SECOND-BEST WORLDS
4.6
First-best or second-best: coping with realities
Do you remember our discussion of firm behaviour from the last chapter? There, we have assumed that our firms behave competitively, that is, they take prices as given and do not try to manipulate markets to their advantage.
Unfortunately, this is a rather optimistic view of most energy markets. In particular, for electricity we often have one (or a few) big suppliers that are able to influence prices. In this step, we will use this example to highlight a crucial difference in designing energy and environmental policies, whether you aim for a first-best or a second-best outcome.
Let’s start with a first-best case. For this, take the equations that you have used in the last chapter to describe firm behaviour in the Output Abatement Choice Model (OACM) model:
(1)
(2)
(3)
Equation (1) represents each firm’s optimization problem and equations (2) and (3) are the necessary conditions for optimality resulting from this problem (excluding corner solutions).
These equations describe what a firm will do. However, how do you know whether this behaviour is good or bad from a societal perspective? In chapter 2, we have introduced the concept of social welfare to this end. In the OACM model with
(4)
The first term,
A benevolent dictator would maximise equation (4) with regard to output and abatement for all firms. Doing this for firm
(5)
(6)
Where
If you compare (2) and (5) as well as (3) and (6), you see that these equations become equal, if you set
This calculation has several remarkable implications. First, you have two decision variables (production quantity and abatement) for each firm (altogether
These are rather strong results for a comparatively simple model. Furthermore, they nicely highlight what constitutes a first-best solution: you can achieve the best possible outcome, social welfare is maximized. In fact, by implementing a policy, you can align the interests of all firms in the economy with societal objectives. If the tax is chosen correctly (ie,
This holds in the benign situation where firms have no market power. Let us for a moment assume that this is not the case. Instead, assume that we only have a single firm, that is, a monopolist. What would this firm do?
A monopolist would maximize his profit taking into account the willingness of consumers to consume at different prices. Thus, we would integrate the inverse demand function,
(7)
(8)
(9)
Again, you have described the maximisation problem in equation (7), and then you derived the necessary conditions from it. The term
Comparing (2) and (8) as well as (3) and (9) shows that there is no value of the tax,
This is typical for a second-best solution: you cannot achieve the best possible outcome but have to choose among less desirable ones. The reason is that the monopolist already produces too little to keep prices up. Thus, taxing the monopolist with the Pigouvian tax,
So, you have to compromise: setting a tax that is somewhat lower than the Pigouvian tax will usually be the best that you can do.
This is a typical situation in most real world problems. We are faced with more problems (market power and emissions, in your example) that we can cope with in terms of policy instruments (you only have a single instrument here). Therefore, we have to make a compromise and accept some welfare losses. It is still possible to increase welfare by introducing a tax but not up to the theoretical benchmark of the first-best solution.
Of course, this is a rather formal argument. What you should take out here is that there are two approaches to environmental and energy policy:
- You can try to achieve the best possible outcome. But to this end, you will typically need a rather complex policy (if you want, you might think about what additional policy instrument could be used to achieve the first-best outcome in the market power case). This is a first-best approach.
- Or, you can accept some welfare losses and make do with the insufficient policy instruments that you have. You still can do some good, but the scope is more limited. This is a second-best approach.