session 4, 5 me

8/14/2019 Session 4, 5 ME

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Managerial Economics

session 4, 5

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8/14/2019 Session 4, 5 ME


Demand & Utility

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What is Utility?

• Satisfaction, happiness, benefit

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Cardinal Utility vs. Ordinal Utility

Cardinal Utility : Assigning numerical values to the

amount of satisfaction

Ordinal Utility : Not assigning numerical values to

the amount of satisfaction but indicating the order

of preferences, that is, what is preferred to what

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What is Util?

A unit of measure of utility

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Total Utility

The amount of satisfaction obtained by

consuming specified amounts of a product

per period of time.

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Example:

TU(X) = U(X) = 16 X – X2

where X is the amount of a good that is

consumed in a given period of time.

5 units of the product per period of time

yields 55 utils of satisfaction

How much will 10 units yield?

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Marginal Utility

The change in total utility (TU) resulting

from a one unit change in consumption (X)

MU = TU/ X

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Diminishing Marginal Utility

Each additional unit of a product

contributes less extra utility than the

previous unit.

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When the changes in consumption are

infinitesimally small, marginal utility is the

derivative of total utility.

MU = dTU/dX

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Calculating MU from a TU Function

Example: TU(X) = 16 X – X2

MU = dTU/dX = ?

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X

X

Total

Utility

Marginal

Utility

TU

MU

X1 X2

X1 X2

Graphs of Total Utility &

Marginal Utility

X2 is where total utility reaches

its maximum.

MU is zero.

This is the saturation point or

satiation point.

After that point, TU falls and

MU is negative.

X1

is where marginal utility

reaches its maximum.

This is where we encounter

diminishing marginal utility.

The slope of TU has reached its

maximum; TU has an inflectionpoint here.

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13

Indifference Curves

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14

Example:

To encourage education, a government isconsidering three different options:

– A lump-sum cash to kids of school age.

– A matching subsidy to each dollar the kidsspend on schooling.

– Provide education for free.

Which is better?

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15

Three Steps Involved In The

Study Of Consumer Behavior

1) We will study consumer preferences.

– To describe how and why people prefer one good to

another.

2) Then we will turn to budget constraints.

– People have limited incomes.

3) Finally, we will combine consumer preferences andbudget constraints to determine consumer choices.

– What combination of goods will consumers buy to

maximize their satisfaction?

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Market basket defined

• A market basket is a collection of one or

more commodities.

• One market basket may be preferred over

another market basket containing a

different combination of goods.

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Ind ifference cu rves represent all combinations of market baskets that

provide the same level of satisfaction to a person. 17

Three Basic Assumptions of

Consumer Preferences

• Preferences are complete.

– Give me any two baskets of goods (A and B), I will be able to tellyou one of the following:

• I prefer A to B

• I prefer B to A

• I am indifferent between A and B

• Preferences are transitive.

– If I prefer A to B and B to C, I must also prefer A to C.

• Non-satiation: Consumers always prefer more of any good to less.

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Preferences over market basket

A 20 30

B 10 50

D 40 20

E 30 40

G 10 20H 10 40

Market

Basket

Units of

Food

Units of

Clothing

E is preferred to

Similarly, A, E, B, H, D are

all preferred to G

…

Much easier to see in a graph.

based on observations :

more good is preferred to

less

G A H

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Easier to see in a graph

The consumer prefers

A to all combinations

in the blue box, while

all those in the pink

box are preferred to A .

Food

(units per week)

10

20

30

40

10 20 30 40

Clothing

(units per week)

50

G

A

EH

B

D

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Easier to see in a graph

U 1

For example:

Combination B,A, & D

yield the same satisfaction

•E is preferred to U 1

•U 1 is preferred to H & G

Food

(units per week)

10

20

30

40

10 20 30 40

Clothing

(units per week)

50

G

D

A

EH

B

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U 1

Food

(units per week)

10

20

30

40

10 20 30 40

Clothing

(units

per

week)50

G

D

A

EH

B

Any market basket lying above and

to the right of an indifference curveis preferred to any market basket

that lies on the indifference curve.

Ind ifferenc e cu rves s lope downward to the r ight .

If it sloped upward it would violate the assumption

that more of any commodity is preferred to less.

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Indifference map An indifference map is a set of

indifference curves that describesa person’s preferences for all

combinations of twocommodities.

– Each indifference curve in the

map shows the marketbaskets among which the

person is indifferent.

U 2

U 3

Food

(units per week)

Clothing

(units

per

week)

U 1

AB

D

Market basket A

is preferred to B.Market basket B is

preferred to D.

