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How to build a numerical model III: Which model type to choose?

Now learn when to choose which type of model: optimizations and equilibrium approaches.
6.3
Now that we have a first understanding of the two modeling approaches, the natural follow-up question is, which type should I choose? Well, that’s a tricky question. The good thing is, that often both model types can be transferred into each other and are thereby equally fitted for your model. Naturally, there are plenty of computational reasons to choose one or the other. We will cover those in the second week on numerical modeling. The clearest indication for a specific model type is the number of objectives. When you have more than one value you would like to optimise but can’t simply add them up, equilibrium approaches are the way to go. OK.
56.1
Those were the unspecific comments and may not be really helpful when you are tasked to transfer a specific real-world market into a reasonable model. So a good approach to start with is to follow your own style of thinking. As optimizations and equilibrium approaches are highly interlinked anyway, you may tend to see your problem in one way or the other.
83.3
Let’s visualise this with a simple example– the case of perfect competition. If the first thing that springs to your mind when you hear perfect competition is that it maximises welfare, well, here you
97.8
go: Optimisation it is. Recalling the video on optimisation models, we will need an objective. In this case, clearly the welfare needs to be maximised. Welfare can be calculated by taking the overall gross consumer benefit, the integral, and subtract total production costs. In addition, we need the same constraints as in the simple optimisation example. Production has to account for capacity limits and overall production needs to satisfy demand.
134.4
Now, if the first thing that springs to your mind is not welfare maximisation but that price equals marginal costs in perfect competition, then you’re also right. But this time, you think in equilibrium terms. Using this logic, we have different market actors. On the one side, there are producers that follow the marginal costs equals price logic we already used in the simple equilibrium example. On the other side of the market, we have consumers following the same given price-demand relation we used in the optimisation case. If the market price P equals their willingness to pay, given by the function P of D, they will consume the respective amount D. If the price is above their willingness to pay, they won’t consume.
186.6
Now we need to bring the two market sides together, which was basically the market balance of supply and demand. This formulation will provide the same outcome as the optimisation problem. So feel free to start your model following your initial intuition about your real-world problem.

Often the optimization and equilibrium approach can be transferred into each other and are thereby equally fitted for your model.

Naturally, there are plenty of computational reasons to choose one or the other. The clearest indication for a specific model type is the number of objectives. When you have more than one value you would like to optimize but can’t simply add them up, equilibrium approaches are the way to go.

As optimizations and equilibrium approaches are highly interlinked anyway, you may tend to see your problem in one way or the other.

So feel free to start your model following your initial intuition about your real world problem!

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Exploring Possible Futures: Modeling in Environmental and Energy Economics

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