Neuromorphic circuits have recently emerged as promising candidates for future computing paradigms. Min-Max circuits are indispensable building blocks in many neuromorphic systems, fuzzy systems and artificial neural networks. An important challenge in the design of state-of-the-art min-max circuits is their area occupancy. Memristor-based min-max circuits have been sought as powerful candidates in the design of min-max circuits due to their miniaturized size. An important characteristic of the memristor is the existence of a Voltage/Current threshold. This threshold places constraints on the values of the input voltages to the circuit. More importantly, these constraints vary with the size (i.e., the number of inputs to the circuit) of the min-max circuit. In this work, the effect of the memristor threshold on memristor-based min-max circuits is modeled. It is shown that for a given memristor with a specified threshold current and Off resistance, there exists a trade-off between the size and the resolution of the circuit (i.e., the larger the size of the circuit, the lower the resolution becomes). All results are validated against Spice simulations by Eldo from Mentor Graphics using the TEAM model.