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

5.14 Application: Conflicts of interest and bargaining over wages, pollution, and jobs

Bruno and Angela have conflicting interests over hours of work and the distribution of grain. We can apply a similar model to cases of conflicting interests about the environment. Conflicts arise because environmental quality is never the same for everyone. When greenhouse gases or pollutants degrade an environment, some people suffer more than others, depending on their location and income, while some benefit from the economic activity that causes the damage.

external effect, externality
An external effect occurs when a person’s action confers a benefit or imposes a cost on others and this cost or benefit is not taken into account by the individual taking the action. External effects are also called externalities.

For example, in 2008 and 2009, two oil spills in the Niger delta of Nigeria destroyed fisheries. The spills resulted from the oil extraction activities of the Anglo-Dutch company, Royal Dutch Shell. Lawyers for the Ogoni people, who suffered these external effects, brought a lawsuit against the Nigerian subsidiary of Shell in the British courts. In 2015, Shell settled out of court and paid £3,525 per person, of which £2,200 was paid to each individual, and the rest to support community public goods. This award amounted to more than most Ogoni people would earn in a year. Lawyers representing the community helped to set up bank accounts for the 15,600 beneficiaries.

The transfers may have partially compensated the Ogoni for the loss of a healthy environment. (The UN Environment Programme has estimated that restoration will cost $1 billion and take 30 years.) For Royal Dutch Shell, the settlement requires them to bear at least some cost for the negative external effects of their activities, and might lead the company’s owners (and others extracting oil in the delta) to change their behaviour.

Years earlier, a similar tale had unfolded in the USA. In 1974, a giant lead, silver, and zinc smelter owned by the Bunker Hill Company was the only major employer in the town of Kellogg, in the state of Idaho, employing 2,300 people. Many children in the town developed flu-like symptoms. Doctors discovered that they were the result of high lead levels in their blood—high enough to impair cognitive and social development.

Three children of Bill Yoss, a welder at the smelter, had been found to have dangerously high levels of lead poisoning. ‘I don’t know where we’ll end up,’ he told a People reporter. ‘We may pull out of the state.’

The company refused to release its own tests of the smelter’s lead emission levels. Unless the state’s emissions regulations were relaxed, it said, the smelter would shut down—which it did, in 1981. Former employees searched for work elsewhere. The value of the homes and businesses in the town fell to a third of its earlier level. The local schools, which were supported by property taxes, did not have the funding to cope with those who remained.

A model of conflicting environmental interests

We model the Bunker Hill situation by considering a hypothetical town, Browneville, with a single firm that employs the entire labour force—but whose toxic emissions are a threat to the health of the citizens. The firm can vary the level of emissions that it imposes on the town, but the cost of emissions abatement means lost profits. The firm’s owner (who bears the cost) lives far enough away that the emissions do not affect the quality of his own environment. Therefore citizens and the firm owner have a conflict of interest over the level of emissions in the town. They also have an employer–employee conflict over the level of wages. You can think of the citizens as valuing ‘environmental quality’, which decreases when emissions increase.

The citizens of the town have some power to affect the outcome because (like Angela in Cases 2 and 3) each is free to leave Browneville and seek employment elsewhere. So the firm must offer a package of environmental quality and wages that is at least as desirable as their reservation option, which is what they expect to receive if they leave Browneville. We call this limit on what the firm must offer the citizens the ‘leave-town condition’.

In 494 BCE in ancient Rome, in response to judicial harassment, indebtedness, and poverty, the poor people (called plebs) left Rome and threatened to settle outside its walls and to draw up their own constitution. The threat to use their reservation option of leaving increased their structural power and got them their own magistrates, along with a judicial and legislative assembly that allowed the plebs to pass their own laws.

Likewise, the firm owner has power in relation to the citizens—he can also ‘say no’. The wage and environment package must not be so costly that he prefers his reservation option, which is to shut down or relocate, leaving the citizens unemployed. This cost limit is the firm’s ‘shutdown condition’. It places limits on the bargain that the citizens can strike with the firm.

We represent the preferences of the citizens and the firm in Figure 5.30, with the wage paid to the employees, w, on the horizontal axis, and the level of environmental quality experienced by the citizens on the vertical axis. For a simple measure of environmental quality, we use the amount that the firm spends on emissions reduction.

We assume that, like Angela, the citizens have indifference curves that are vertical shifts of each other (quasi-linear preferences). Their marginal rate of substitution (MRS) between wages and environmental quality depends only on the wage; so at each wage the indifference curves all have the same slope.

