1. Module 12: Indifference Curves and Budget Constraints
Objectives:
Define an indifference curve and understand the significance of
the slope of an indifference curve.
Define a budget constraint, understand how to graph a budget line,
and understand the significance of the slope of the budget line.
Understand how to identify the utility-maximizing bundle
and illustrate this graphically.
Understand how the rule of equal marginal utility per dollar holds
at the consumer’s equilibrium bundle.
Understand how to derive a demand curve using indifference
curves and budget lines.

2. Define an indifference curve……
Objective 1
Define an indifference curve……
Indifference curves are a mechanism for illustrating consumers’
tastes and preferences.
Two key assumptions in indifference curve analysis:
1. Consumers are able to rank different bundles of goods
2. Preferences are transitive.
In our analysis, we will consider a simple two-good model and only
the consumption of goods that are desirable to the consumer as
opposed to “undesirables”. Desirable goods are products that give
the consumer satisfaction.

3. A consumer’s indifference curve shows the various
A consumer’s indifference curve shows the various combinations of two goods that give the consumer the same level of utility or satisfaction.
Erin’s indifference curve: Erin is indifferent between bundles a, b and c.
Sara, please eliminate the scale

4. Three properties of indifference curves:
Higher indifference curves represent higher levels of satisfaction.
Indifference curves are negatively sloped and they are bowed toward the origin.
Indifference curves cannot cross.

5. Objective 1: ..……and understand the significance of the slope of an indifference curve.
An indifference curve is negatively sloped and it is bowed toward the origin (convex).
The slope of an indifference curve tells us the rate at which Erin is willing to trade coffee for an additional bagel with no loss in satisfaction.
A convex Indifference curve

6. The slope of the indifference curve is referred to as the marginal rate of substitution (MRS).
The marginal rate of substitution is the rate at which a consumer is willing to give up good Y for an additional unit of good X with no loss in satisfaction
The marginal rate of substitution falls as we move down a given indifference curve.

7. Define a budget constraint ……
Objective 2
Define a budget constraint ……
The budget constraint indicates the amount of income a
consumer allocates to goods and services.
Suppose Erin has $I to spend on bagels and coffee.
Let Pb = price of bagels and Pc = price of coffee.
We can write an equation for Erin’s budget constraint:
Where = Price of bagels × Quantity of bagels = expenditure on bagels
= Price of coffee × Quantity of coffee = expenditure on coffee and
I = income

8. Equation of a budget constraint ……
Suppose Erin has $18 to spend on coffee and bagels.
The price of coffee is $3 and the price of bagels is $2.
Let’s plug this information into the equation of her budget constraint:

9. Objective 2 …understand how to graph a budget constraint
First find the intercept values: divide the total income by the price of the
good in question.
Example: Erin has $18 a week and the price of bagels is $2. If she spends all her income ($18) on bagels, she can buy (income ÷ price of bagels) $18÷$2 = 9 bagels. This is the X-intercept.
The Y-intercept value is (income ÷ price of coffee) $18÷$3 = 6 cups of coffee.

10. Objective 2 …and understand the significance of slope of the budget line
The slope of the budget line is the negative of the price ratios: −
The negative sign indicates that the consumer has to give up some of one good to get more of the other.
Y= coffee and X= bagels
Slope = rise ÷ run

11. For example, the slope = − , which means Erin has
to give up 2/3 units of coffee to buy 1 additional bagel or 2 units of coffee for 3 additional bagels.

12. Objective 3
Understand how to identify the utility-maximizing combination
of goods and illustrate graphically.
The equilibrium bundle gives the consumer the highest satisfaction, given her budget constraint. This means that Erin wants to reach the highest indifference curve possible that lie on her budget line.
Erin’s optimal bundle is “b” which contains 4 cups of coffee and 3 bagels. Her expenditure on this bundle exhausts her income.

13. Objective 3…. illustrate the utility-maximizing bundle graphically.
At the point of optimal consumption, the indifference curve is tangent to the budget line.

14. …….the significance of slope of the budget line
Key Points:
The slope of the budget line equals the negative of the price ratio, −
The slope indicates how many units of good Y you have to forego to obtain an additional unit of good X.
The ratio of prices is also called the relative prices.
The price ratio is the opportunity cost or the rate of exchange dictated by the market.

15. Objective 4
Understand how the rule of equal marginal utility per dollar holds in equilibrium.
Recall, the optimal consumption bundle (1) exhausts income, and
(2) satisfies the rule of equal marginal utility per dollar holds.
Since bundle “b” lies on the budget line, the budget is exhausted.
Recall the rule of equal marginal utility per dollar:
For the last unit, a dollar spent on bagels yields the same utility as a dollar spent on coffee.

16. Objective 4 ……the rule of equal marginal utility per dollar holds in equilibrium.
Does bundle “b” satisfy the rule of equal marginal utility per dollar?
Rearrange the equation above
ratio of
marginal utilities
ratio of prices

17. YES! The rule of equal marginal utility per dollar holds at the
point of tangency between the indifference curve and the
budget line.
The ratio of marginal utilities is the slope of the indifference curve or the marginal rate of substitution
The price ratio or relative prices is the slope of the budget line

18. Objective 6
Understand how to derive a demand curve using indifference curves and budget lines.
The demand curve shows the quantities of a good that the consumer is willing to purchase at alternative prices.
At a price of $2, Erin’s utility-maximizing choice is 3 bagels.

19. Objective 6….. deriving a demand curve
To derive the demand for bagels curve we must change the price
of bagels and observe what happens the quantity demanded, holding all else constant.
Suppose the price of bagels falls to $1.50. What happens?
First, the budget line changes. The new intercept value is 12 bagels (income ÷ new price of bagels). The coffee intercept does not change.

20. What happens to her optimal bundle?
Now, her optimal bundle is bundle “h” containing 4 cups of coffee and 4 bagels. Note “h” lies on her new budget line.
Thus, when the price of bagels falls from $2.00 to $1.50, Erin
increases her quantity demanded from 3 to 4 bagels.

21. With these two price-quantity combinations, we can derive Erin’s demand for bagels curve
Our result is consistent with the law of demand.