# To lobby or not to lobby: How to decide whether you should manipulate your government

A company will lobby government in order to influence a decision that will effect them. This effect is usually economic, so the company will lobby in order to give themselves the best economic outcome. However there is a trade-off for the company: they can lobby government to benefit themselves economically, however lobbying costs money which isn’t economically beneficial. So when does a company decide to lobby or not? And how do they decide the amount of money to spend on lobbying? This blog post shall explore the question from an economic point of view. First it shall describe supply-demand, externalities and Pigovian tax, then it shall describe how a company can make a decision based on this framework.

This post doesn’t require a background in economics, however I shall be using the supply-demand curve without deriving it (because that’s a blog post in itself). If you do not know about the supply-demand curve then you’ll have to take my word on a couple of things, but you should still understand the thrust of my reasoning.

Supply and Demand as Benefit and Cost

Let’s say the company we are looking at is an energy company. An energy company supplies a product (i.e. energy) and meets the demand of users. The supply-demand curve for their product will look something like this:

Now the energy company decides the quantity of energy it will produce, once it does that it looks at the demand for that quantity and sets the price. This is shown below, the company chooses to produce the amount q1 of energy, q1 will produce a certain demand for the product, which corresponds to price p1. Therefore the company sells the energy at p1 because they chose to produce q1.

The revenue a company receives is (price of good x quantity of good sold). In the graph above this is the area of the black box bounded by q1 an p1. The demand curve can therefore be thought of as determining the amount of revenue, or the amount of benefit, the company will get for a given quantity.

Just as the demand curve can be thought of as the benefit for a company, the supply curve can be thought of as the cost to a company. Let’s say the company wanted to produce q1 amount of energy, to figure out how much it would cost to produce that amount you now go to the red line and see what the corresponding price is. The important thing to remember is the supply curve = cost of making the product.

So it turns out that things in economics seems to happen when two lines meet. This is no exception. If a company wants to maximize its profits (i.e. every company) it will achieve this where the supply and demand curve meet. The point where the lines meet is called an equilibrium because if a market starts away from that point (eg. the firm produces q1 at price p1) over time it will tend to the equilibrium (the company will eventually figure out that it benefits them more to produce the quantity at the equilibrium point).

Not only is this point an equilibrium but it is also an efficient equilibrium. An efficient equilibrium in one in which the maximum amount of welfare is shared between the consumers and the company. I won’t explain what maximum welfare means here, but it’s important to know that economists want a market to be at the point where the lines meet. If the market is operating away from where they meet the market is inefficient, there is wasted welfare, and economists get grumpy and try and change the market so that it acts efficiently.

Externalities and Taxation

When you make a supply-demand curve you are modelling what’s happening in the real world. However models are always imperfect, they can never capture exactly what is happening. Instead modelling helps simplify the world so we can analyse it more easily. Because of this there are always going to be unmodelled effects that haven’t been taken into account, but they can often be important. An unmodelled effect is what economists call an externality. So what does an externality look like? Let’s return to the energy company.

Remember how I said that the supply curve is how much it costs for a company to produce a product? Well that wasn’t completely accurate. In fact the supply curve is the total cost of producing the product. The total cost is the company cost + the social cost. The social cost is a measure of how bad the product is for society, whereas the company cost is simply how much the product costs to make. The company produces energy, however they also produce CO2 when making the energy. This co2 emission is bad for society and hence there is an added social cost of producing that energy. This added social cost was not modelled in the supply-demand curve above and is therefore an externality. When this externality is accounted for the supply curve looks different. The new supply curve will be steeper than the original one because there is an extra cost involved:

Let’s take a moment to think about this graph. First note that the new supply line is a better model of the real world because we’re taking into account a factor that wasn’t considered originally. Second note that this new supply line has changed where the equilibrium is (the new equilibrium has a lower quantity and higher price). Because the new supply line is more accurate than the old one we can say that the new equilibrium is more efficient than the old one.

The new equilibrium is at a lower quantity than the old equilibrium (the lines cross further to the left at the new equilibrium), meaning there is less energy in the market. This works intuitively as once we take into account the bad effects of CO2, it makes sense for the energy companies to produce less energy.

The last thing to note about this graph is that there is a tension between the two equilibria. The new equilibrium from the better model is the one at which economists want the market to operate, because they like the most efficient equilibrium. However the energy company only cares about it’s own cost and so wants the market to operate at the old, less efficient (but more beneficial to them) equilibrium. So how do we resolve this tension? If energy firms are allowed to do what they want then they’ll operate at the equilibrium that isn’t good for society, so the answer is to not let them do what they want. Enter taxation.

