Wine productivity per farm size: A maximum entropy application

The size of a farm is one of the factors that influence its productivity, in an ambiguous relationship that is often discussed in the industrial economy. In Portugal, the Demarcated Douro Region (DDR) is characterized by very small farms. Usually, this trend is considered a limitating factor in the profitability of the wine farms. In order to assess the correctness of this sentence, the variation of wine productivity per land size, from 2010 to 2016, was studied in the DDR, considering its three distinctive areas: Baixo Corgo, Cima Corgo and Douro Superior. The farms were categorized in nine different size ranges; as these variables outnumber the available seven observations, the Generalized Maximum Entropy (GME) estimator was used, since it suits the need to solve an ill-conditioned problem. GME was applied with the MATLAB (MATrix LABoratory) software along with the Bootstrap technique. According to the simulations, larger farms (with an area greater than 20 ha) on Douro Superior and Cima Corgo reveal higher marginal productivity given the current state of the region. On the other hand, Baixo Corgo's results suggest that medium-sized farms (with area ranges between 2 and 5 ha) display higher marginal increments to the region wine productivity.