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Indifference Curves Cannot Cross

U 1U 2

Food

(units per week)

Clothing

(units per week)

A

D

B

If crossed the consumer should be indifferent

between A , B and D . However, B contains

more of both goods than D . Thus, given

transitivity assumption, the assumption

of more is preferred to less is violated.

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The amount of clothing given up for unit

of food decreases with amount of food

A

B

D

E G-1

-6

1

1

-4

-21

1

Observation: The amount

of clothing given up for

a unit of food decreases

from 6 to 1

Food

(units per week)

Clothing

(units

per week)

2 3 4 51

2

4

6

8

10

12

14

16

Question: Does this

relation hold for giving

up food to get clothing?

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Marginal Rate of Substitution

Food

(units per week)

Clothing

(units

per week)

2 3 4 51

2

4

6

8

10

12

14

16A

B

D

E G

-6

1

1

1

1

-4

-2-1

MRS = 6

MRS = 2

The marginal rate of substitution

(MRS ) quantifies the amount of one

good a consumer will give up to

obtain more of another good

MRS is measured by

the slope of the

indifference curve

MRS = - C / F

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Assumption: Diminishing Marginal Rate of Substitution

Food

(units per week)

Clothing

(units

per

week)

2 3 4 51

2

4

6

8

10

12

14

16A

B

D

E G

-6

1

1

1

1

-4

-2-1

MRS = 6

MRS = 2

Along an indifference curve there is a

dim inishin g marginal rate of

subst i tu t ion.

Example: the MRS for AB was 6, while

that for DE was 2

Indifference curves are convex

because as more of one good

is consumed, a consumer

would prefer to give up fewer

units of a second good to get

additional units of the first one.

That is, consumers prefer a

balanced market basket.

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Perfect Substitutes

Orange Juice

(glasses)

Apple

Juice

(glasses)

2 3 41

1

2

3

4

0

Perfect

Substitutes

Two goods are perfect

substitutes when the marginal

rate of substitution of one good

for the other is constant.

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Perfect Complements

• You need exactly 4 tireswith 1 car body (ignoringthe spare tire).

• Having more than 4 tireswith 1 car body doesn’tincrease utility.

• Also having more than 1car body with only 4 tiresdoesn’t increase utilityeither.

tires

car bodies

1 2

8

4IC1

IC2

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Goods versus Bads

As you get more of a

bad, you need more of

a good to compensate

you, to keep youfeeling equally happy.

So IC of a good & a

bad slopes upward.

production

pollution

IC1

IC2

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Odd special cases that are not consistent

with the characteristics listed previously.

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“Neutral” Good

•Your utility is unaffected

by consumption of aneutral good.

Neutral good

Desired

good

IC1 IC2 IC3

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Addict

•The more substance 1 the

addict has the more he is

willing to give up of

substance 2 to get a littlemore of 1 (& vice versa).

•So the IC’s are concave

instead of convex.

Substance 1

Substance 2

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The slope of the indifference curve is the

rate at which you are willing to trade off

one good to get another good.

It is called the marginal rate of substitution

or MRS.

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What is the MRS or slope of the IC?•Suppose points A & B are on the same

indifference curve & therefore have thesame utility level.

•Let’s break up the move from A to B into 2parts.

•AD: TU = C (MUC)

•DB: TU = F (MUF)•AB:

0 = TU = C (MUC) + F (MUF)

• C (MUC) = – F (MUF)

•

C/

F = – MUF / MUC

IC1

Food F

A

D

Clothing C

B

IC2

So along an indifference curve, the slope or MRS is the negative ofthe ratio of the marginal utilities (with the MU of the good on thehorizontal axis in the numerator).

MRS = – MUF / MU

C 34

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For example,Suppose IC1 is the 90-utilindifference curve & IC2 is the 96-utilindifference curve

Point A is 7 units of food & 6 ofclothing

B is 9 units of food & 5 of clothing

Since an additional unit of clothing

gives you 6 more utils of satisfaction,the MU of clothing must be 6

Since an additional 2 units of foodalso give you 6 more utils ofsatisfaction, the MU of food must be 3

So, MRS = – MUF / MUC = -3/6 = -0.5

You’d give up 2 units of food to get1 unit of clothing

IC1 =90

Food F

A

D

Clothing C

B

IC2 = 96

6

5

7 9

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Budget Constraint or Budget Line

This equation tells you what you can buy. For example, suppose you have $24, & there are two

goods.

The price of the first good is $3 per unit & the price of

the second good is $4 per unit. So, if you buy X units of the first good for $3 each, you

spend 3X on that good.

