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.

  • 3
    $\begingroup$ 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. $\endgroup$
    – Bayesian
    Commented Jan 6, 2021 at 14:04

2 Answers 2


One that was not mentioned in question is the quadratic utility (aka preference for extremes):

$$U(x,y) = x^2+ y^2$$

This one is less common but still used in micro courses.


Square root utility : $ U (x,y) = \sqrt{x+y} $

  • 5
    $\begingroup$ Which is I guess perfect substitutes $U(x,y) = ax+by$ with $a=1$ and $b=1$ by positive monotone transformation $h(z) =\sqrt z$. $\endgroup$ Commented Jan 6, 2021 at 15:20

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