# Utility Theory: Expected & Marginal

Instructor: James Walsh

M.B.A. Veteran Business and Economics teacher at a number of community colleges and in the for profit sector.

This lesson will explain expected utility theory, which is used as a tool for making decisions under conditions of uncertainty and marginal utility, which quantifies the satisfaction obtained from consuming additional units of a product or service.

## Making Decisions

Fred is a farmer who is deciding what to plant for the next year. His first choice is always corn because he knows it well. It can be a temperamental crop, though, that needs the right mix of rain and sun. He has been following the projected weather for the growing season to get an idea of how corn might turn out. He is also playing with some numbers and wants to know what kind of utility or satisfaction he can expect if he decides on corn. He measures utility by the size of the crop, since a bigger harvest means more money for Fred and his family.

## Expected Utility

Expected Utility theory is going to help him find the answer. The expected utility from Fred's corn crop under the uncertainty of the weather is the weighted average of the different outcomes that will come under different weather conditions. He will subjectively assign different utility values that will value different crop sizes. A big crop that will come with good weather has a value of 100, with smaller crops that will come with less than ideal weather getting lesser values.

He decides to set up a table to help him with the calculations. He first lists his conditions of uncertainty as good weather, fair weather and poor weather. Then he lists the utility he can expect from each. Last of all he needs the probability for each weather condition. The weather forecasts have been optimistic about Fred's corn getting the right amount of rain and sun for good growth. He decides to weight good weather higher than fair or poor.

Sixty-four units is the is the expected utility of his corn crop under uncertain weather conditions. He can adjust the different weather probabilities if forecasts change and get a different result. If you try this with a 40% probability of poor weather and 30% for fair and good, you will see the final utility number at the bottom goes down!

## Uses for Expected Utility Theory

Expected utility calculations can be used for a wide range of decisions made under uncertainty. Fred can use this when he decides what to plant. He can do another calculation for soybeans, then compare it corn and see which is best.

An investor might use this calculation to calculate the expected utility from returns on various investments under different economic conditions. Businesses can use it to compare the utility from returns on different projects under an uncertain political climate. It has an added benefit over expected value calculation as individualized utility values allow for a more personalized result

## Marginal Utility

After a day of work on the farm, Fred gives his two sons some money and lets them go to the store for treats! After they both finish large bottles of soda pop, they will have to make a decision. Do they get another one or buy something else? Let's introduce the concept of marginal utility to help them out.

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