Similarly, if you buy Y units of the second good, you

spend 4Y on that good. Your total spending is 3X+4Y.

If you spend all 24 dollars that you have, 3X+4Y=24.

That equation is your budget constraint.

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Example: Budget constraint for $24 of income,

and $3 & $4 for the prices of the two goods.

X

Y

(0,6)

(8,0)0

If you spent all $24 on the 1st good, youcould buy 8 units.

If you spent all $24 on the 2nd good, you

could buy 6 units.

So we have the intercepts of the budgetconstraint.

The slope of the line connecting these

two points is

Y/X = – 6/8 = – 3/4 = – 0.75 .

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Let’s generalize Keep in mind that income was $24

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Let s generalize. Keep in mind that income was $24

and the prices of the goods were $3 & $4. The equation of the

budget constraint in our example was 3X + 4Y = 24.

X

Y

(0,6)

(8,0)0

So the budget constraint is p1X + p2Y = I

Solving for Y in terms of X, p2Y = I – p1X,

or Y = I /p2 – (p1/p2)X

So from our slope-intercept form, we see that the

intercept is I /p2, and the slope is –p1/p2

The intercept is income divided by the price of the

good on the vertical axis.

The slope is the negative of the ratio of

the prices, with the price of the goodon the horizontal axis in the

numerator.

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We have the intercept as I /p2,

& the slope is –p1/p2 .

What if income increased?

The slope would stay the same & the budgetconstraint would shift out parallel to the original one

Suppose in our example with income of 24 &

prices of 3 & 4, income increased to 36Our new y-intercept will be 36/4 =9

& the new X-intercept will be 36/3=12

X

Y

(0,6)

(8,0)0

(0,9)

(12,0)

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Suppose the price of the good on the X-axis increased.

•If we bought only the good whose price

increased, we could afford less of it.•If we bought only the other good, our purchases

would be unchanged.

•So the budget constraint would pivot inward

about the Y-intercept.

X

Y

(0,6)

(8,0)0 (6,0)

For example, if the price increasedfrom $3 to $4, our $24 would only buy6 units.

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Similarly, if the price of the good on the Y-axis

increased, the budget constraint would pivot in

about the X-intercept.

X

Y

(0,6)

(8,0)0

(0,4)

Suppose the price of the 2nd good

increased from $4 to $6. If you bought

only that good, with your $24, your $24would only buy 4 units of it.

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Let’s combine our indifference curves & budget

constraint to determine our utility maximizing

point.

•Point A doesn’t maximize

our utility & it doesn’t

spend all our income. (It’sbelow the budget

constraint.)

X

Y

0

IC1

IC2

IC3

A

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•Points B & C spend all our income

but they don’t maximize our utility.We can reach a higher indifference

curve.

X

Y

0

IC1

IC2

IC3

B

C

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•Point D is unattainable. Wecan’t reach it with our budget.

X

Y

0

IC1

IC2

IC3

D

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•Point E is our utility-maximizing point.

•We can’t do any better than at E. •Notice that our utility is maximized at the

point of tangency between the budget

constraint & the indifference curve.

X

Y

0

IC1

IC2

IC3

E

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Recall from Principles of Microeconomics, to maximize your

utility, you should purchase goods so that the marginal utility

per dollar is the same for all goods

If there were just two goods, that means that

MU1/P1 = MU2/P2

MU1/MU2 = P1/P2

-P1/P2 = slope of the budget constraint.

- MU1/MU2 = slope of the indifference curve.

slope of indifference curve must be=slope of budget constraint

If at a particular point, two functions have the same slope, theyare tangent to each other.

That means your utility-maximizing consumption levels arewhere your indifference curve is tangent to the budgetconstraint.

This is the same conclusion we reached using our graph.

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E l If TU 10X 24Y 0 5 X2 0 5 Y2 h i f h

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Example: If TU = 10X + 24Y – 0.5 X2 – 0.5 Y2, the prices of the

two goods are 2 and 6, and we have $44, how much should you

consume of each good?

• Taking the derivatives of TU we have

MU1 = 10 – X and MU2 = 24 – Y

• Since MU1/MU2 = P1/P2 , we have

(10 – X) / (24 – Y) = 2 / 6 ,

• or 60 – 6 X = 48 – 2Y ,

• or 6X – 2Y = 12 .

• This an equation with two unknowns.• Our budget constraint provides us with a 2nd equation.

Combining the two equations, we can solve for X & Y.

• The budget constraint is 2X + 6Y = 44 .47

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So our two equations are

6X – 2Y = 12 and 2X + 6Y = 44

• Multiplying the second equation by 3 yields6X + 18Y = 132 .

