1. The basic assumption about consumer behavior

A basic assumption about the behavior of consumers is that they try to make themselves as well off as they can in the circumstances they find themselves in.

More precisely they are assumed to:
Maximize their utility subject to their budget constraint.

Utility is a measure of well-being or satisfaction.

A budget constraint is a measure of the resources the consumer has available to them: the income they have available to them and what it will buy in terms of the prices of the goods the consumer wants to buy.

In terms of the modeling of consumer behavior, we develop a theory of consumer preferences (how utility is determined) then we combine it with a representation of the budget constraint and we use these to examine how a consumer will choose the amounts of various goods to purchase.

We will look at each of these in turn, starting with the budget constraint because it is more intuitive.
 

2. The budget constraint

One can imagine that if we assume that “more is better” when it comes to consuming goods and services, that in the absence of any constraints consumers would want to consume infinite amounts of the good and services they like.

What prevents them from doing that?  Scarcity.

The representation of scarcity at the level of the individual consumer is what we call their budget constraint.

What are the components of the budget constraint?

Income:   A person will have a certain amount of income to spend on goods and services in some time period.
              We refer to this as their nominal or money income as it is expressed in $

Prices:     How much is a person’s nominal income worth?  That depends on what they can buy with it.  Price of goods determine how much of a good a person
                can purchase with a given nominal income.
 

Example: Let’s look at a simple example to illustrate the budget line concept.

Assume a person buys two goods in a week: lattes (l) and bagels (b).  Now suppose the person has a weekly income of I, and the prices of lattes and bagels are respectively Pl and Pb.

What is the total amount this person can spend on the two goods in a week?

   Pl*l + Pb*b = I

The price of a latte multiplied by the number of lattes bought, plus the price of a bagel multiplied by the number of bagels bought, must add up to the person’s income.

Note:  We could say that spending must be less than or equal to income but we will assume that a person spends all of their income so that expenditure and income are equal.

Graphically this is referred to as the budget line.
Graph (insert here):
 

Note: Let’s put lattes on the horizontal axis and bagels on the vertical axis.

To plot a straight line the easiest thing to do is to plot each of the points on the axes then connect them:

If the person consumes all lattes and no bagels the number of lattes they will be able to afford is: I/Pl

If the person consumers all bagels and no lattes the number of bagels they will be able to afford is: I/Pb
 

Note on terminology:  I/P is called the person’s real income as opposed to nominal income.  It measures the purchasing power of the person’s nominal income (where purchasing power refers to what the person can buy with their income).  We talk about I/Pl as the person’s real income in terms of lattes and I/Pb as their real income in terms of bagels.
 

Q. What does the budget line remind you of?
 

Q. If “more is better” where will the consumer want to be in terms of the budget line?
 
 

a. Slope of the budget line

The slope of the budget line can be obtained by the formula:
Slope  = rise/run
          = I/Pb / I/Pl
          = - Pl/Pb

Q. Why is the slope of the budget line negative?
 
 

So the slope of the budget line is given by the ratio of the price of the good on the horizontal axis to the price of the good on the vertical axis.

That has a nice interpretation:  it is a measure of the opportunity cost of buying more of the good on the horizontal axis (in this case lattes):
The slope tells us, if the person wants to buy one more latte how many bagels must they give up.

b. Changes in the budget line

The budget line will change if either of the prices change and if income changes.

(i) Changes in income.

If income changes the budget line shifts parallel.

* An increase in income shifts the budget line out (away from the origin) parallel.

* A decrease in income shifts the budget line in (towards the origin) parallel.

Q. Why is the shift a parallel shift?
 
 

(ii) Changes in prices

A change in one of the prices will cause the curve to shift and the slope will change.

* An increase in the price of the one of the goods will shift the budget line in at the axis for that good.

* A decrease in the price of one of the goods will shift the budget line out at the axis for that good.

Note: You can think about various combinations of changes in the prices of the two goods based on this.
 

