Friedman-Savage hypothesis: A clear outlook5 min read

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The Friedman-Savage hypothesis is the improvement in Neumann-Morgenstern hypothesis. Friedman and Savage hypothesized that any individual can be risk-averter or risk-taker which depends on the level of income. In other words, the curvature of the individual’s utility functions depends on the amount of wealth the individual has[1].

According to them, if the level of income is below the minimum threshold, then the consumer is risk averter; within a certain range of income (above the minimum threshold), the consumer is risk taker; similarly, after the certain level of high income, the consumer is risk averter.

It means the same individual can be either risk taker or risk averter based on the level of income.

Friedman-Savage hypothesis

The figure shows the different behavior of an individual regarding the risk-taking activities under a different level of income. If the individual has less than M1 income then the marginal utility of money is decreasing which means the individual is risk averter.

If the individual has an income between M1 and M2 the marginal utility of money is increasing and, hence the individual becomes a risk taker. If the income level is higher than M2, the individual is risk averter.

This shows the different behavior of the same individual at a different level of income. This also represents a real behavior of the different income group people in society.

The low – income people are generally risk averter because they are busy in the activities just to join hand to mouth. So, they neither have sufficient income to invest in risky business nor they have an idea and time to think for.

Similarly, the rich people have already a sufficient level of income and assets, so they want to avoid risk by choosing less risky activities.

It is the middle-income group of people who want to graduate from middle-income to high-income group at any time that motivates them to be engaged in risky business or activities.

Why do people buy insurance and gamble (buy lottery tickets) at the same time?

The Friedman-Savage hypothesis is the extension of N – M Utility hypothesis. Neumann and Morgenstern introduced risk and uncertainty in demand analysis.

According to Friedman-Savage hypothesis, an individual is risk averter when the marginal utility of money is diminishing, risk taker when the marginal utility of money is increasing, and risk-neutral when the marginal utility of money is constant.

Furthermore, they suggest that an individual can be either risk averter or risk lover, but cannot be either risk-averter or risk-lover at the same time.

Friedman-Savage hypothesis proclaimed that an individual might be risk-taker or risk-averter at the same time depending upon the level of income he or she has. Thus, an individual tends to buy insurance when he or she has less wealth; and the same individual gets to indulge in gambling when he or she has high wealth accumulation. We can illustrate the Friedman – Savage hypothesis through the figure.

Friedman-Savage hypothesis

The figure reveals the total utility curve, which consists of both concave and convex curves. X-axis measures income and Y-axis measures total utility.

The utility curve is increasing at a decreasing rate up to F; the utility curve is increasing at the increasing rate from F to K. The curvature of the total utility function depicts the nature of the individual, that is, risk-taker or risk-averter. Let us suppose that income from the house is ‘OF’ and the utility derived from OF income is FF1.

If the house is brought down by an earthquake or any natural calamity, then the income shrinks to OA with the derived utility of AA1. Further, joining A1F1 we get utility points between two unforeseen circumstances. If the probability of no fire is P, then the expected income is:

Y(E1) = P (OF) + (1-P) (OA)

Let us assume that Y(E1) = OE. The utility derived from the OE, the expected income, is E1E, where E1 lies on the line A1F1. Accordingly, if DF is the amount of insurance premium, then the certain sum of money obtained by the individual is OD (OF – DF). The utility from OD income is DD1, which is higher than the expected income OE. Hence, it is lucrative for an individual to buy insurance.

Out of the total income of OD, an individual buys a lottery ticket worth BD income. If an individual wins the lottery then he or she attains the income level of OK with the derived utility of KK1, and if he or she does not win the lottery, then his or her income falls to OB with the derived utility of BB1. If we join B1K1, we obtain the utility points.

Let us assume that P’ be the probability of not winning, then the expected income of not winning the lottery is:

Y(E2) = P'(OB) + (1-P’) (OK)

If the expected income Y(E2) is equivalent to OC, then the derived utility will be CC1, where C1 lies on B1K1.

With the rising marginal utility of money, which depends upon the curvature of the total utility function, the risk-taking propensity of individual increases.   Thus, if OG is the expected income, then the expected derived utility is GG1.

We have obtained the expected income of OC and OG with their respective derived utility of CC1 and GG1; both the derived utilities are greater than DD1. Thus, an individual buys lottery tickets also.


Chand, S. (2018). Theory of consumer choice under risk in economics. Retrieved from

Friedman-Savage hypothesis | Marginal Revolution University

Friedman-Savage hypothesis | Chicago University

Friedman-Savage hypothesis | JSTOR

Katuwal, Khagendra. (2018). Friedman-Savage hypothesis [Class Handout]. Department of Economics, Tribhuvan University, Kathmandu

[1] Wikipedia. (2018). Friedman–Savage utility function. Retrieved from


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