The owner of the firm cares about its total costs—the wage bill plus spending on emissions reduction. We can show indifference curves for the firm by drawing lines through combinations of wages and environmental quality that have the same total costs. Along this line, total costs are constant so each additional dollar spent on the environment is associated with a reduction in the wage bill by a dollar. This means that the firm’s MRS is constant: its indifference curves are straight lines. Work through the analysis in Figure 5.30 to determine the possible outcomes of the interaction.

In this diagram, the horizontal axis displays the wage. The vertical axis displayes environmental quality and ranges between 0 and 100. A downward-sloping, straight line connecting the two axes represents the firm’s shutdown condition. Above this line, the firm’s costs would be higher than its revenues. There is another downward-sloping, straight line, which is parallel to, and lies below, the firm’s shutdown condition line at all points. There are three downward-sloping convex curves representing the citizens’ leave-town condition. One curve is tangential to the firm’s shutdown condition line at point C (w-star, E_max), while the other line is tangential to the lower straight line at point F (w-star, E_min). The third curve lies between the former two, passes through point P which corresponds to wage w-star, and intersects the firm’s shutdown condition line in two points. At any given wage, the slope of the curves is the same. The area between the firm’s shutdown condition line and the lowest curve is the feasible set.
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Figure 5.30 Conflicts of interest over wages and environmental spending.

The firm’s shutdown condition: In this diagram, the horizontal axis displays the wage. The vertical axis displayes environmental quality and ranges between 0 and 100. A downward-sloping, straight line connecting the two axes represents the firm’s shutdown condition. Above this line, the firm’s costs would be higher than its revenues.
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The firm’s shutdown condition

This line joins combinations of wages and environmental quality at which the firm’s total costs (wage bill plus emissions reduction) would be equal to its revenue. Above this line, it would be unable to make a profit and would shut down.

The firm’s indifference curves: In this diagram, the horizontal axis displays the wage. The vertical axis displayes environmental quality and ranges between 0 and 100. A downward-sloping, straight line connecting the two axes represents the firm’s shutdown condition. Above this line, the firm’s costs would be higher than its revenues. There are two other lines, which are parallel to, and lie below the firm’s shutdown condition line at all points.
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The firm’s indifference curves

Each line joins combinations of wages and environmental quality that have the same total cost for the firm. Lower lines correspond to lower costs and higher profit.

The citizens’ indifference curves: In this diagram, the horizontal axis displays the wage. The vertical axis displayes environmental quality and ranges between 0 and 100. A downward-sloping, straight line connecting the two axes represents the firm’s shutdown condition. Above this line, the firm’s costs would be higher than its revenues. There are three downward-sloping convex curves representing the citizens’ leave-town condition. One curve lies above the firm’s shutdown at all points, while the other lines intersect the firm’s shutdown condition line in two points. At any given wage, the slope of the curves is the same.
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The citizens’ indifference curves

The citizens care about the wage and the quality of the environment. At a given wage, every indifference curve has the same slope (MRS). The lowest indifference curve shown corresponds to their reservation utility. Below this, they would leave town.

The feasible set: In this diagram, the horizontal axis displays the wage. The vertical axis displayes environmental quality and ranges between 0 and 100. A downward-sloping, straight line connecting the two axes represents the firm’s shutdown condition. Above this line, the firm’s costs would be higher than its revenues. There are three downward-sloping convex curves representing the citizens’ leave-town condition. One curve lies above the firm’s shutdown at all points, while the other lines intersect the firm’s shutdown condition line in two points. At any given wage, the slope of the curves is the same. The area between the firm’s shutdown condition line and the lowest curve is the feasible set.
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The feasible set

Combinations of wages and environmental quality in the area between the firm’s shutdown condition and the citizens leave-town condition are feasible outcomes.

If the rules of the game favoured the citizens: In this diagram, the horizontal axis displays the wage. The vertical axis displayes environmental quality and ranges between 0 and 100. A downward-sloping, straight line connecting the two axes represents the firm’s shutdown condition. Above this line, the firm’s costs would be higher than its revenues. There are two downward-sloping convex curves representing the citizens’ leave-town condition. One curve is tangential to the firm’s shutdown condition line at point C (w-star, E_max), while the other line intersects the firm’s shutdown condition line in two points. At any given wage, the slope of the curves is the same. The area between the firm’s shutdown condition line and the lowest curve is the feasible set.
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If the rules of the game favoured the citizens

Suppose the citizens could impose a legally enforceable level of environmental quality in the town, and set their own wages. To reach the highest indifference curve in the feasible set, they would choose allocation C where their indifference curve is tangent to the firm’s shutdown condition, with a wage w* and environmental quality Emax.

