N-M Utility Theory is the first theory in microeconomics that introduced risk and uncertainty in the demand analysis. Neumann and Morgenstern introduced risk and uncertainty in demand analysis. They introduced a completely new concept in consumer behavior analysis in Theory of Games and Economic Behavior (1944).

According to Encyclopedia Britannica (2018), “N-M Utility shows that when a consumer is faced with a choice of items or outcomes subject to various levels of chance, the optimal decision will be the one that maximizes the expected value of the utility (i.e., satisfaction) derived from the choice made.” [1]

They argue that the earlier theory of demand analysis are static in the sense that they do not incorporate risk and uncertainty in explaining the consumer behavior as these theories take is granted that outcome or result is certain.

However, in reality, an individual faces the situation of risk and uncertainty and has to make a certain decision in such a situation. So, Neumann and Morgenstern developed a theory to explain the consumer’s behavior during the risky and uncertain situation.

According to this theory, the outcome is not certain, but they can be expected with a certain probability of occurrence. So, the consumer is not the actual utility maximizer rather try to maximize the expected utility of an event.

According to Neumann and Morgenstern for a rational individual, we can construct a utility index and based on the index we can say whether the individual is a risk taker, risk avoider or risk neutral.

So, this theory integrates the theory of probability with the utility and examines the individual’s behavior in risk and uncertainty.

### Assumptions

- Individuals make a decision in amidst of risk and uncertainty
- An individual always tries to maximize expected utility.
- The choices are transitive.
- Probability of occurrence of an event lies between 0 to 1.
- The individual prefers the lottery ticket with a higher probability if two lottery tickets offer the same prize.
- The consumer is expected to be able to rank the items or outcomes in terms of preference, but the expected value will be conditioned by their probability of occurrence.

### N-M Utility Index

Neumann and Morgenstern suggest the following procedure to develop a utility index for an individual.

**Step I: Identify the possible outcome of the event**

Let there is a lottery ticket with a price of Rs. 10000 for a winner and no other prizes.

Winner (W) = Rs. 10000

Looser (L) = Rs. 0

**Step II: Estimate the probability of occurrence of each outcome**

Let the probability of winning be 70 percent and 30 percent be losing probability.

P (W) = 70 percent

P (L) = 30 percent

**Step III: Assign the utility for each outcome arbitrarily**

Let the utility derived from winning be 100 utils and utility from losing be 0.

Utility (W) = U (Rs. 10000) = 100 utils

Utility (L) = U (Rs, 0) = 0 utils

**Step IV: Calculate the expected utility of the outcome**

E (U) = P (W) X U (W) + P (L) X U (L)

= 0.7 X 100 + 0.3 X 0

= 70 utils

**Step V: Find certainty equivalent**

Certainty equivalent is the certain sum of money that an individual is ready to pay for the lottery ticket with the said probability and prizes. This is obtained by asking the individual how much money he or she is ready to pay for the ticket. Let the individual who says that he or she is ready to pay Rs. 500 for the ticket, then it is certainty equivalent. It is assured that this certainty equivalent has the same utility as of the lottery ticket.

Therefore, U (500) = 70 utils

Income |
Utility |

0 | 0 |

500 | 70 |

10000 | 100 |

There is a utility index and if we repeat the question to the same individual altering the probability and outcomes, we get a complete list of certainty equivalent and a complete N-M Utility index for the individual. The general form of the N-M Utility index can be written as:

Income |
Utility |

I_{1} |
U_{1} |

I_{2} |
U_{2} |

… | … |

I_{n} |
U_{n} |

Based on this utility index, we can say that individual is either risk taker if the marginal utility of money is increasing or risk averter if the marginal utility of money is decreasing or risk neutral if the marginal utility of money is constant.

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# References

Chand, S. (2018). *Theory of consumer choice under risk in economics*. Retrieved from http://www.yourarticlelibrary.com/economics/theory-of-consumer-choice-under-risk-in-economics-managerial-economics/28614

[1] Encyclopedia Britanica. (2018). *Von Neumann–Morgenstern utility function*. Retrieved from https://www.britannica.com/topic/von-Neumann-Morgenstern-utility-function

Katuwal, Khagendra. (2018). Neumann – Morgenstern Theory [Class Handout]. Department of Economics, Tribhuvan University, Kathmandu

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