Modelling Price Discovery in an Agent Based Model for Agriculture in Luxembourg

Abstract

We build an ABM for simulation of incentives for maize to produce bio-fuels in Luxembourg with an aim to conduct life cycle assessment of the additional maize and the consequent displacement of other crops in Luxembourg. This paper focuses on the discovery of market price for crops. On the supply side we have farmers who are willing to sell their produce based on their actual incurred costs and an expected markup over costs. On the demand side, we have buyers or middlemen who are responsible for quoting prices and buying the output based on their expectation of the market price and quantity. We have N buyers who participate in the market over R rounds. Each buyer has a correct expectation of the total number of buyers in each market. Thus in each round, the buyer bids for a quantity $q_b^r=\frac {Q_b^e}{N \times R}$, where $Q_b^e$ is the expected total output of a crop. The buyer at each round buys $\min (q_b^r,S_t^r)$, the minimum of the planned purchase at each round r and the total supply $S_t^r$ by farmers in the round at a price $p_b^r$. The market clears over multiple rounds. At each round, the buyers are sorted by descending order of price quotes and the highest bidder gets buying priority. Similarly the farmers are sorted according to the ascending order of quotes. At the end of each round, the clearance prices are visible to all agents and the agents have an option of modifying their bids in the forthcoming rounds. The buyers and sellers may face a shortfall which is the difference between the target sale or purchase in each round and the actual realised sale. The shortfall is then covered by smoothing it over future rounds (1–4). The more aggressive behaviour is to cover the entire shortfall in the next round, while a more calm behaviour leads to smoothing over multiple (4) rounds. We find that there is a statistically distinct distribution of prices and shortfall over smoothing rounds and has an impact on the price discovery.