Objectives:Objectives:

Define an Define an indifference curveindifference curve and understand the significance of and understand the significance of the slope of an indifference curve.the slope of an indifference curve.

Define a Define a budget constraintbudget constraint,, understand how to graph a budget line, understand how to graph a budget line, and understand the significance of the slope of the budget line.and understand the significance of the slope of the budget line.

Understand how to Understand how to identify the identify the utility-maximizingutility-maximizing bundle bundle and illustrate this graphically.and illustrate this graphically.

Understand how the Understand how the rule of equal marginal utility per dollarrule of equal marginal utility per dollar holds holds at the consumer’s equilibrium bundle.at the consumer’s equilibrium bundle.

Understand how to Understand how to derive a demand curvederive a demand curve using indifference using indifference curves and budget lines. curves and budget lines.

Module 12: Indifference Curves and Budget Module 12: Indifference Curves and Budget ConstraintsConstraints

Define an indifference curve……Define an indifference curve……

Indifference curves are a mechanism for illustrating consumers’ Indifference curves are a mechanism for illustrating consumers’ tastes and preferences. tastes and preferences.

Two key assumptions in indifference curve analysis:Two key assumptions in indifference curve analysis:1.1. Consumers are able to Consumers are able to rank rank different bundles of goods different bundles of goods2.2. Preferences are Preferences are transitive.transitive.

In our analysis, we will consider a simple two-good model and only In our analysis, we will consider a simple two-good model and only the consumption of goods that are desirable to the consumer as the consumption of goods that are desirable to the consumer as opposed to “undesirables”. Desirable goods are products that giveopposed to “undesirables”. Desirable goods are products that givethe consumer satisfaction. the consumer satisfaction.

Objective 1Objective 1

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 combinations of two goods that give the consumer the same level of utility or satisfactionsame level of utility or satisfaction. .

Erin’s indifference curve: Erin is indifferent between bundles a, b and c.

4

Three properties of indifference curves:Three properties of indifference curves:

Higher indifference curves represent Higher indifference curves represent higherhigher levels of levels of satisfaction.satisfaction.

Indifference curves are Indifference curves are negatively slopednegatively sloped and they are and they are bowed toward the origin.bowed toward the origin.

Indifference curves Indifference curves cannot crosscannot cross..

Objective 1:Objective 1: ..……and understand the significance of the ..……and understand the significance of the slope of an indifference curve.slope of an indifference curve.

An indifference curve is An indifference curve is negatively slopednegatively sloped and it is and it is bowed toward the origin bowed toward the origin (convex).(convex).

The The slopeslope of an indifference of an indifference curve tells us the rate at curve tells us the rate at which Erin is willing to which Erin is willing to trade coffee for an trade coffee for an additional bagel with additional bagel with no no loss in satisfaction. loss in satisfaction.

A convex Indifference curve

The slope of the indifference curve is referred to as The slope of the indifference curve is referred to as the the marginal rate of substitution (MRS).marginal rate of substitution (MRS).

The The marginal rate of substitutionmarginal rate of substitution is the rate at is the rate at which a consumer is willing to give up good Y for which a consumer is willing to give up good Y for an additional unit of good X with no loss in an additional unit of good X with no loss in satisfactionsatisfaction

The marginal rate of substitution The marginal rate of substitution fallsfalls as we move as we move down a given indifference curve.down a given indifference curve.

Objective 2Objective 2

Define a budget constraint ……Define a budget constraint ……

The The budget constraintbudget constraint indicates the amount of income a indicates the amount of income a consumer allocates to goods and services.consumer allocates to goods and services.

Suppose Erin has $I to spend on bagels and coffee. Suppose Erin has $I to spend on bagels and coffee. Let Let PPbb = price of bagels and = price of bagels and PPcc = price of coffee. = price of coffee.

We can write an equation for Erin’s budget constraint:We can write an equation for Erin’s budget constraint:

cbBagels CoffeeP + P = I

Where = Price of bagels × Quantity of bagels = expenditure Where = Price of bagels × Quantity of bagels = expenditure on bagelson bagels

= Price of coffee × Quantity of coffee = expenditure on coffee = Price of coffee × Quantity of coffee = expenditure on coffee

and and

II = income = income

cCoffeeP

bBagelsP

Suppose Erin has $18 to spend on coffee and bagels. Suppose Erin has $18 to spend on coffee and bagels. The price of coffee is $3 and the price of bagels is $2. The price of coffee is $3 and the price of bagels is $2.

Let’s plug this information into the equation of her budget Let’s plug this information into the equation of her budget constraint:constraint:

× ×$2 Bagels+ $3 Coffee = $18

Equation of a budget constraint ……Equation of a budget constraint ……

cbBagels CoffeeP + P = I

Objective 2Objective 2 …understand how to graph a budget constraint …understand how to graph a budget constraint

First find the First find the intercept valuesintercept values: divide the total income by the price of the : divide the total income by the price of the good in question.good in question.

Example: Erin has $18 a week and the price of bagels is $2. If she spends all her 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 income ($18) on bagels, she can buy (income ÷ price of bagels) $18÷$2 = 9 bagels. This is the bagels. This is the X-intercept.X-intercept.

The The Y-intercept valueY-intercept value is (income ÷ price of coffee) $18÷$3 = 6 cups of coffee. is (income ÷ price of coffee) $18÷$3 = 6 cups of coffee.

