Rent-seeking and the distribution of surplus

Rent-seeking and the distribution of surplus

DEVP 233

Spring 2017


Rent is one of the most important concepts in economics. It is the amount paid for a factor of production above and beyond what it needs to be economically viable. Practically speaking, if you operate a firm with labor, machines, and space, the difference between your revenue and the cost of the inputs in a competitive market is the rent for the unique resource which is your entrepreneurship. The economic rent is what people would consider above ‘normal’ profit. The textbook model in economics is a competitive system with the right properties (technology with decreasing returns to scale, many agents, full information) where at the equilibrium, firms operate with normal profit. But, economics realizes that some agents have unique capacities. So, they obtain rents for these capacities. For example, if you have farmers with different degrees of productivity, for farmers operating at the margin, price will be equal to average cost, which will include return on investment and cover operating costs, while other farmers will gain additional surplus, i.e. rent. So, we can relate the notion of rent to the that of producer surplus, and one can even expand it and interpret consumer surplus as the rent for the consumer who is not at the margin, where the price paid is smaller than the marginal utility.


To understand the concept of rent seeking better, let’s look at simple graphs comparing monopoly with perfect competition. Under perfect competition, social welfare, which is the sum of consumer and producer surplus, is higher than under monopoly. Moving to monopoly results in deadweight loss (DW) in social welfare because the monopoly reduces production from  to  , which results in a price increase from   to  . In this movement, consumer surplus declines significant, but producer surplus increases. If a government issues a policy that provides a company monopoly power, it creates rent. This happens often – for example, government issues business licenses for an exclusive right to import wheat, Coca Cola, computers, etc to one firm. There are of course international agreements that try to circumvent these policies, but governments will pursue these policies anyway. So the policy that prevents competition is a simply policy that reduces social welfare, but generates rent to the monopolist. In many cases, the politician will benefit through this type of policy and may get a kickback. We can envision a situation where policy makers would be for sale. He will give someone a monopoly to sell a product in his country for both direct kickbacks and campaign contributions.


One can develop a model to determine optimal design of a bribing scheme by a regulator or politician. The regulator may have an agreement with the industry that would establish a regulation that would control overall supply. The interaction is complex because there is a negotiation between the regulator and the industry. Let’s take a simple case (which is still complex) where government regulation moves the output of the industry from the competitive outcome, , to a lower level, which we will call . This means that the regulation doesn’t move it to a monopoly, but restricts quantity nevertheless. The gain to the industry  is a function of   that is determined by the politician and the industry. This gain is increasing the smaller is  and reaches its maximum when . But the industry has to pay a certain amount to the politician, which we denote by X. Since consumers may lose from higher prices, the politician may lose political support, and this loss is a function of the reduction in consumer surplus, which is .

Let’s consider a simple case where the politician and industry have an agreement that they will share the total gain generated by the regulation. This gain includes increased revenue and reduced cost, , but it may lead to increased likelihood of losing power, and in this case, the politician will use their gain from power, which we denote as . The probability of loss of power is affected by reduction in consumer surplus, but ultimately it is a function of the new supply level, and we denote it as . The probability of loss of power increases as  is declining, and therefore , is a decreasing function and is likely to decline faster as  decreases. The total net expected gain for the two parties is , which is expected gain from higher producer surplus, minus , which is the loss from losing of power. The optimization problem of the two parties is



Obviously, if the politician is a safe in power, then =0 for every  and the optimal outcome will be the monopoly that maximizes the producer surplus. If any regulation would lead to loss of power, , and  is large relative to consumer surplus gain, then there will be intervention and . In case that higher price increases the risk of losing power, there may be an internal solution where the first order condition that determines  is



For simplicity, we didn’t write explicitly in all the functions (i.e.  ). We can rearrange terms and the first order condition becomes



At the optimal solution, the marginal expected gain in producer surplus from reducing supply is equal to the expected economic loss associated with the marginal increase in the probability of losing power due to restricted supply. This expected economic loss is the product of the marginal increase in probability of losing power,  times by the loss of both producer surplus and benefit from holding power for the regulator, .


This model suggests that as the producer gain from restricting supply is increasing, for example when demand is more inelastic, or when the vulnerability to lose power due to restricted supply is low, then restrictions on supply will be stronger. The more politicians gain from their power and the more vulnerable they are, the less they engage in introducing cartels and monopolies. This model suggests that manipulation of power to benefit the few is less likely in a democracy where consumers are aware of the political process and are able to mobilize their power against artificial restriction of supply.


