Unit 10 Women’s right to vote and the reduction in child mortality in the United States

10.7 Modelling a self-interested political elite: Rent-seeking

How and why did societies governed by inherited royalty and wealthy individuals who used their political power to promote their status and amass fortunes make the transition to democratically elected representatives of competing political parties? We suggested in Section 10.5 that this occurred because the political elites were increasingly challenged by those excluded from political power, and in the face of challenges they either conceded to democratic reforms or were replaced by other more democratically inclined leaders.

To better understand this process we model the decisions of a political elite in an undemocratic system of rule who are interested only in increasing their own income. We can then examine how it might come to concede to a transition to democracy.

Modelling government decisions

We will develop a model of a government choosing the level of taxation it will set in order to collect revenue from the people. This could take one of the common forms of taxation (such as an income tax or a sales tax), but it can also be thought of more broadly to include other ways that the government can obtain revenue. An example from Unit 9 describes how in Tanzania, agricultural marketing boards bought cash crops from farmers at low prices but sold them in international markets at much higher prices. Other ways of generating income might be to sell valuable minerals to foreign mining companies, or to collect bribes from the citizens. The overall effect is similar to a tax in each case: the government takes income that would otherwise go to the citizens.

To analyse its choice we need to specify:

• the government’s preferences
• the constraints which determine which actions and outcomes are feasible.

Just as managers and owners of firms have a wide variety of motivations, so do government leaders. When we write that ‘governments’ have preferences, take actions or make decisions, we are referring to government leaders. The following motives are common among those in leadership roles in government:

• Benevolence: to improve the well-being of citizens
• Nepotism: to give special favours to members of their own family or a particular group, such as the region from which a government leader comes, or a particular religion
• Ideology: for example, a government’s wish to implement policies according to an ideology to which they adhere strongly
• Self-interest: using the power of the government position for personal enrichment.

Depending on its preferences and the constraints it faces, the government may use the tax revenues it collects for a variety of purposes, which may include:

• The provision of services to all citizens: These include schooling, health services, and the construction and maintenance of public infrastructure.
• The delivery of government services or other benefits to a narrowly targeted group: These might be well-paying jobs, or special reductions in tax obligations.
• Granting substantial incomes to its own members, or other economic benefits to themselves or their families.

Self-interested government: Political rent and isorent curves

Suppose that the government is entirely self-interested: its main objective is to benefit its own members, or other members of an elite minority, rather than providing good governance and services to the citizens of the country. To keep the model simple we assume that it must nevertheless spend a fixed, minimal amount, C, each year to provide public services (such as basic health services or schooling). In other words, public spending, C, is taken as given. The government chooses only how much to collect in taxes.

economic rent

Economic rent is the difference between the net benefit (monetary or otherwise) that an individual receives from a chosen action, and the net benefit from the next best alternative (or reservation option). See also: reservation option.

political rent

Political rent is the difference between the net benefit (monetary or otherwise) that an individual receives as a result of their political position, and the net benefit from their next best alternative (what they would receive in the absence of a privileged political position). See also: economic rent.

employment rent

The economic rent a worker receives when the net value of their job exceeds the net value of their next best alternative (that is, being unemployed). Also known as: cost of job loss.

innovation rent

Profits in excess of the opportunity cost of capital that an innovator gets by introducing a new technology, organizational form, or marketing strategy.

The costs of the public service include what the members of the governing elite would earn as normal civilians, because this is the least that they would have to receive in income in order for them to be part of the government. The difference between the tax revenue and the cost of public services provision is captured by the elite for itself (rather than being saved up for the future like a regular budget surplus). It is a form of economic rent, which we call a political rent:

• It is a rent: This is what the members of the elite get above and beyond their next best alternative (namely, working as ordinary civilians).
• The rents are political: They exist as a consequence of the political institutions in force. The elite uses its political power to obtain an income higher than what they could otherwise obtain.

