Certainty Equivalent
What is Certainty Equivalent?
The certainty equivalent is the guaranteed amount of money that gives a person the same utility as a risky gamble.
The certainty equivalent converts a gamble into a single sure dollar figure the decision maker would accept in its place. You find it by computing the gamble's expected utility, then asking what guaranteed wealth produces that same utility level, which means inverting the utility function. For a risk-averse person the certainty equivalent is below the gamble's expected value, and the difference is the risk premium. A risk-neutral person's certainty equivalent equals the expected value exactly, and a risk-loving person's sits above it. The measure is useful because it puts risky and safe options on one scale in dollars, which is how firms compare an uncertain project against a guaranteed contract.
Certainty Equivalent: a worked example
A contractor faces a project worth $2,500 if the permit is denied and $8,100 if it is approved, each equally likely. With utility equal to the square root of wealth, the two outcomes give utilities of 50 and 90, so the expected utility is 0.5 × 50 + 0.5 × 90 = 70. The wealth whose square root is 70 is 70 × 70 = $4,900, so the certainty equivalent is $4,900. The expected value is 0.5 × $2,500 + 0.5 × $8,100 = $5,300, so the contractor would accept a guaranteed $4,900 contract instead, sacrificing $400 to remove the uncertainty.
The mistake students make with certainty equivalent
Students often set the certainty equivalent equal to the expected utility number itself. Expected utility is measured in utils, not dollars; you must run it back through the utility function to get a dollar amount. With the square root of wealth, an expected utility of 70 becomes a certainty equivalent of 70 squared, not $70. Squaring or otherwise inverting the function is the step people skip.
Certainty Equivalent questions
How do you calculate a certainty equivalent?
Compute the gamble's expected utility, then find the sure wealth level whose utility equals that number by inverting the utility function. With square-root utility that means squaring the expected utility; with other functions you undo whatever operation the function performs. The answer comes out in dollars, which is what makes it comparable to a sure offer.
What does a certainty equivalent tell you about someone's risk preferences?
Comparing the certainty equivalent to the expected value reveals the person's attitude toward risk: below means risk averse, equal means risk neutral, above means risk loving. The size of the gap measures how strongly they feel, since a bigger shortfall means a larger risk premium. Two people facing the same gamble can have very different certainty equivalents.
Where is the certainty equivalent used in practice?
Firms use certainty equivalents to compare a risky project against a guaranteed alternative on a single dollar scale. Insurance runs on the same idea, since a risk-averse buyer will pay more than the expected loss because the certainty equivalent of bearing the risk alone falls short of its expected value. The logic also explains why many workers accept a lower guaranteed salary over commission pay with a higher average.
Formula / Example
Related terms
Common comparisons
Get AP Econ exam tips in your inbox
Occasional emails with study tips, new interactive graphs, and exam-season reminders. Free, no spam.
No spam. Unsubscribe anytime. Read our privacy policy.
Keep track of what you have studied
A free EconLearn account adds progress tracking, your quiz history, and achievements. Studying here is free either way, and there is nothing to pay for as a student.
Create a free accountAlready have one? Sign in
Last updated