The sharing of the spoils between regulator and industry can be modeled by a complex negotiation framework, but we will simplify it. Let  be the share of the gain received by the politician and  be the share of the gain received by the industry. The stronger the politician, the greater is . In many cases, the politician will share the gains by having themselves or a family member become a partner in a company with monopoly power. For example, Putin may be one of the richest people in the world.[1]


We can expand the model in many ways. For example, the probability of losing power may be a function of the politician’s share in the spoils. In this case, one can show that if the politician makes the regulatory decision they will tend to distort the market less. One can go a step further and show that when politicians lose when people know about kickback, we begin to see cover-ups. This is the reason it is important to have effective media and freedom of press.   


The politician is gaining extra income X but it may lead to the loss of position due to unsatisfied consumers. The probability of losing the position is increasing with the function of consumer surplus loss due to the decreased supply, , which we defined as . The politician’s loss in case of losing his position is denoted by . The gain for the politician is the transfer amount X, so the net gain is . The industry gains  as long as the politician stays in power, but it loses transfer payment X with certainty. So, the net gain of the industry .The  determination of  and X is result of negotiation between the two parties.


Let’s assume a simple model, where the politician and the industry negotiate to maximize a weighted sum of their gains from a combination of contributions (X) and regulations (). Their joint objective function is


where  is the relative power of the politician and  is the relative power of the industry.


Assuming an internal solution, , the first order condition with respect to is

Leading to

The right-hand side presents the weighted marginal gain to the coalition from reduction in quantity-expected increase in producers’ surplus, while the left hand side is expected marginal cost from marginal reduction in regulated output. A reduction in probability of winning will reduce the well-being of both politician and industry. At the optimal level of regulation, the marginal benefit is equal to the marginal cost.  One can show that the greater is the industry power ( the more strict is the regulation (the lower Q is). For example, when a politician depends strongly on domestic manufacturers, he may set regulations that limit import opportunities. This was a key element in the export substitution strategy in Latin America.


The first order condition with respect to  is

Leading to

  • =

The left hand side reflects the marginal gain to the politician from increased donation, weighted by its relative political power . The marginal gain from increased donation is a dollar in income plus the expected extra political gain from higher spending (remember that  is negative; the more you spend on elections, the less likely you are to lose). The right hand side reflects the marginal cost to the donor. This marginal loss is the expenditure of money (1 unit) minus the gain due to reduction in expected political risk due to donation . When  is higher, the politician has more political power, and thus can negotiate a larger contribution from industry for a given level of extra surplus he provides the industry by regulation. Similarly, when the marginal effect of campaign contribution is larger, the bigger will be the donation.





The impact of power distribution among sectors on political choices


There are many models of political economy- each highlighting various aspects of politics. The political economic framework is used to determine a certain policy variable- for example Grossman and Helpman (1992) studied determination of level of protection of domestic producers from trade through say a protective tariff. One can use it to analyze the negotiation to establish a pollution control policy.  In each case the negotiation between parties aim to establish a level of policy parameters. The first time in the analysis is to compute how various levels of the policy parameters will affect the welfare of different parties that may participate in the political process.  For example- in negotiation to establish the level of a defensive tariff, it is important be able to compute how the level of the tariff affects (relative to free trade) the consumer surplus of domestic consumers (who are likely to lose from a higher tariff), surpluses of domestic producers and workers who may gain, surplus of foreign producers who may lose etc. In a case of a pollution control policy – say pollution tax- it is important to assess how various levels of the tax will affect consumers’ surplus, producers’ surplus, government expenditure, environmental surplus etc.

Here we present a simple model where political decisions are viewed as outcomes of parties that vary in their power. This model can reflect a situation where we have a government that includes a coalition of labor and environmentalists, so they will have a higher wage than business. It may also reflect a situation where government is composed of individuals from one tribe, and so their concerns are weighed more heavily than other tribes. Another possibility is having a ruler that worries more about the welfare of urban poor and middle class, and therefore gives them more weight in decision making. But the model itself is very simple in structure but can be used to tell many stories, and can rely on economic models that we develop in other classes.

We will assume that the economy consists of N identified groups. These groups can be divided according to functions in the economy (consumer, producer, environment, government) as well as location. One of the groups may be corn producers in Iowa and another can be meat consumers in Ghana. Each group has its welfare, measured in dollars, that depend on policy variables. Let the welfare of group i be denoted by  as function of the levels of the policy parameter . We will consider the case where welfare is measured in dollars and is equal to economic surplus. Let  be the weight of group i and let’s assume that  and the sum of . Standard welfare analysis assumes that when we have i groups, then  . But in political economy, these weights may differ.