• Now we have 6X + 18Y = 1326X – 2Y = 12

--------------------• So, 20Y = 120

• and Y = 6 .

• Plugging 6 in for Y in the 2nd equation yields 6X – 12 = 12,

• or 6X = 24.

• So, X = 4 .

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Let’s see if all this works.

We had $44, the prices were 2 & 6, andMU1 = 10 – X & MU2 = 24 – Y. We bought 4 units of the

1st good & 6 of the 2nd good.

First, did we spend exactly what we had?

We spent (2)(4) + (6)(6) = 8 + 36 = 44 Good.

Is the marginal utility/dollar the same for both goods?

For the 1st good: MU1/P1 = (10 – X)/2 = (10-4)/2 = 3

For the 2nd good: MU2/P2 = (24 – Y)/6 = (24-6)/6 = 3

So they’re equal and things look fine.

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What happens to consumption when incomerises?

• For normal goods, consumption increases.• For inferior goods, consumption decreases.

• What does this look like on our graph?

50

Two Normal Goods

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Two Normal Goods

•As income increases, the

budget constraint shifts out &we are able to reach higher &

higher IC’s.

•The points of tangency are athigher & higher levels of

consumption of both goods.

X

Y

IC1

IC2

IC3

C

B

A

Y3

Y2

Y1

X1 X2 X3

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Income Consumption Curve

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Income-Consumption Curve

•The curve that traces out

these points is called theincome-consumption curve.

•For two normal goods, the

curve slopes upward.

•It may be convex (as drawn

here), concave, or linear.

X

Y

IC1

IC2

IC3

C

B

A

Y3

Y2

Y1

X1 X2 X3

52

One Normal Good & One Inferior

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One Normal Good & One Inferior

Good

•Suppose the good on thehorizontal axis is normal &

the one on the vertical axis is

inferior.

•Then X will rise & Y will fallas income increases.

X

Y

IC1 IC2IC3

CBA

X1 X2 X3

Y1

Y2

Y3

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Income-Consumption Curve

•The result is a downward slopingincome-consumption curve.

X

Y

IC1 IC2IC3

CBA

X1 X2 X3

Y1

Y2

Y3

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Engel Curve

An Engel curve describes how household expenditure on a particular good or service varies with household income

•The Engel Curve showsthe quantity of a goodpurchased at each incomelevel.

•The graph has income onthe vertical axis and thequantity of the good onthe horizontal.

•It slopes up for normalgoods & down for inferiorgoods.X

Income

C

B

A

X1 X2 X3

I3

I2

I1

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Quantity

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We can also look at consumption levels of two

goods when the price of one of them changes.

•Suppose there is an increase in the price ofthe 1st good (the good on the X-axis).

•The budget constraint pivots inward.

• Here we see X drop & Y increase.• In this case, our 2 goods are

substitutes.

X

Y

X3 X2 X1

Y3Y2

Y1

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If we connect the points, we have the

price consumption curve.

•It shows the utility-maximizing

points when the price of a good

changes.

X

Y

X3 X2 X1

Y3Y2

Y1

57

If l k h i f d & h f i

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If we look at the price of a good & the amount of it

consumed, we have the demand curve for our

particular individual.

•As the price decreases the

quantity demanded increases &vice versa.

X

P

X1 X2 X3

P1

P2

P3

58

We can separate the effect of a change in the price of a good on

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its consumption level into two parts:

the Income effect (Hicksian Approach)

& the Substitution effect. (Slutsky’s Approach)

Suppose the price of thefirst good increases

The budget constraint wasoriginally the blue line and we

were at A consumingquantities XA & YA

After the price change, thebudget constraint is the redline, and we’re at Bconsuming XB & YB

X

Y

ABYB

YA

XB XA

59

We first want to capture the effect of the price change without

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We first want to capture the effect of the price change without

the effect of the change in income.

X

Y

H

AB

YH

YB

YA

XB XH XA

we draw a line parallel to the new budget constraint and

tangent to the old indifference curve. (The consumer’s realincome is so increased that he buys the same combination of

the two goods at H as he was buying at B.

XH < XA ; YH > YA

Since X is now relatively more expensive

compared to Y, we will substitute, increasing Y &decreasing X.

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X

Y

H

AB

YH

YB

YA

XB XH XA

As a result of the increase in the relativeprice of X, we reduce our consumption of itand consume more of Y

The movement from A to H is the substitution

effect

61

Now we move from H to B

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Now we move from H to B

XX

Y

H

AB

YH

YB

YA

XB XH XA

Our purchasing power has been reduced by theprice change. That results in the income effect

In our graph, we now hold the relative pricesconstant at the new level, but income has fallen.Our budget constraint has shifted inward

If both goods are normal, as a result ofthe change in income, we reduce ourconsumption of both goods, and X & Y fall

This is the income effect of theprice change

62

T t l Eff t f P i I

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Total Effect of Price Increase

X

Y

H

AB

YH

YB

YA

XB XH XA

The total effect is to move from A to B.

