6a - Consumer Decisions: Utility Maximization  


Consumer Behavior -
Consumer Decisions: Utility Maximization

I. Introduction

A. An example of diminishing marginal utility
  • Read the following from an online skiing discussion forum and answer the question WHY?
    • From epicski.com Barking Bears Forum:

      Skiing in/past March: why not popular?

      So, here in Oregon, we continue to get hammered by cold storms. Last week it was snow down in Portland, and dry, deep snow up in the Cascades (16-20" new overnight): the stuff that happens once every couple of years in Oregon. Today, there is another 7" of new snow on the mountain, and snow predicted on/off for the next two weeks. Base is at 175" and is very consolidated (we have had plenty of rain with that snow): that is all-natural, non-manmade snow.

      But, for some reason, people just stop skiing. WHY? I just don't understand. The skiing is great, the snow is superb! What else can they do this time of year? Sit inside and watch it rain? We get BIG dumps, and nobody is on the hill. Likewise in late April/early May, which has primo spring conditions (and the occasional good storm, followed by a bluebird day, which doesn't get any better) and again, nobody is on the hill!

B. Consumer and Producer Decisions

1. Consumer Decisions
  • How much to buy?
  • Goal: maximize utility
  • Lesson 6a

2. Producer Decisions

  • How much to produce?
  • Goal: maximize profits
  • Lessons 8/9, 10, and 11

C. Review

1. Definition -- Economics
2. Definition -- Benefit-Cost Analysis
3. Definition -- Utility
  • Definition: the want-satisfying power of a good or survice; the satisfaction or pleasure on gets from consuming a good or service
  • "utility" does not mean "usefulness"
  • Utility is subjective - varies from person to person
  • Utility cannot be measured / it can be compared
    • we will assume that utility can be measured in units called "utils"

D. Law of Diminishing Marginal Utility

An explanation of the Law of Demand

As a consumer increases the consumption of a good or service the marginal utility obtained from each additional unit of the good or service decreases.

II. Theory of Consumer Behavior

A. Total Utility and Marginal Utility
1. utility
The want-satisfying power of a good or service; the satisfaction or pleasure a consumer obtains from the consumption of a good or service

2. total utility / graph

The total amount of satisfaction derived from the consumption of a single product or a combination of products.

3. marginal utility

a. definition
The extra utility a consumer obtains from the consumption of one additional unit of a good or service;

b. calculation

equal to the change in total utility divided by the change in the quantity consumed.

MU = TU / Qconsumed

c. graph

1. yellow page

2. textbook

d. law of diminishing marginal utility

As a consumer increases the consumption of a good or service the marginal utility obtained from each additional unit of the good or service decreases.

3. MU, demand, and elasticity

a. Diminishing MU explains the law of demand

b. MU and elasticity

(1) if MU declines quickly as more is consumed, then demand is less elastic

if the price declines, only A LITTLE more will be purchased since LITTLE extra utility is recieved

Demand is less elastic

(2) if MU declines slowly as more is consumed, then demand is more elastic


if the price declines, A LOT more will be consumed since the MU of these additional units remains HIGH

Demand is more price elastic


B. Consumer Choice and the Budget Constraint: Utility Maximizing Rule (benefit-cost analysis)

1. assumptions
a. rational behavior
b. preferences are known and measurable
c. budget constraint
d. prices

2. utility maximizing rule

To obtain the greatest utility the consumer should allocate money income so that the last dollar spent on each good or service yields the same marginal utility.

MUx/Px = MUy/Py = MUz/Pz (see below)

3. But this is really just Benefit-Cost Analysis (see Ch 1):

a. Benefit-Cost-Analysis:
select all where: MB > MC
up to where: MB = MC
but never where: MB < MC

b. utility maximizing rule:

MBx = MUx/Px

The MB of product X can be measured by finding the MU per dollar spent on product X

Why divide by price?

  • because you cannot compare a $1 beer with a $3 steak sandwich
  • dividing by price means that we are comparing a dollar's worth of beer with a dollar's worth of a steack sandwich

MCx = MUy/Py

The MC of product X can be measured by finding the MU that you are not receiving from a dollar's worth of your next best alternative (product Y)




MUx/Px = MUy/Py = MUz/Pz

To obtain the greatest utility the consumer should allocate money income so that the last dollar spent on each good or service yields the same marginal utility.


4. example 1:

A consumer is consuming the following quantities of two goods both with a price of $1 and recieving the MU indicated:

MU Received from the last unit:

Good A (price $1)


Good B (price $1)


Is this consumer maximizing his/her utility?

If not, should they consume :

(1) more A and less B? or
(2) more B and less A?

If one more of B is consumed and one less of A is consumed:

What happens to the MU of B and the MU of A?
What happens to the TU received?
What happens to the total dollars spent?


5. example 2: beer and steaks (yellow page)


III. Utility Maximization and the Demand Curve

A. Deriving the Demand Curve
1. What is the Law of Demand? -- WHY?

2. Use the utility maximizing rule:

If you have $10 and apples cost $1 and oranges cost $2, use the table below to determine:
  • how much of each will be bought?
  • total utility received?

