The paper deals with two specific types of utility functions displaying decision maker's risk aversion at expressing the utility of monetary values. These functions are following: w(c) = 1 - e-x/R, u(x) = ln(x + R), where x is a monetary value and R is a constant expressing the degree of risk tolerance. Basic properties of the above mentioned functions and formulas for calculations of certainty equivalents and risk premiums are derived. Some properties of the analyzed functions are numerically and graphically illustrated by concrete examples.