indifference curves and budget constraints indifference curves and budget constraints module 12 1

Indifference Curves and Budget Constraints


Module 12Module 12Module 12Module 12

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

ObjectivesObjectivesObjectivesObjectives

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


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


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


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

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


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

Define an indifference curve …Define an indifference curve …Define an indifference curve …Define an indifference curve …Objective 1Objective 1Objective 1Objective 1

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Two key assumptions in indifference curve analysis:Two key assumptions in indifference curve analysis:

1. Consumers are able to1. Consumers are able to rankrank different bundles of different bundles of goods. For example, given two bundles of goods, goods. For example, given two bundles of goods,

bundle A and bundle B, a consumer is able to say:bundle A and bundle B, a consumer is able to say:Bundle A is preferred to bundle B; orBundle A is preferred to bundle B; orBundle B is preferred to bundle A; orBundle B is preferred to bundle A; orBundle A is equally preferred to bundle BBundle A is equally preferred to bundle B


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Two key assumptions in indifference curve analysis:Two key assumptions in indifference curve analysis:

1. Consumers are able to1. Consumers are able to rankrank different bundles of different bundles of goods. For example, given two bundles of goods, goods. For example, given two bundles of goods,

bundle A and bundle B, a consumer is able to say:bundle A and bundle B, a consumer is able to say:Bundle A is preferred to bundle B; orBundle A is preferred to bundle B; orBundle B is preferred to bundle A; orBundle B is preferred to bundle A; orBundle A is equally preferred to bundle BBundle A is equally preferred to bundle B

2.2. Preferences are Preferences are transitive. transitive. That is, if bundle A is That is, if bundle A is preferred to bundle B and bundle B to bundle C,preferred to bundle B and bundle B to bundle C,then bundle A must be preferred to bundle C.then bundle A must be preferred to bundle C.


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

Desirable goods are products that give the consumer Desirable goods are products that give the consumer satisfaction such as movies, clothing, music, etc..satisfaction such as movies, clothing, music, etc..

““Undesirables” do not give the consumer satisfaction, Undesirables” do not give the consumer satisfaction, for example, pollution. for example, pollution.


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A consumer’s A consumer’s indifference curveindifference curve shows the shows the various combinations of two goods that give the various combinations of two goods that give the consumer the same level of utility or satisfactionconsumer the same level of utility or satisfaction. .

Define an indifference curve … Define an indifference curve … Define an indifference curve … Define an indifference curve … Objective 1Objective 1Objective 1Objective 1

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A consumer’s A consumer’s indifference curveindifference curve shows the shows the various combinations of two goods that give the various combinations of two goods that give the consumer the same level of utility or satisfactionconsumer the same level of utility or satisfaction. .


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Erin’s indifference curveErin’s indifference curve

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

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

Indifference curves … properties …Indifference curves … properties …Indifference curves … properties …Indifference curves … properties …

Objective 1Objective 1Objective 1Objective 1

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

Indifference curves: properties Indifference curves: properties Indifference curves: properties Indifference curves: properties


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

Indifference curves Indifference curves cannot crosscannot cross..

Indifference curves: propertiesIndifference curves: propertiesIndifference curves: propertiesIndifference curves: properties


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Objective 1: … understand the significance of the Objective 1: … understand the significance of the slope of an indifference curveslope of an indifference curveObjective 1: … understand the significance of the Objective 1: … understand the significance of the slope of an indifference curveslope 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).

Note that the slope of the Note that the slope of the indifference curve indifference curve gets gets flatter (becomes smaller)flatter (becomes smaller) as we move down the as we move down the indifference curve.indifference curve.

A convex A convex Indifference Indifference curvecurve

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

Slope gets smaller Slope gets smaller as we move down as we move down the indifferencethe indifference

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


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Slope gets smaller Slope gets smaller as we move down as we move down the indifferencethe indifference

The slope of the indifference curve is referred The slope of the indifference curve is referred to as the to as 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 which a consumer is willing to give up good Y for an additional unit of good X with no loss in for an additional unit of good X with no loss in satisfaction.satisfaction.