2. What happens if the price of a product falls? Price of oranges now = $1

If you still have $10 and apples still cost $1 and oranges now cost $1 too, use the table above to determine:
  • how much or each will be bought?
  • total utility received?


3. the demand schedule and curve for ORANGES:

P = $2; Q = 4

p = $1; Q = 6

IV. Applications and Extensions of the Theory of Consumer Demand

A. Consider This … Vending Machines and Marginal Utility
  • Newspaper vending machines normally allow one to take multiple papers
  • Soft drink vending machines distribute one can or bottle at a time


  • WHY?


    1.Newspaper vending machines normally allow one to take multiple papers; publishers allow this because they believe that people rarely take more than one paper because the marginal utility of the second paper is often zero, and it has little "shelf life."

    2.Soft drink vending machines distribute one can or bottle at a time. Even if the marginal utility of the second unit of soda is low in the short run, the long shelf life would allow people to keep sodas for later consumption.


B. The Diamond-Water paradox:

Some essential goods like water have lower prices than luxuries like diamonds. WHY?
  • The paradox is resolved when we look at the abundance of water relative to diamonds.
  • Theory tells us that consumers should purchase any good until the ratio of its marginal utility to price is the same as that ratio for all other goods.
  • The marginal utility of an extra unit of water may be low as is its price, but the total utility derived from water is very large.
  • The total utility of all water consumed is much larger than the total utility of all diamonds purchased.
  • However, society prefers an additional diamond to an additional drop of water, because of the abundant stock of water available.


C. Cash and Noncash Gifts

Noncash gifts may yield less utility to the receiver than a cash gift of equal monetary value
  • Because the noncash gift may not match the receiver's preferences.
  • Individuals know their own preferences better than the gift giver


V.  Prospect Theory

A. Traditional theory asserts that people are always rational and are not impacted by emotion.

B. Behavioral economics focuses on consumers’ decisions in light of emotion and negative possible outcomes.

1. Status quo – gains and losses are essentially measured against the change in the status quo.

2. We know about diminishing marginal utility with goods but there’s also diminishing marginal disutility with losses where there’s a much greater decrease in marginal utility with the first loss.

3. People are loss averse and will feel losses to a greater magnitude than gains of an equal amount.

C. Examples and applications

1. Losses and Shrinking Packages.
a. When making purchases, consumers tend to focus only on price when determining their gains and losses.

b. Therefore to makeup for increased costs, Hershey’s decreased the size of their chocolate bar in order to avoid an increase in price.

c. The important point is that consumers don’t view this as a loss because they focus on price and price didn’t change (no observable change in status quo).

2. Framing Effects and Advertising

a. Evaluation of gains and losses largely depends on a person’s mental frame and when new information is introduced to change a person’s frame their gains/losses are called framing effects.

b. For example, making $100,000 may be appealing to someone until they find out they had been earning $140,000.

c. Another example of framing is in advertising.  Often hamburger producers label hamburger as “80% lean” not “20% fat” because 80% lean is framed as a gain.

3. Anchoring and Credit Card Bills

a. People’s value of an item is influenced by irrelevant information which is called anchoring.

b. Example: Students asked to write down the last 2 digits of their social security numbers are then asked to write down the value of a good like a wireless keyboard.  Those with lower ending social security numbers were likely to provide lower estimates while those with higher ending numbers provided higher estimates.

c. Credit card companies use anchoring by requiring very low monthly payments thereby inducing consumers to make smaller payments and increasing the total amount paid on the debt.

4. Mental accounting and over priced warranties

a. Sometimes consumers don’t view all of their consumption options simultaneously as predicted by the utility-maximization rule.  Richard Thaler called it mental accounting when consumers looked at some purchases as isolated transactions.

b. When making big-item purchases like a $1,000 TV, the buyer is offered a warranty.  The buyer often looks at this transaction in isolation, viewing this as a potential $1,000 loss if the TV breaks.  The buyer is usually enticed to buy the warranty even though there’s a small possibility of it breaking because the consumer doesn’t consider their future income.

5. The endowment effect and market transactions

a. There is a tendency for people to have a higher value of an item if they own it, called the endowment effect.

b. For example, a coffee mug that I don’t own is worth $10 to me, but once the mug is mine the value of the mug increases to $15.  As a result of strong endowment effects, transactions between buyers and sellers are difficult.

c. The endowment effect is in part due to people being loss averse where parting with an item they own is viewed as a loss and people tend to feel potential losses 2.5 times more than potential gains.

6. Consider This…Rising consumption and the Hedonic Treadmill

a. Hedonic treadmill is the idea that people get used to a certain level of consumption and when consumption increases they are happier for awhile, but then they get used to it and they aren’t any happier than they were at lower consumption levels.

b. for example:

  • people with different incomes report similar levels of satisfaction
  • if you start saving for retirement you will initially notice the loss in consumption, but you will get used to it and your overall level of satisfaction will remain the same