# Utility function for introductory microeconomics

What are the utility functions standardly used in introductory microeconomics courses. My own list would include

1. Perfect substitutes: $$U(x,y) = ax+by$$
2. Perfect complements: $$U(x,y) = \min(ax,by)$$
3. Cobb Douglas: $$x^\alpha y^{1-\alpha}$$
4. Quasi-linear: $$x + y^\alpha$$
5. CES: $$U(x,y) = (x^\rho+y^\rho)^{1/\rho}$$

Anyone else that would be typically included?

EDIT: To be more specific I am primarily interested in different types of preferences not positive monotone transformations of the above specifications.

• The same preferences can also be expressed by other utility functions that are a positive monotone transformation. Such as the $\alpha \log x + (1-\alpha) \log y$ for Cobb-Douglas. – Bayesian Jan 6 at 14:04

$$U(x,y) = x^2+ y^2$$
Square root utility : $$U (x,y) = \sqrt{x+y}$$
• Which is I guess perfect substitutes $U(x,y) = ax+by$ with $a=1$ and $b=1$ by positive monotone transformation $h(z) =\sqrt z$. – Jesper Hybel Jan 6 at 15:20