(iii) Changes in prices and changes in income

One or both of the prices of the goods may change and income may change.  Given what we know from above we can figure out the specific effect on the budget line from a specific combination of changes.

Example:  Suppose the consumer’s income doubles and the prices of lattes and bagels double.
Q. What would happen to the budget line?
 

c. In summary

Definition of the budget line:
The budget line shows all the combinations of two goods that a person can afford to buy with their income for given prices of the two goods.

The budget line captures the combinations of two goods that a person has available to them, given their income and the prices of the goods.  In order to determine which combination the person will actually choose to buy, we need to consider their preferences.

3. Utility

Definition of utility:
Utility refers to the total satisfaction that a person gets from the goods and services they consume.

Although there is no measure of utility, economists find it a useful concept for explaining consumer choices.

Why?  If a person is able to rank all possible combinations of goods as follows:

Combination A is preferred to combination B
Combination B is preferred to combination A
Combination A and combination B are liked equally well

Then the person’s preferences over all combinations of goods can be expressed in terms of a function.  That function is called a utility function and the values attributed to the various combinations (utility) are not important in explaining a person’s preferences, the relative rankings are important (one combination is better than another).

Graphically, a person’s ranking of all possible combinations of two goods is represented by what are called indifference curves.

Definition of an indifference curve:
An indifference curve shows all the combinations of two goods that yield the same level of satisfaction to the consumer.

Graph of an indifference curve (insert here):
 

The slope of the indifference curve:

The slope of the indifference curve is negative –  holding their utility constant, this tells us that the person is willing to trade-off some of one good for more of the other good.

There is an economic interpretation to the slope of an indifference curve – the slope represents the person’s subjective rate of trade-off between the two goods.

Slope of IC = MU x / MU y

Where:   MU is the extra utility a person receives from consuming an extra unit of a good.

If the MU x / MU y = 5 for example: to consume an extra unit of good x the person will be willing to give up 5 units of good y, holding utility constant.
 

The shape of the indifference curve:
The indifference curve has a convex shape – this is to represent the assumption that consumers prefer balance in their consumption bundles, to extremes.
 

The indifference map:
All combinations of goods fall on one indifference curve or another.  Higher indifference curves represent higher levels of utility since there are more of both goods as we move in a northeast direction on the graph.

Q. If “more is better”, where will a person want to be given their indifference map?
 
 

Summary:  The concept of indifference curves represents a person’s preferences.  Now we can go back to the budget constraint and model the consumer’s choice of goods.

4. Utility maximization

Graphically (insert graph here) utility maximization can be represented as follows:

More is better – the person wants to be on the highest indifference curve

Scarcity – the person is constrained by the resources they have available to them – their purchasing power (given by their income and the prices of the goods)

Maximizing utility subject to the budget constraint – the person wants to be on the highest indifference curve possible, given the budget line.
 

Utility maximizing choice is where an indifference curve is tangent to the budget line – that is the highest indifference curve the person can reach given the budget line.

Tangency point:  at the tangency point the slope of the indifference curve is equal to the slope of the budget line.
         Slope of the IC:  the subjective trade-off between the goods.
         Slope of the BC: the market trade-off between the goods.

The tangency point gives the combination of the two goods that will maximize the person’s satisfaction subject to their budget constraint: x*, y*.

5. An example: Lattes and Bagels

Going back to our example about lattes and bagels.

Suppose income is I = $100 per week
Suppose the price of a latte is Pl = $2
Suppose the price of a bagel is Pb = $1

a. Draw the budget line (lattes on the horizontal axis and bagels on the vertical axis).

b. What is the slope of the budget line?

c. Suppose the utility maximizing combination of lattes and bagels is l*= 30, b*= 40.  Draw an indifference curve to show that this is the utility maximizing choice.

d. What is true about the slope of the indifference curve at this point?

e. What does the slope tell us about the actual trade-off between lattes and bagels at this combination?