To conduct political economy analysis that determines the value of a policy parameter x, for example tax on import, upper bound on pollution or subsidy to farmers in a given region, we first solve the economic model that allows us to calculate  and then solve the optimization problem.


Let the optimal political economy policy parameter be denoted by . The first order condition is

In a political economy context, the weighted sum of the marginal welfare over all groups is equal to zero. In contrast, the efficient policy parameter which is a result of standard welfare analysis is denoted by  and it is determined where


Let’s illustrate how to solve the political economy equilibrium with two simple cases. First, a policy maker has to determine the quantity of output the industry can produce. The two groups are consumer surplus, where  is  and producer surplus, where  is . Now let’s assume that x is quantity produced and demand is  and supply is .

Let’s suppose that the government sets a quantity and supplier must provide this quantity to the market. The consumer surplus, in this case, is the area of the triangle, which is equal to . The producer surplus is equal to the trapezoid of revenue, , minus costs, .), which together are . Let’s suppose the political weight of consumers is  and producers is .















The political economy optimization problem is

The output under this scenario, , solved from the first order condition is


This means that


Leading to

Note that when , and we are in the welfare optimization problem, the  is equal to the socially optimal solution, , that is achieved under competition. When  and all the power lies with the producer, we get the monopolistic solution, . If  is greater than 1, and consumers have more power, then  and consumers benefit from lower prices and producers lose. Similarly, if  is positive but less than 1, then .

            We see in this simple example that relative power distribution among groups in the political process affect policy making and distribution of welfare. The analysis here can become more complex. For example, if we have an externality problem, and a policy maker needs to determine the level of tradable permits of pollution x. In this case, we can calculate consumer surplus , producer surplus , and environmental surplus . If  is consumer power,  is producer power and  is environmentalist power, then

where .

We will not solve this problem here, but as the power of the environmental group increases, the political economy equilibrium, , gets smaller; as the power of the consumer increases, increases; and as producer power increases,  tends toward . In many real-world situations, the parties affected by policymakers vary significantly. For example, producers can be divided in different groups based on, say, region, soil quality, or size. Consumers may be divided by region and income, for example. In considering a policy like taxation, the government becomes part of the decision-making framework.  Thus, one key element of political economy analysis is to identify the affected parties, their respective weights in the decision-making, and have a quantitative model that will allow assessing the impact of policies on each group.

            One can conduct two types of political economy analysis. If one has capacity to compute the impact of various policies on different groups and the weight of these groups, then the political economy model can help determine the optimal policy. Alternatively, if one knows policy choices and how they affect various groups, then they can use it to assess the implied power of each group that contribute to the emergence of a decision.


Determination of the political power of groups

The alpha coefficient of each group may be affected by several variables. These values are not stable – they may change over time, especially during regime change. When in the US the democrats win, the influence of labor and environmentalists increase and business declines.

 With Reagan, California had a lot of influence. With Bush, Texas had more influence. In Nigeria, for example, division of power is more often between Christians and Muslims. Obviously, we are aware that in Syria the Alawite, representing a minority of the population, were in power, while the majority of Sunni felt denied access to power. In Iraq, the Sunni majority was dominant. Obviously, some of the factors may complement one another. For example, in the US, presidents selected by Midwestern states will tend to have more sympathy towards agriculture.

            The influence of different groups in a given government depend on several factors: (i) how many voters they control, in the case of a democracy, (ii) their ability to donate contributions, (iii) capacity to recruit volunteers, and (iv) capacity to cause trouble or unrest. Government may not engage policies that totally alienate non-supporters because they want to avoid strong negative responses. Opposition groups may have a threshold of tolerance, and if it is exceeded, they may resort to destructive activities (rebellion, violence, war, civil disobedience). Thus, the political economy models can be expanded to introduce constraints that may reflect thresholds of tolerance of different groups and their behavior.

            Furthermore, the literature of political economy has identified several important factors that affect the power of different groups. First, Olson (1965) suggested that small groups, where each individual has a large stake in a policy, may have significant political power compared to larger groups where each member is affected little by a policy. To illustrate, when we have a few producers that each gain significantly from agricultural support programs, and many consumers that lose from it, but the loss per person is relatively low, the producers will organize more effectively to push the support program through the government. They will have a much higher alpha coefficient than the consumers. Small groups with strong interests in a certain policy agenda may be more effective in the political arena because they will have lower transaction costs to organize and achieve their goal.