If the rules of the game favoured the owner: In this diagram, the horizontal axis displays the wage. The vertical axis displayes environmental quality and ranges between 0 and 100. A downward-sloping, straight line connecting the two axes represents the firm’s shutdown condition. Above this line, the firm’s costs would be higher than its revenues. There is another downward-sloping, straight line, which is parallel to, and lies below, the firm’s shutdown condition line at all points. There are two downward-sloping convex curves representing the citizens’ leave-town condition. One curve is tangential to the firm’s shutdown condition line at point C (w-star, E_max), while the other line is tangential to the lower straight line at point F (w-star, E_min). At any given wage, the slope of the curves is the same. The area between the firm’s shutdown condition line and the lowest curve is the feasible set.
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If the rules of the game favoured the owner

On the other hand, if the firm could announce a take-it-or-leave-it ultimatum, it would choose allocation F, to keep its costs as low as possible in the feasible set. The line of equal costs at F is tangent to the citizens’ leave-town condition, with a wage w* and environmental quality Emin.

The difference between Emax and Emin: In this diagram, the horizontal axis displays the wage. The vertical axis displayes environmental quality and ranges between 0 and 100. A downward-sloping, straight line connecting the two axes represents the firm’s shutdown condition. Above this line, the firm’s costs would be higher than its revenues. There is another downward-sloping, straight line, which is parallel to, and lies below, the firm’s shutdown condition line at all points. There are three downward-sloping convex curves representing the citizens’ leave-town condition. One curve is tangential to the firm’s shutdown condition line at point C (w-star, E_max), while the other line is tangential to the lower straight line at point F (w-star, E_min). The third curve lies between the former two, passes through point P which corresponds to wage w-star, and intersects the firm’s shutdown condition line in two points. At any given wage, the slope of the curves is the same. The area between the firm’s shutdown condition line and the lowest curve is the feasible set.
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The difference between Emax and Emin

The distance between F and C is a measure of the surplus from the interaction between the citizens and the business. Within the shaded area, any outcome is preferred by both parties to their outside option, but only the ones on the line FC, such as P, are Pareto efficient.

The situation illustrated in Figure 5.30 is similar to Case 3 for Angela and Bruno, in which there was a range of Pareto-efficient outcomes over which they could negotiate. Here again, because of our assumption about the citizens’ preferences, we can measure the surplus as the vertical distance between the reservation indifference curves of the firm and the citizens, and the Pareto efficiency curve is a straight line.

The Pareto efficiency curve

Pareto-efficient allocations of wages and environmental quality maximize the joint surplus. They occur where the indifference curves of the firm and citizens are tangent to each other:

\[\text{citizens’ MRS} = \text{firm’s MRS}\]

This happens at all allocations with wage w*: the Pareto efficiency curve is the vertical line at w* in Figure 5.30.

Digging a bit deeper, our assumptions—that both environmental quality, E, and the wage, w, are measured in dollars, and that citizens have quasi-linear preferences—give us an easy way to measure changes in utility, and calculate the MRS.

marginal utility
The additional utility resulting from a one-unit increase in the amount of a good.

Citizens value improvements in environmental quality in the same way, irrespective of the wage. So we can say that an increase of $1 in E raises their utility by $1, whatever the wage. However, an increase in $1 spent on wages raises utility by an amount we denote by MU, standing for the marginal utility. Citizens have diminishing marginal utility of wages: they value wage increases highly when the current level of wages is low, but MU diminishes as wages rise.

We can use this to understand the curved shape of the citizens’ indifference curves. To calculate the slope (MRS), suppose wages rise by $1. The downward slope of the indifference curve is the reduction in E that is needed to keep utility constant. The wage rise increases utility by MU dollars, so the required reduction in E is MU dollars:

\[\text{citizens’ MRS} = \text{marginal utility of wages}\]

The flattening of the indifference curves as wages rise corresponds directly to the diminishing marginal utility of wages.

We can calculate the firm’s MRS in the same way. Remember, the firm is indifferent between combinations of w and E that have the same total cost. If n is the size of the town’s labour force employed by the firm, the firm’s costs are given by:

\[\text{total cost} = E + wn\]

Suppose the wage rises by $1. The wage bill increases by n dollars. To keep total costs constant, E must be reduced by n dollars. So the downward slope of the firm’s indifference curves is n dollars:

\[\text{firm’s MRS} = n\]

Pareto-efficient allocations of wages and environmental quality occur at tangency points of the indifference curves—that is, where the citizens’ and firm’s MRS are equal. So the condition for Pareto efficiency is:

\[\text{MU} = n\]

In Figure 5.30, w* is the wage at which this condition is satisfied.

How will the allocation be determined?

