Determinación del umbral de pobreza en Guanajuato: un enfoque innovador mediante la ley de Engel y el criterio de la segunda derivada

The objective is to determine the poverty threshold in the state of Guanajuato using Engel's law, which relates household income and food expenditure (FE) as variables. This income represents what families need to earn in order to escape poverty. The method employed is based on Engel's law to determine the cubic function with income and FE as variables. To solve the cubic function, the second derivative criterion and the inflection point were used. This approach contributed to the traditional method, yielding a monthly income of $11 889.83 Mexican pesos. Additionally, by calculating the inflection point, the monthly food expenditure was determined to be $6565.40 Mexican pesos. This finding made it possible to observe the correlation between income and FE using the cubic function, obtaining the FE value which was traditionally not calculated.