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A convex A convex Indifference Indifference curvecurve

Objective 1: … understand the significance Objective 1: … understand the significance of the slope of an indifference curveof the slope of an indifference curveObjective 1: … understand the significance Objective 1: … understand the significance of the slope of an indifference curveof the slope of an indifference curve

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

Going from point “Going from point “aa” to ” to point “point “bb”, the slope ”, the slope equals 2equals 2÷÷1 = 2. Going 1 = 2. Going from point “from point “bb” to point ” to point ““cc”, the slope equals ”, the slope equals 1÷2=½. 1÷2=½.

Erin is willing to give up Erin is willing to give up

less coffee for each less coffee for each additional bagel, the additional bagel, the more bagels she has.more bagels she has.

Key Points:Key Points:

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


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

The The slopeslope of an indifference curve measures the of an indifference curve measures the consumer’s consumer’s marginal rate ofmarginal rate of substitutionsubstitution between between two goods.two goods.


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

The The slopeslope of an indifference curve measures the of an indifference curve measures the consumer’s consumer’s marginal rate of substitutionmarginal rate of substitution between between two goods.two goods.

The The marginal rate of substitutionmarginal rate of substitution falls as we move falls as we move down a convex indifference curve.down a convex indifference curve.


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Objective 2Objective 2 Objective 2Objective 2

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

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

The budget constraint is also called an The budget constraint is also called an income income constraint.constraint.

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

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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:

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

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

II = income = income

cCoffeeP

bBagelsP

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cbBagels CoffeeP +P = I

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

Objective 2: … equation of a budget Objective 2: … equation of a budget constraint constraint Objective 2: … equation of a budget Objective 2: … equation of a budget constraint constraint

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

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

× ×$2 Bagels+$3 Coffee = $18

Objective 2: … equation of a budget Objective 2: … equation of a budget constraintconstraintObjective 2: … equation of a budget Objective 2: … equation of a budget constraintconstraint

cbBagels CoffeeP +P = I

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Objective 2: How to graph a budget constraintObjective 2: How to graph a budget constraintObjective 2: How to graph a budget constraintObjective 2: How to graph a budget constraint

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

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

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

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Objective 2: how to graph a budget constraintObjective 2: how to graph a budget constraintObjective 2: how to graph a budget constraintObjective 2: how to graph a budget constraint

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

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

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

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We can draw Erin’s budget line.We can draw Erin’s budget line.

Erin can afford all the bundles that lie in the Erin can afford all the bundles that lie in the shaded triangle and on its boundaries. shaded triangle and on its boundaries.

The combination of goods on the line exhaust The combination of goods on the line exhaust her income of $18. her income of $18.

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The slope of the budget line is the The slope of the budget line is the negativenegative of the of the

price ratios:price ratios:

Objective 2: … understand the significance of Objective 2: … understand the significance of slope of the budget lineslope of the budget lineObjective 2: … understand the significance of Objective 2: … understand the significance of slope of the budget lineslope of the budget line

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X

Y

P

P

Objective 2: … understand the significance Objective 2: … understand the significance of of slope of the budget lineslope of the budget lineObjective 2: … understand the significance Objective 2: … understand the significance of of slope of the budget lineslope of the budget line

Y X

X

Y

bagels

coffee

I I= ÷

P P

P=

P

P=

P

Y= coffee and X= bagels

Slope = rise ÷ run

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The slope of the budget line is the The slope of the budget line is the negativenegative of the of the

price ratios: price ratios: −−

The The negative signnegative sign indicates that the consumer has to indicates that the consumer has to

give up some of one good to get more of the other. give up some of one good to get more of the other.

