How to build a numerical model II: Balancing the world

Contrary to an optimization problem, an equilibrium model has no objective but consists of the respective conditions that need to hold when the market or system is in equilibrium, meaning in a stable state. As explained in the tutorial, there are two general equilibrium conditions we need to account for: zero-profit conditions and market clearing conditions. Both conditions follow a simple logic: what economic incentives drive the behaviour of the market participants?

In case of the zero-profit condition the underlying question relates to the activity of the involved market actors: what incentivizes an actor to become active (ie produce or consume a good)? It’s the obtainable benefit! A firm will start to produce if the price it can get for its product is at least as high as its production costs. The firm will stop increasing its production when the price equals its production costs (at least in a perfect competitive market) → the condition is in equilibrium.

In case of the market clearing conditions the underlying question relates to the basic economic principle of supply and demand. If a market is undersupplied (supply < demand) the resulting high price will give producers an incentive to increase production (via the zero-profit condition) up to the point where the market is in equilibrium (supply = demand). If the market is oversupplied (supply > demand) the product has no value, as there are excess supplies available. The market at hand does not need to be a ‘real’ market; ie also production constraints represent a supply (available production capacity) and demand (requested output) logic.

Equilibrium models are flexible designs suited for a large variety of model applications. Generally two types of equilibrium models are distinguished: partial equilibrium models that capture only one or a subset of markets/sectors while prices and quantities on other markets are taken as given; and general equilibrium models that capture the whole economy with many interacting markets/sectors. The latter is the main approach in top-down modeling; termed computable general equilibrium (CGE), while the former is used for bottom-up models. In general, equilibrium models are the first choice when deviating from perfect competition or monopolistic competition in a market setting.

Recommended readings:

In the literature recommendation below, you find a combined natural gas and electricity market model (Abrell and Weigt, 2010). As natural gas is a fuel input in electricity generation the two markets present a classical example of upstream and downstream markets. In addition both markets rely on networks introducing spatial components into the market design. The paper at hand provides a comprehensive design of both markets. As we did not yet cover the mathematical functionalities of equilibrium models or the interplay with optimization models you may want to focus on the above described decision conditions for zero-profit constraints and market clearing.

Abrell, J., & Weigt, H. (2010). Combining energy networks. Dresden University of Technology, WP-EM-38 (Journal Version: Abrell, J., & Weigt, H. (2012). Combining energy networks. Networks and Spatial Economics, 12(3), 377-401)