Now that you have learned about all the elements needed to design sophisticated models, it is time to put those pieces together to have a look at possible futures.

Let’s start with a problem. As this course is named ‘Exploring Possible Futures’, we will make this our driving research question for the last model: what are possible future developments for our little example market?

Before deciding what type of model to use, think about how many possible layers of detail the research question still leaves open: are you only interested in the future or also in the path towards this future? What are your ‘choice variables’: costs, market prices or policies? And what policies would be the ones to include? What level of competition does your market possess?

All those follow-up questions help you to decide which model design to choose. This is the iteration between the problem and model phase we mentioned throughout the course.

For our final model example we have chosen to test the policy choices we discussed in the last chapters, namely CO₂ taxes, nuclear premiums, and renewable subsidies. We will keep the model in the first-best world and stick with a competitive market framework. Namely, we will rely on the model discussed at the end of chapter 3, the first model exercise with a responsive demand.

Now we have a research question and a basic model layout. However, there isn’t much future development involved yet. The model of chapter 3 was just a one period model. To analyze the future you could adjust the underlying data to represent future expectations (eg, change the investment costs or fuel prices according to your assumption on future developments). That is the simplest way of setting up a ‘future’ model.

Let’s go a step further and aim to not only look into the future but link it to decisions we make today. There are again multiple ways how such a dynamic system can be modelled. For example, you could add a further model index to account for the flow of time (eg, years) and link each period with its preceding periods (eg, the capacity in year, $$t$$, is equal to the capacity in the previous year, $$t - 1$$, plus any additions, minus decommissioned units).

For our final model example, we follow this approach but implement it in a more simplified way: we design two individual models; one for today, one for the future, where the data input for the future-model depends on the results of the today-model. Namely, we assume that renewable investment costs will decrease in the future. The actual extent of this decrease will depend on the amount of renewables utilised today.

All other future parameters (demand dynamics, fuel costs, investment costs for fossil and nuclear plants) are unchanged. This allows us to trace back the future developments to the choices you will make (CO₂, nuclear and renewable levels) and the renewable cost decrease.

The implementation is rather simple: the today-model is equivalent to the model of chapter 3 and solved for your choice variables. Given this market result the output of PV ($$q_{PV}^{today}$$) and wind ($$q_{wind}^{today}$$) generation is then used to calculate the future costs:

---

$$c_i (q_i )=α_i \cdot q_i+\frac{β_i-ηq_i^{today}}{2} \cdot q_i^2$$

---

The total costs for wind or PV generation again increase more than proportionally with production. However, the increasing cost block is now adjusted for today’s renewable output with $$η$$ representing how large the impact of today’s output on future cost levels is. As today’s output ($$q_i^{today}$$) is known and fixed in the future, it is treated as an external variable for the model; in other words, we only adjust the cost parameters for the future model.

Now we have all the pieces together for an interesting model with some hopefully equally interesting results.