what

Bargaining power

Reservation options

Economically feasible allocations

Technically feasible allocations

PREFERENCES

INSTITUTIONS

BIOLOGY

TECHNOLOGY

Figure 12. Institutions, mutually beneficial interactions and distribution.

Aside from the government and families, the most important institutions of a modern economy are markets and firms. In the next unit, we study how firms (business organisations) address questions of allocation. We need to know how they work, and how well they work.

In the units that follow we study markets. Some have single firms selling to many buyers, others have large number of buyers and sellers. We investigate how they may implement allocations that allow mutual gains from exchange, and how they influence how those gains are distributed among buyers, sellers, and others. We


also study the combination of markets and firms that make up the modern capitalist economy, and ask how successfully this set of institutions allows for Pareto efficient allocations and fair distributions. In later chapters we will ask what we can do to make the results more nearly Pareto efficientand more fair.

UNIT 5 KEY POINTS

1. There are technological and biological limits on the economic outcomes that can occur.

2. Every economic interaction results in an outcome (allocation) with two aspects: the extent to which potential mutual gains are full exploited, and the distribution of these gains compared to a situation in which the interaction had not occurred.

3. Private ownership (property) is the right to use and to exclude others from the use of something, including the right to sell it.

4. For any particular interaction, a persons reservation option is what that person would get if the interaction did not take place.

5. Those with better reservation options and those with more power typically get more in the resulting allocation.

6. Institutions, including the ownership of private property and government, are an important influence on both the efficiency and the fairness of allocations.

7. When an allocation is not Pareto efficient, it may be possible either for government policies or private bargaining to introduce win-win policies that improve the wellbeing of most parties.


UNIT 5: READ MORE

INTRODUCTION

The law and economics of piracyModern-day pirates in the Indian Ocean also use constitutions, though much less equitable than that of The Rover: LINK.The Economist. 2013. More sophisticated than you thought, 13 October.

To find out more about 17th and 18th century pirate captains of European descent like Roberts, read Leesons article (and book): LINK.Leeson, P. 2007. An-Argh-Chy: The Law and Economics of Pirate Organization. Journal of Political Economy, 115, pp. 1050-94.

The Invisible Hook: The Hidden Economics of Pirates. Princeton: Princeton University Press.

At the same time Chinese pirates, including the famous woman pirate commander Ching Shih, operated on a grand scale, and also used constitutions.Murray, D. 1987. Pirates of the South China Coast, 1790-1810. Stanford, California: Stanford University Press.

MORE

Institutions and their long-term effectsDell, M. 2010. The Persistent Effect of Perus Mining Mita. Econometrica, 78, pp. 1863-903.

Institutions in the New World: LINKSokoloff, K. and Engerman, S. 2000. Institutions, Factor Endowments, and Paths of Development in the New World. Journal of Economic Perspectives, 14(3), pp. 217-32.

Institutions and the path to the modern economyGreif, A. 2006. Institutions and the Path to the Modern Economy: Lessons from Medieval Trade. Cambridge: Cambridge University Press.

The birth of impersonal exchange: LINKGreif, A, 2006. The birth of Impersonal Exchange: the Community Responsibility System and Impartial Justice, Journal of Economic Perspectives 20(2). pp. 221-236.

Property RightsAlchian, A. 1987. Property Rights. J. Eatwell, M. Millgate and P. Millgate, The New Palgrave. London: Macmillan, pp. 1031-34.


This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-nd/4.0/ or send a letter to Creative Commons, 444 Castro Street, Suite 900, Mountain View, California, 94041, USA.

Power as an economic conceptBowles, S and Gintis, H. 2007. Power. S. Durlauf and L. Blume, The New Palgrave Encyclopedia of Economics. London: McMillan.

Division of the pie: A historical case Hobsbawm, E. and Rude, G. 1968. Captain Swing. New York: Pantheon.

The effects of labour conf lict in producing defective tyresKrueger, A. and Mas, A. 2004. Strikes, Scabs, and Tread Separation: Labor Strife and the Production of Defective Bridgestone/Firestone Tires. Journal of Political Economy, 112(2), pp. 253-89.

Ravenswood: The steelworkers victoryJuravich, T. and Bronfenbrenner, K. 1999. Ravenswood: The Steelworkers Victory and the Revival of American Labor. Ithaca: Cornell University Press.

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