In order to make the energy company operate at the point that is best for society, it should be the case that the externality of CO2 emissions translates into a tangible cost for the company. This cost takes the form of taxation. The government adds a cost to the product (the energy) in order to change the supply line to cross at where the best equilibrium is. Note that the way taxation changes the supply line doesn’t have to be exactly the same as how the externality changes the supply line, instead the taxation and externality supply lines must have the same equilibrium (they must cross the demand line at the same point) because that is where the market operates.

So let’s say that the government introduces a fixed amount of tax, c, whenever you buy energy. This then changes the old supply line. The company now has the cost of producing energy + c, the fixed tax. The taxation supply line will now look like the old taxation supply line but shifted up by c, as shown below:

See how the Old Supply + Tax line now has the same equilibrium as the Company Cost + Social Cost line? That is because of the taxation. As the government is able to tax, it can change the dynamics of a market in order to make it reach the best equilibrium for society. This equilibrium is not the best one for the energy company (they prefer the old equilibrium), but it is best overall. Therefore, in theory, taxation is a way for governments to account for negative social externalities, safeguarding the public from being exposed to inefficient markets where welfare is lost.

But that’s not the end of the story. The energy company can now hire lobbyists to convince the government to get rid of a tax in order to operate at the equilibrium they prefer, the more profitable one….

Modelling Lobbying

The energy company wants to maximize profit. The profit before tax is: revenue – cost of production. However if a tax is introduced the profit for the company is now: revenue – cost of production – tax. So the amount a firm’s profit will decrease is the same as the amount of tax, c, that the lobbyists are working against.

When deciding how much to spend on lobbying, the company can put bounds on the amount it is willing to spend. The lower bound is obviously 0, as the least amount you can spend is 0 (you can’t spend a negative amount on lobbying). The upper bound is c, the amount of tax they will have to pay. If the company spends more on lobbying than it would in tax, even if the lobbying is successful, it is not beneficial to the company. They may as well pay the tax if it costs them less than the amount it would cost to lobby the tax away. So the company has to decide on a number between 0 and c to spend on lobbying.

Now lobbing is not guaranteed to be successful. When you throw money at lobbyists you can never be sure that they’ll influence the law in the way you want. Instead it is more sensible to model lobbying in terms of probability: if I spend x amount on lobbying how likely is it that it will be successful? If you think about this for a second it is clear what a graph of this will look like. The more money you spend on lobbying, the more likely it is that you will be successful. Therefore more money = higher probability of success:

Note how the line doesn’t continue after c, because the company is not willing to spend any more on lobbying than it is on tax.

If the probability of success reaches 1 (i.e. success is certain) before the money spent reaches c, then it makes sense to spend the amount of money that makes success certain. However this will never be the case as you can never be certain of success. It is also worth noting that the steepness of this line will depend on the situation being lobbied. For instance if you are trying to overturn a well established, highly valued law (e.g. the right to unionize), then even if you spend a lot of money it is not likely that the law will be overturned, therefore the line will not be steep. However if you are lobbying a law that is ready for change and not many people are interested in, then you don’t have to spend much money to get a high chance of success, therefore the line will be very steep.

So how does the company make a decision on money spent on lobbying? Well one way to do it would be to set a threshold probability that they are willing to accept. For instance let’s say that the company doesn’t want to invest in lobbying unless it has at least a 0.6 chance of being successful. We can plot this line on the graph:

The company looks at the amount of money, x, it would have to spend to get the chances it wants. If this is less than c, the maximum it will spend, then it can spend x amount on lobbying. We have therefore bounded the amount of lobbying money again, as now that we know the boss won’t take a risk of less than 0.6, any amount spent below x is not worth it. So the boss has to choose a number between x and c to spend.

It is possible to find the optimum amount of money between x and c the company should spend on lobbying. This could be done by maybe optimizing a first (or second?) order condition, however I won’t go into that here.

As a last note, consider welfare in terms of lobbying. The taxation was originally introduced by the government in order to maximize social welfare, adding a cost c onto the product. When a company engages in lobbying it is willing to spend up to c to stop taxation. For argument’s sake let’s say that a company spent c on lobbying were successful. Success to the company means that the market stays at the inefficient point and social welfare is not maximized. However the company spent an extra cost c to do this, so what happened to that? Well that amount c went to the lobbying company and its employees. Therefore instead of the company allowing the extra money c to be spent on social welfare it made a few people rich.

This blog has gone through some of the basic economic principles of supply-demand, externalities and taxation. It has then used these concepts to view lobbying in an economic framework.  I hope you found it interesting!

## One thought on “To lobby or not to lobby: How to decide whether you should manipulate your government”

1. I thank you because the article has told me something new. I really didn’t know this lobbyist acting as a mouthpiece for people and using their communication skills and legislative knowledge to influence people in power. The way you explain is very easy to understand.