In Kenya there are obstacles to access to information at the county level which include among other issues-Language barrier. This has impeded public participation hindering county development. This is augmented by Kenya Institute of Economic Affairs report, World Bank report and First Devolution Conference report. The financial jargon used in Homa Bay County’s budget discourse texts hinders public participation which has formed a communication breakdown between the county government of Homa Bay and the public. Findings on Discourse Analysis from various linguists do not explain “discourse exclusion”, a peculiar case where the county government and the people are constitutionally mandated to engage in a discourse but fails to do so due to relevance. This research article looked into processing effort at both lexical and phrasal levels in order to analyze the processing effort at both the lexical and phrasal levels of the financial budget discourse texts of Homa Bay County Government. Theory used is Relevance Theory (Sperber &Wilson,2004)whose tenets include; cognitive effects, processing effort and contextual assumptions. The study used descriptive design; the research area is Homa Bay County Kenya. The population includes 428,911 persons who had attained the voting age of 18 years and budget discourse texts between 2014 and 2016.Snowballing was used to sample 43 members of the public, and 20 linguistic items that formed the budget discourse text between 2014 and 2016.Data collection techniques involved; use of questionnaires, structured oral interviews, tape recording and content analysis of available documents. Data analysis was done thematically and presented in textual and tabular forms and in line with literature and theory used; descriptive design was used. Findings show that phrasal processing effort is cognitively more involving than lexical processing effort. The study is significant in building pragmatic theories, editing and enhances public communication mechanisms for the wider economic development.