X

Y

P

P

Objective 2: … understand the significance of Objective 2: … understand the significance of slope of the budget lineslope of the budget lineObjective 2: … understand the significance of Objective 2: … understand the significance of slope of the budget lineslope of the budget line

X

Y

bagels

coffee

Pslope =

P

P=

P

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In our example, the price of bagels = $2 and the price of In our example, the price of bagels = $2 and the price of

coffee = $3. Therefore, the slope = coffee = $3. Therefore, the slope = −− , which , which

means Erin has to give up 2/3 units of coffee to buy 1 means Erin has to give up 2/3 units of coffee to buy 1

additional bagel or 2 units of coffee for 3 additional additional bagel or 2 units of coffee for 3 additional

bagels. bagels.

bagels

coffee

2

3

P=

P

Objective 2: … understand the significance Objective 2: … understand the significance of of slope of the budget lineslope of the budget lineObjective 2: … understand the significance Objective 2: … understand the significance of of slope of the budget lineslope of the budget line

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The slope of the budget line equals the negative The slope of the budget line equals the negative

of the price ratio, .of the price ratio, .

The budget line The budget line Key Points Key PointsThe budget line The budget line Key Points Key Points

X

Y

P

P

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


X

Y

P

P

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

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


X

Y

P

P

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The slope of the budget line equals the negative of the The slope of the budget line equals the negative of the

price ratio, price ratio,

The The slopeslope indicates how many units of good indicates how many units of good YY you you have to forego to obtain an additional unit have to forego to obtain an additional unit of good 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 or the rate of exchange dictated by the market.exchange dictated by the market.


X

Y

P

P

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

Identify the utility-maximizing combination Identify the utility-maximizing combination of goods and illustrate graphicallyof goods and illustrate graphicallyIdentify the utility-maximizing combination Identify the utility-maximizing combination of goods and illustrate graphicallyof goods and illustrate graphically

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

Identify the utility-maximizing combination Identify the utility-maximizing combination of goods and illustrate graphically.of goods and illustrate graphically.Identify the utility-maximizing combination Identify the utility-maximizing combination of 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.

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

Objective 3: … illustrateObjective 3: … illustrate the utility-maximizing the utility-maximizing combination of goods and graphicallycombination of goods and graphicallyObjective 3: … illustrateObjective 3: … illustrate the utility-maximizing the utility-maximizing combination of goods and graphicallycombination of goods and graphically

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


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




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

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




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

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

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




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.

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

coffeebagels

bagels coffee

MU MU=P P

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

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


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

Rearrange the equation above to get:Rearrange the equation above to get:

ratio of marginal utilities

ratio of marginal utilities ratio of prices ratio of prices

coffeebagels

bagels coffee

MU MU=P P

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



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bagels bagels

coffee coffee

MU P=

MU 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





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bagels bagels

coffee coffee

MU P=

MU P



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





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bagels bagels

coffee coffee

MU P=

MU P





YES! The rule of equal marginal utility per dollar YES! The rule of equal marginal utility per dollar

holds at the point of tangency between the holds at the point of tangency between the

indifference curve and the budget line.indifference curve and the budget line.



bagels bagels

coffee coffee

MU P=

MU P


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

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

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

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To derive a demand curve using indifference To derive a demand curve using indifference curves and budget linescurves and budget linesTo derive a demand curve using indifference To derive a demand curve using indifference curves and budget linescurves and budget lines

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

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

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

Objective 5: … deriving a demand curveObjective 5: … deriving a demand curveObjective 5: … deriving a demand curveObjective 5: … deriving a demand curve

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To derive the demand for bagels curve we must change the To derive the demand for bagels curve we must change the price of bagels and observe what happens the quantity price of bagels and observe what happens the quantity demanded, holding all else constant.demanded, holding 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 First, the budget line changes. The new intercept value is 12 bagels (income ÷ new price of bagels = 18 ÷$1.50). The coffee bagels (income ÷ new price of bagels = 18 ÷$1.50). The coffee intercept does not change.intercept does not change.


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What happens to her optimal bundle?


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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.


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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.


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


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

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


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End of Module 12End of Module 12End of Module 12End of Module 12

Song: Can’t Buy Me LoveAlbum: Bugs and Friends Sing the BeatlesArtists: Bugs Bunny & Daffy Duck

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indifference curves and budget constraints indifference curves and budget constraints module 12 1

Documents

bundle b

indifference curve objective

indifference curve analysis

consumers equilibrium

demand curve

budget lines

budget constraints module

illustrating consumers