            Second, the structure of the political system matters. The US has a bicameral legislative system, where the representation in the House of Representatives is proportional to population per state, and representation in the Senate is equal across states. Representatives of small states need to address fewer issues and therefore can use their vote more effectively to achieve outcomes desired for their state. This is especially important given that states partake in “horse trading” where state representatives trade votes with other states in order to achieve gain support for their agenda. So, the many agricultural states in the US are able to gain support for their policies, even though they represent a small portion of the overall population. Furthermore, in the case of agricultural policy, there exists a coalition between agricultural and urban states where urban states support agricultural subsidies while the agricultural states support welfare reform. The agricultural sector has strong support in many developed countries because in most of these countries the national system allocates representation based both on regions as well as number of people. In many developing countries, especially in the past, government might have been concerned more with satisfying the urban population than the rural population, and agriculture had a relatively low alpha coefficient and was taxed, explicitly or implicitly.

            Thus far the political economy analysis we considered was static. But, political economy is a dynamic phenomenon and there are recent studies that recognize it. Policymakers engage in policies both the provide gain to their supporters as well as to be elected in the future. Furthermore, while members of the population have some political affiliation, they change their mind as reality changes and performance of policymakers is revealed. So voter behavior is affected by both what they see as well as what they learn from the media and otherwise. In the next lecture, we’ll go over decision-making under uncertainty and about models of learning in more detail. Generally speaking, the Bayesian formula provides a foundation of how people should update their probabilistic belief about outcomes based on observed reality, as we saw in an earlier lecture. For example, if people think that there is a 75% chance of economic prosperity under a republican, and there are several years of recession under a republican president, then viewing this reality, they the formula suggests that they should adjust their assessment and estimate that the probability of economic prosperity under a republican is now, say, 25%. If we have another person that believes there is a 90% chance of prosperity under republicans, after several years of recession, his belief will move to, say 30%. The reality is that people don’t follow the Bayesian formula rigorously, but the idea that people update believes based on performance and news is evident, and there are empirical studies that show it. Different people are influenced by different information, and update their belief and choices differently. Campaigning, to some extent, is a process where politicians aim to affect voters’ beliefs with new information. Since campaigning requires resources, candidates will engage with potential donors in order to obtain resources in exchange for favorable policy consideration if they are elected. But it is clear that donors will contribute to candidates that have views or operated in the past in a manner consistent with their interests. The understanding of the dynamics of voting, campaigning, and the role of the media are important topics in political economy.


Qualitative analysis of political economy


The bottom line is that political systems affect economic systems by various regulations that reflect the political structure, the intensity of impact of polices on interest groups, the political strength of these groups and their ability to affect the political debate.  Political power is changing, and regulation and policy change too, but political economic analysis starts with identifying who are the parties affected by a policy. This analysis will also consider their intensity of concerns, their economic and political power, and their credibility with the public. Once we understand the players and their interests we can start developing quantitative models and analyze specific developments. Historical analysis of development of policy issues are very instructive to understand political economy and development. Path dependency is crucial element of development.


One simple example to illustrate the difference between economics and political economics is trade policy. First, the simple economic analysis. Suppose that there are two countries, China and the US. US has relative advantage in computers and China in textiles. Overall, they will gain from trade. Before trade, China under-produced textiles and over-produced computers, while the US over-produced textiles, and under-produced computers. With trade, China will export textiles and the US will export computers. Obviously, this is a simple model, which removes dynamic factors and others. The economic literature suggests that, overall, there will be gains from trade, consumers gain (more computers and more textiles), and producers in both countries gain. But, producers and workers in textiles in US and in computers in China may lose. The overall gain is greater than the loss for these groups, but we need some compensation in order to have everyone happy. And this is what we call safety nets.



Political economy models suggest that the power of different groups is different. If, for example computer producers in the US and textile producers in China are dominant groups, and then consumers will form coalitions that will be pro-trade. But what happens if we don’t have appropriate compensation to the losers, and they have strong political power, then the anti-trade policy that they support may win.


If we look at the world today, there is something to this story. In countries like Mexico, where the gains from trade were well distributed, there is general support for NAFTA. In China, while there is protectionism, there is support for trade. In the US, because of the political system, there is a strong anti-trade movement. Personally, I think that people don’t realize how much they gain from trade (e.g. low-income people in the US gain immensely from cell phones and clothes produced internationally). Many job losses are the result of automation and other factors, although today unemployment is low. And the opening to China, which is the result of peace between the US and China, increases the labor pool and reduces the value of low-skilled labor. Still, the basic model suggests that political power may lead to outcomes that may not be consistent with basic economic logic.



Grossman, Gene M., and Elhanan Helpman. Protection for sale. No. w4149. National Bureau of Economic Research, 1992.


Olson, Mancur. Logic of collective action public goods and the theory of groups. Revised edition. 1965.




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