Marginal rate of substitution, topics

Summary

• $MRS$ for perfect substitutes is constant, independent of $x_1$ and $x_2$
• $MRS$ for perfect complements is either $0$ or $∞$ or undefined
• With (strictly) convex preferences:
• $MRS$ (strictly) increas ing in $x_1$
• $\left| MRS \right|$ (strictly) decreas ing in $x_1$
• We have (strictly) d iminishing marginal rate of substitution (ignoring sign)