Implementation of a mathematical model derived from the Douglas Cobb function for the evaluation of coffee exporters in Honduras

Abstract

The international price of coffee and climate change are factors that affect the profits of coffee farms in Honduras. The international price reduces profit margins when it is too low, while climate change puts coffee production at risk. Coffee farmers must decide how they will process their coffee each year whether it will be exported or sold to the domestic market. In this work a method is proposed to calculate the optimal point for export and coffee for sales in the domestic market. This method relates the COBB Douglas production function and the lagrange optimizer. The main result was the application of the model to a coffee exporter with its budget line having a general distribution of 98.3% with 1.6%. It was shown that it is possible to use the logarithmic demand curve to obtain the parameters α y β of the production function. The Katz & Kan model of coffee we can observe the abstract process of the market in which the demand is found, where consumers who may or may not change their consumption habits affecting the profits of coffee companies The mathematical model showed that the percentage of coffee for local consumption increases as the budget decreases. However, export coffee is never less than local consumption coffee because the Honduran domestic market cannot assimilate all the coffee.