Inthis article, we propose a new class of production functions in the new classicaltheory of economics and study its qualities based on Euler’s relation ofquasi-homogeneous functions. In a market economy environment, it is crucial toestablish a firm’sprofitability and draw conclusions about the operation and to make a variety ofassumptions using a function that is more consistent with reality in thefuture. We showed that the quasi-homogeneous function is a general form of thewell known production functions such as Cobb-Douglas and Constant Elasticity ofSubstitution (CES). We have made some qualitative and quantitative analysis andcompare our results with the classical models using statistical data of Japan.
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