In general, economic rent can play a useful role by providing incentives that benefit the economy: for example, the employment rent that encourages workers to work hard and well, or the temporary innovation rents received by firms. In contrast, these political rents play no useful role in the economy. They are simply a reward for having power.

But no government’s power is absolute. Even a powerful dictatorship may be ended by discontented citizens through civil unrest or even revolution, or by defeat at the hands of another nation. The government’s objective is to maximize the total political rent that it can expect to get over its period in office. This depends on both on the annual level of taxation, T, and the expected duration in office, D. The total amount of rent is the annual rent (\(T-C\)), multiplied by the number of years, D:

\[\text{Expected political rent} = (T - C) D\]

The rent-seeking government would like both taxation and duration to be as high as possible. For example, the fortune obtained by President Boigny of Ivory Coast was accumulated over more than 30 years in office. But a government that sets annual taxation too high will strengthen opposition, loosening its grip on power and reducing expected duration.

constrained choice problem

A problem in which a decision-maker chooses the values of one or more variables to achieve an objective (such as maximizing profit, or utility) subject to a constraint that determines the feasible set (such as the demand curve, or budget constraint).

So we can model a self-interested government as facing a constrained choice problem, similar to the model of consumer choosing which goods to buy to maximize utility subject to a budget constraint, or the owners of a firm setting a price to maximize profits subject to a demand curve. And we can solve the problem in a similar way, using a diagram with the two things the government cares about, T and D, on the axes. We start in Figure 10.11 by drawing curves joining the points in the diagram that give equal amounts of rent—that is, isorent curves—assuming that the cost of basic public services, C, is $5 million.

indifference curve

A curve that joins together all the combinations of goods that provide a given level of utility to the individual.

An isorent curve is made up of all the points where the government obtains a particular level of total political rent (the government’s indifference curves). For all levels of rent above zero, the curves have a similar shape:

• They are downward-sloping.
• They are ‘bowed’ inwards towards the origin (that is, convex).
• Curves representing higher levels of rents are further from the origin.

marginal rate of substitution (MRS)

The trade-off that a person is willing to make between two goods. At any point, the MRS is the absolute value of the slope of the indifference curve. See also: marginal rate of transformation.

In the same way as the slope of an indifference curve measures the consumer’s marginal rate of substitution (MRS) between two goods, the slope of an isorent curve measures the government’s MRS between duration and annual taxation.

The slope of the isorent curves at each point represents the trade-off between annual taxes and duration for the given amount of rent. For example, at point E the slope of the isorent curve is −12. This means that to increase duration by a year while maintaining total rent at $300 million, annual taxes would have to be $12 million lower. It is the trade-off that the government would be willing to make, because it doesn’t change the total rent.

The isorent curves represent the rent-seeking government’s preferences; the level of taxation it will choose depends on the constraints that it faces; in other words, what combinations of T and D are feasible, given the political environment. Below we consider the constraints facing a hypothetical dictator, and how these determine his taxation choice. In Section 10.8 we will analyse other political conditions.

The constrained choice problem for a dictator

Suppose that the government is a dictatorship, or what political scientists today call a closed autocracy. Even in these conditions, a dictator faces a feasibility constraint: his powers are not unlimited, because if he takes too much from the population, he may be removed from office by an uprising of citizens, or a military coup.

For example:

• The Romanian people revolted against Nicolae Ceausescu in 1989 after he had been in office for 29 years. The armed forces joined the revolt, and he and his wife were executed.
• Louis XVI of France was removed from power during the French Revolution in 1789 during which thousands of armed men and women besieged the Palace of Versailles. The heavy tax on salt (the gabelle) was a major source of discontent. Louis was executed by guillotine in 1793.
• The Assad regime ruled Syria for more than 50 years. Bashar al-Assad himself is still alive, but after 13 years of civil war he was removed from power in December 2024 by a coalition of Syrian rebels.

