Let x be a payoff amount in dollars. Let U(x) be a continuous,increasing function of x.
The function U(x) gives an individual's level of satisfaction in fictional "utils" from receiving payoff amount x, and is known as a utility function.
If a certain payoff of $25 is preferred to the gamble,(due to risk aversion) then we want a utility function that satisfies:
U($25)> .25 U($100) + .75 U9($0)
The left hand side is the utility of the certain payoff and the right hand side is the expected utility from the gamble.
Any concave function U(x) will work. for example U(x)= SR (x)
(my SR =square root)
SR(25)>.25 SR(100) +.75 SR(0)
5>2.5
End of copy
I figured(probably wrong) that for the left side to equal the right it would be 400.