In most cases, computational models of biochemical reaction networks are described using time-dependent ordinary differential equations (ODEs). However, to obtain the cellular response when the system is in a steady state, which is closely relevant to various crucial phenotypic events, ODEs can be converted to time-independent algebraic equations. By exploiting the solutions of the equations, the relationships between the strength of an extracellular signal and the magnitude of the cellular response (i.e., the stimulus/response relationship) are obtained. In this study, we investigated the dependence between the number of solutions (the multistability) of the equations and the gradient of the inflection point (steepness) of the stimulus/response curve on a kinetic parameter space, which was defined by the ratios of the catalytic efficiency (referred to as λ1 and λ2) of bi-connected elementary cellular reaction cycles, composed of a substrate and two enzymes. As a result, we found that, when λ2 was initially small and then increased (λ1 was fixed), the steepness also increased, leading to the monostability to bistability transition. This was the case with the λ1 axis, although, when λ1 increased (λ2 was fixed), the steepness decreased, resulting in the bistability to monostability transition. This is the first report to systematically show that the steepness is closely correlated with the stability of the elementary cellular reaction systems. Furthermore, the effects of a positive feedback loop (PFL) upon the responses of a bi-connected elementary reaction cycles were investigated by exploring the stability of the steady state equations. We found that the origin of the bistability to monostability transition, which had not been found previously, was the significantly lower Michaelis-Menten constant in the PFL, leading to the sequestration of the substrate through the tight binding of the enzyme and substrate.