The slope of the budget line is the The slope of the budget line is the negative negative of the price ratios: of the price ratios: −−

The The negative signnegative sign indicates that the consumer has to give up some of one indicates that the consumer has to give up some of one good to get more of the other. good to get more of the other.

X

Y

P

PX

Y

P

P

Objective 2Objective 2 …and understand the significance of …and understand the significance of slope of the budget slope of the budget lineline

Y= coffee and X= bagels

Slope = rise ÷ run

For example, the slope = For example, the slope = −− , which means Erin has , which means Erin has

to give up 2/3 units of coffee to buy 1 additional bagel or 2 units of to give up 2/3 units of coffee to buy 1 additional bagel or 2 units of

coffee for 3 additional bagels. coffee for 3 additional bagels.

bagels

coffee

2

3

P

P

Objective 3Objective 3

The equilibrium bundle gives the consumer the highest satisfaction, The equilibrium bundle gives the consumer the highest satisfaction, given her budget constraint. This means that Erin wants to reach the given her budget constraint. This means that Erin wants to reach the highest indifference curve possible that lie on her budget line.highest indifference curve possible that lie on her budget line.

Understand how to identify the utility-maximizing combinationUnderstand how to identify the utility-maximizing combinationof goods and illustrate graphically.of goods and illustrate graphically.

Erin’s optimal bundle is “Erin’s optimal bundle is “b”b” which contains 4 cups of coffee which contains 4 cups of coffee and 3 bagels. Her expenditure and 3 bagels. Her expenditure on this bundle exhausts her on this bundle exhausts her income.income.

At the point of optimal consumption, the indifference curve isAt the point of optimal consumption, the indifference curve is tangenttangent to the budget line.to the budget line.

Objective 3…. illustrate the utility-maximizing bundle Objective 3…. illustrate the utility-maximizing bundle graphically.graphically.

Key Points:Key Points:

The slope of the budget line equals the negative of the price ratio, The slope of the budget line equals the negative of the price ratio, −−

The The slopeslope indicates how many units of good indicates how many units of good YY you have to forego to you have to forego to obtain an additional unit of good obtain an additional unit of good XX..

The ratio of prices is also called the The ratio of prices is also called the relative pricesrelative prices..

The price ratio is the The price ratio is the opportunity costopportunity cost or the rate of exchange or the rate of exchange dictated by the market.dictated by the market.

X

Y

P

P

………….the significance of .the significance of slope of the budget lineslope of the budget line

Recall, the optimal consumption bundle (1) exhausts income, andRecall, the optimal consumption bundle (1) exhausts income, and(2) satisfies the rule of equal marginal utility per dollar holds. (2) satisfies the rule of equal marginal utility per dollar holds.

Since bundle “Since bundle “b”b” lies on the budget line, the budget is exhausted. lies on the budget line, the budget is exhausted.

Recall the rule of equal marginal utility per dollar: Recall the rule of equal marginal utility per dollar:

Objective 4Objective 4

Understand how the rule of equal marginal utility per dollar Understand how the rule of equal marginal utility per dollar holds in equilibrium. holds in equilibrium.

coffeebagels

bagels coffee

MU MU=P P

For the last unit, a dollar spent on bagels yields the same utility as a dollar spent on coffee.

Does bundle “Does bundle “b”b” satisfy the rule of equal marginal utility per dollar? satisfy the rule of equal marginal utility per dollar?

Objective 4 ……the rule of equal marginal utility per dollar Objective 4 ……the rule of equal marginal utility per dollar holds in equilibrium. holds in equilibrium.

coffeebagels

bagels coffee

MU MU=P P

Rearrange the equation aboveRearrange the equation above

bagels bagels

coffee coffee

=MU PMU P

ratio of marginal utilities ratio of prices

bagels bagels

coffee coffee

=MU PMU P

The ratio of marginal The ratio of marginal utilities is the slope of the utilities is the slope of the indifference curve or the indifference curve or the marginal rate of substitutionmarginal rate of substitution

The price ratio or The price ratio or relative prices is the relative prices is the slope of the budget lineslope of the budget line

YES! The rule of equal marginal utility per dollar holds at the YES! The rule of equal marginal utility per dollar holds at the

point of tangency between the indifference curve and the point of tangency between the indifference curve and the

budget line.budget line.

Objective 6Objective 6

The demand curve shows the quantities of a good that the consumer is The demand curve shows the quantities of a good that the consumer is willing to purchase at alternative prices. willing to purchase at alternative prices.

At a price of $2, Erin’s utility-maximizing choice is 3 bagels. At a price of $2, Erin’s utility-maximizing choice is 3 bagels.

Understand how to derive a demand curve using indifference Understand how to derive a demand curve using indifference curves and budget lines.curves and budget lines.

To derive the demand for bagels curve we must change the price To derive the demand for bagels curve we must change the price of bagels and observe what happens the quantity demanded, holding of bagels and observe what happens the quantity demanded, holding all else constant.all else constant.

Suppose the price of bagels falls to $1.50. What happens? Suppose the price of bagels falls to $1.50. What happens?

First, the budget line changes. The new intercept value is 12 bagels First, the budget line changes. The new intercept value is 12 bagels (income ÷ new price of bagels). The coffee intercept does not change.(income ÷ new price of bagels). The coffee intercept does not change.

Objective 6….. deriving a demand curveObjective 6….. deriving a demand curve

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.

With these two price-quantity combinations, we can derive Erin’s With these two price-quantity combinations, we can derive Erin’s demand for bagels curve demand for bagels curve

Our result is consistent with the law of demand.Our result is consistent with the law of demand.