To model the constraint we assume there are two types of reasons for removing the dictator:

• Performance-related reasons: In our model, performance is represented by the level of taxes. A dictator risks removal from office if he collects too much tax.
• Reasons unrelated to performance: There may be a revolution or coup for reasons beyond the dictator’s control.

If the probability of removal in each year were smaller—say 5%—the expected duration would be longer: 20 years. In general, the expected duration is 1 divided by the probability.

Suppose that every year, the probability of removal from office for reasons other than taxes is 10%. Then if taxes were only sufficient to cover the cost of public services (\(T=C\)), the dictator would earn no rent, but could expect to remain in office for 10 years on average. The dictator will want to raise taxes above this level, to maximize the total political rent that he can expect to get over his period in office. But this makes an uprising more likely—his expected period in office will be shorter. He can reasonably expect that there is a trade-off between the taxation level, T, that he imposes and his duration, D, in office: the higher the tax level (for a given level of public services) the more likely he is to be removed from office, and the shorter his expected duration.

The duration curve in Figure 10.12 captures this trade-off. If taxes were set at $89 million, the dictator’s expected duration would be only 2 years. To stay in office for 8 years, he should set taxes no higher than $26 million. The duration curve is a downward-sloping relationship between taxes and duration, with a maximum expected duration of 10 years at the point where \(T=C\).

feasible frontier

The curve or line made of points that defines the maximum feasible quantity of one good for a given quantity of the other. See also: feasible set.

feasible set

All of the combinations of goods or outcomes that a decision-maker could choose, given the economic, physical, or other constraints that they face. See also: feasible frontier.

opportunity cost

What you lose when you choose one action rather than the next best alternative. Example: ‘I decided to go on vacation rather than take a summer job. The job was boring and badly paid, so the opportunity cost of going on vacation was low.’

The downward-sloping duration curve is the feasible frontier for the dictator. Points on or below it are in the feasible set (the shaded area), but points above it are infeasible. So points P and Q on the duration curve are feasible, as is point R below it (with taxes at $50 million he could choose a duration of 5 years if he wished, although longer is possible). But point S is not in the feasible set: he cannot expect to stay in office for 8 years if he sets taxes at $40 million.

The slope of the feasible frontier in Figure 10.12 is −10.5 (using points P and Q, \(\text{slope} = (26 − 89)/6\)). This is a measure of the trade-off that constrains the dictator in his taxation decision: the opportunity cost of an additional year of expected duration is annual rent of $10.5 million.

The dictator chooses a tax to maximize his total rents

By bringing together the isorent curves that capture the dictator’s preferences for high taxes and long durations, and the duration curve capturing the feasible combinations of taxes and duration, we can find the tax level he will choose: the level that maximizes total rents. This is at point M in Figure 10.13, where the feasible frontier reaches the highest possible isorent curve; all other points in the feasible set give him lower rent. For example, points K and L are both feasible, but they are on a lower isorent curve than M.

The tax level that maximizes total rent is T* = $57.5 million, with expected duration D* = 5 years. The total amount of rent is given by

\[\begin{align*} (T^* - C)D^* = (57.5 - 5) \times 5 = \$262.5 \text{ million} \end{align*}\]

marginal rate of substitution (MRS)

The trade-off that a person is willing to make between two goods. At any point, the MRS is the absolute value of the slope of the indifference curve. See also: marginal rate of transformation.

marginal rate of transformation (MRT)

The quantity of a good that must be sacrificed to acquire one additional unit of another good. At any point, it is the absolute value of the slope of the feasible frontier. See also: marginal rate of substitution.

In other words, the dictator’s marginal rate of substitution between tax level and duration is equal to the marginal rate of transformation, measured by the slope of the duration curve. Like the consumer maximizing utility, the dictator chooses the point where MRS = MRT.

At the chosen point, the slope of the isorent curve is equal to the slope of the feasible frontier (the duration curve). In other words, the trade-off between tax level and duration that the dictator would be willing to make (because it doesn’t change total rent) is equal to the trade-off that he is constrained to make (because staying in office longer requires lower taxes).