Over the past year(s), government’s aggregate expenditure has been less than its aggregate expenditure the present year(s) in Nigeria and Ghana. This has made the government size of these economies big enough to command a significant economic growth in these countries, but this is not the case in these countries. This work adopted a concave parabolic model from the origin which portrays the Armey curve model to empirically validate not only the existence of Armey curve hypothesis but also to fond the optimizing government expenditure of Ghana and Nigeria, using time series data from 1970 to 2014. The result showed that Armey curve hypothesis exists both in Nigeria and Ghana. However, the result shows a strong statistical influence of Armey hypothesis in Nigeria than in Ghana. Adopting the Relative Maxima methodology, the Government of Nigeria and Ghana should spend and 9.8 respectively, of her gross domestic product (GDP) to attain the optimal growth of ?9.96 Trillion Naira and ?6.422 million respectively. The researcher recommends that these governments should cut down their expenditure to the optimizing size of their governments so as to grow effectively and efficiently which is a macroeconomic goal of every economy.
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