Editing Marginal rate of substitution (section)

==Using MRS to determine Convexity==
When analyzing the utility function of consumer's in terms of determining if they are convex or not. For the horizon of two goods we can apply a quick derivative test (take the derivative of MRS) to determine if our consumer's preferences are convex. If the derivative of MRS is negative the utility curve would be concave down meaning that it has a maximum and then decreases on either side of the maximum. This utility curve may have an appearance similar to that of a lower case n.  If the derivative of MRS is equal to 0 the utility curve would be linear, the slope would stay constant throughout the utility curve. If the derivative of MRS is positive the utility curve would be convex up meaning that it has a minimum and then increases on either side of the minimum. This utility curve may have an appearance similar to that of a u. These statements are shown mathematically below.
:<math>\ \frac{dMRS_{xy}}{dx}<0 \text{   Non Convexity of Utility Function}</math> 
:<math>\ \frac{dMRS_{xy}}{dx}=0 \text{   Weak Convexity of Utility Function}</math>
:<math>\ \frac{dMRS_{xy}}{dx}>0 \text{   Strict Convexity of Utility Function}</math>

For more than two variables, the use of the Hessian matrix is required.