This has been a tough chapter with some complex mathematics and economics. So let’s recap the most important take home messages for this chapter.

First, we have examined more detailed aspects of designing equilibrium models and their linkage with optimization models. Remember, many problems can be addressed with both model types, so you can use the one you are more comfortable with. As the basic design of equilibrium models aims to represent the underlying incentive structure of the different market actors, a solid understanding of economics is helpful when designing them and a good understanding of equilibrium modelling can help you to interpret your model results (also optimization models!).

Second, we moved from the first-best models of the previous chapters into the challenges of modelling real world market imperfection – the second-best approach. We have added monopolies and oligopolies to the modelling world and seen how changing the level of competitiveness can alter the results of policy choices. Often you will have to live with the trade-off between an increasing complexity of your policy design to overcome all caveats of the underlying market or accept some imperfections and inefficiencies while keeping the policies reasonable.

The different forms of competition (perfect, monopoly, and oligopoly) also provide you with a set of market designs to test the robustness of your policy ideas. If a policy works as intended under perfect competition but fails in other markets it may not be the best solution to go for. And the setup also provides you with a good roadmap for designing your more complex models: start with a simple perfect competitive model first and add the complexities of strategic competition afterwards. You will not only learn a lot about the economic aspects of your problem but also more likely get to know your model better this way.

We now have finalised the toolkit on model designs and toolkits for this course. There are plenty of more modelling aspects and challenges left, but the concepts of optimization and equilibrium, system and market perspective, building blocks, first-best and second-best covered in the last three chapters should provide you with a solid backpack to climb larger modelling mountains.

We also extended on the model solving aspects by going into detail on optimization and equilibrium modelling and their relation. By doing so, we had a first look at how to interpret your model findings and what they mean from an economic perspective.

We are not done yet. We will extend on the model solution and interpretation aspects in the upcoming chapter and also provide some hands-on recommendations for your model coding and data handling. But most importantly, we will finally explore the possible future of our little example market. Will you make it a fossil one or a green one? And what will it cost you?