Structural power

The outcome of the conflict will be one of:

  • the firm shuts down
  • the citizens leave town
  • the conflict is resolved somewhere between the shutdown condition and the leave-town condition.

The position of the shutdown and leave-town conditions reflects the structural power of the firm’s owner and the citizens. This is because the conditions are determined by the owner’s and the citizens’ next best alternative: the profits the firm could make by locating somewhere else or how the citizens would fare in some other town.

Bargaining power

If the firm does not shut down and if the citizens do not leave, then the outcome of the conflict—somewhere between the two conditions—will be determined by the bargaining power of the owner and the citizens. Any combination of wages and environmental quality in the shaded area in Figure 5.30 is a feasible allocation.

Allocations on the vertical line between C and F are both feasible and Pareto efficient. If the outcome is on this line, the distance between C and F (EmaxEmin) is the total surplus. Citizens get higher rents close to C; the firm’s rent is higher near F. We cannot say which outcome will occur, though, unless we know more about the bargaining power of the citizens and the firm.

The firm has all the bargaining power

If the firm could simply announce a take-it-or-leave-it ultimatum, then it would choose point F. We say that the firm has all the bargaining power. Its costs will then be well below shutdown level; it will be making high profits, and freely emitting toxic materials. The difference (EmaxEmin) shows up as profit in the firm’s accounts. But environmental quality is at the minimum level citizens can accept: (EmaxEmin) also shows up as exposure to health hazards in their medical records.

Citizens have all the bargaining power

If citizens have the power to choose for themselves, they would impose point C, with environmental quality Emax. The utility (or welfare) of the town’s residents would be as high as possible, given that the firm has to make enough profit to continue in business.

Dividing the mutual gains

How the surplus from an interaction—the pie—is divided between two parties depends on their relative bargaining power. If both citizens and firm have some bargaining power, they may be able to achieve an outcome between C and F, sharing the surplus (EmaxEmin).

A point such as P in Figure 5.30 might be possible if the citizens, acting jointly through their town council, imposed a legal minimal level of welfare for the business to continue to operate. Acting together, they would have more bargaining power than if they used the threat to leave town as individuals: they could require that the business’s decisions should provide a higher level of utility for citizens than the one on their individual leave-town condition.

Bargaining power in this case would be affected not only by the two parties’ reservation options but also by:

  • Enforcement capacity: The town government may not have enforcement capacities to impose an emissions limit on the firm.
  • Verifiable information: The citizens may not have sufficient information about the levels and dangers of emissions to win a case in court. If so, the firm would not comply with an agreed-upon emissions level corresponding to point P.
  • Citizen consensus: If the town’s citizens were not in agreement about the dangers of the emissions, the elected officials of the town who legislate an emissions limit might not be re-elected.
  • Lobbying: The firm may be able to convince the citizens that their health concerns were misplaced, or had little to do with the firm’s emissions.
  • Legal recourse: The firm may be legally entitled to emit any level of emissions that it finds profitable (perhaps subject to having purchased permits allowing it to do this).

Question 5.10 Choose the correct answer(s)

Consider a town with a single firm that employs the entire labour force, whose toxic emissions are a threat to the health of the citizens. Figure 5.30 shows the firm’s shutdown curve (the combination of wages and environmental quality offered by the firm that would just about keep the firm operating) and the citizens’ indifference curves for the quality of environment and their wage income. The citizens’ reservation indifference curve is also shown.

Based on this information, read the following statements and choose the correct option(s).

  • All points below the citizens’ reservation indifference curve and above the firm’s ‘shutdown’ curve are infeasible.
  • If the firm has all the bargaining power, then point C is chosen.
  • If the citizens have all the bargaining power, then they will choose the point in the feasible set with the highest possible wage.
  • Point C is the only Pareto-efficient choice.
  • At any of these points, at least one of the parties would prefer to take their outside option.
  • Point F would be chosen, because it is the point that maximizes profits while satisfying the citizens’ ‘leave-town condition’.
  • Point C would be chosen, because it is the point that places citizens on their highest indifference curve while satisfying the firm’s ‘shutdown condition’. They strictly prefer C to the point where the ‘shutdown’ curve intersects the horizontal axis, which is the highest feasible wage.
  • All points within the feasible set where the firm’s and citizens’ indifference curves are tangent are Pareto efficient (the line CF), including C, P, and F.

Exercise 5.11 Wages and environmental quality

Redraw Figure 5.30 to illustrate what happens in the following situations, and how the range of Pareto-efficient outcomes might differ from the scenario shown in Figure 5.30.

  1. The firm finds a highly profitable alternative place to relocate to.
  2. The government offers assistance for workers to find jobs in other towns.