X has fallen.

Both the substitution & income effects lead to

a drop in X.

Y has increased in this case.

The substitution effect

increased consumption of Y, but

the income effect reduced it less

than the substitution effectincreased it.

YH > YB > YA

63

Let’s do a price decrease for X

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Let’s do a price decrease for X

X

Y

H

B

A

YB

YA

YH

XA XH XB

The budget constraint moves from the blue line to

the red lineWe draw a line parallel to the new budgetconstraint and tangent to the old indifferencecurve

H is the tangency of the hypothetical budgetconstraint with the old indifference curve

The substitution effect is themovement from A to H

We substitute increasing X &decreasing Y

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The movement from H to B is the income effect.

X

Y

H

B

A

YB

YA

YH

As a result of the higher income (greaterpurchasing power), we consume more of bothgoods, if they are normal goods.

XA XH XB

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Total Effect

X

Y

H

B

A

YB

YA

YH

The total effect is to move from A to B.

X has increased.Both the substitution & income effects led to anincrease in X.

Y has also increased in this case.

The substitution effect decreased consumption of

Y, but the income effect increased it by more thanthe substitution effect decreased it.

XA XH XB

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Income and Substitution Effects, in words

The income effect is the result of the change in

purchasing power. If the price of a normal good increases, you feel

poorer, and the income effect is to consume less.

If the price of a normal good decreases, you feel

richer, and the income effect is to consume more. The substitution effect is the result of a change in

relative prices.

If the price of a good increases, the substitution

effect is to consume less of it & more of the othergoods that are now relatively cheaper.

If the price decreases, the substitution effect is toconsume more of it & less of the goods that are nowrelatively more expensive.

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What if the price changed of an inferior good?

The substitution effect would be the same

but the income effect would be the opposite.

Let’s see how?

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Price increase for an inferior good

Income effect (I.E.): Your purchasing power has decreased. You feel poorer.

So you consume more of the inferior good.

Substitution effect:

The good is now relatively more expensive than othergoods, so you consume less of it and more of other goods.

Notice the I.E. & S.E. are in opposite directions in this case.

If the S.E. is larger than the I.E., you will consume less ofthe good.

If the I.E. is larger than the S.E., you will consume more ofthe good.

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An inferior good for which the IE is larger than

the SE is called a Giffen good.

It is a good for which consumption rises when

the price increases, and consumption falls whenthe price decreases.

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Price decrease for an inferior good

Income effect:Your purchasing power has increased. You feel richer. So you

consume less of the inferior good.

Substitution effect:

The good is now relatively cheaper than other goods, so youconsume more of it and less of other goods.

Again the IE & SE are in opposite directions in this case.

If the SE is larger than the IE, you will consume more of thegood.

If the IE is larger than the SE, you will consume less of the good.

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8/14/2019 Session 4, 5 ME


We previously looked at the demand curve for

individuals.

How do we get the market demand curve fromthe demand curve for individuals?

We just horizontally sum up the individualdemand curves.

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Market Demand Curve: 3-person example

8/14/2019 Session 4, 5 ME


Market Demand Curve: 3 person example

Person A Person B Person C Market

P P

Q Q

2

1

2

1

2 4

PP

Q Q

2

1

2

1

4 91 31 2

At a price of $1, person A will buy 4 units of a good, B will buy 2 units, &

C will buy 3 units. So at a price of $1, the quantity demanded by theentire 3-person market is 9 units.

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8/14/2019 Session 4, 5 ME




P P

Q Q

2

1

2

1

2 4

PP

Q Q

2

1

2

1

4 91 31 2

At a price of $2, person A will buy 2 units of a good, B will buy 1 units, &

C will buy 1 units. So at a price of $2, the quantity demanded by theentire 3-person market is 4 units.

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8/14/2019 Session 4, 5 ME




P P

Q Q

2

1

2

1

2 4

PP

Q Q

2

1

2

1

4 91 31 2

Continuing the process, we get the market demand curve.

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The Demand for a product can be expressed as a

8/14/2019 Session 4, 5 ME


The Demand for a product can be expressed as a

function of

1. its price(changes which lead to movements along the demandcurve), and

2. other determinants such as income, prices of related goods,

& expectations (changes which lead to shifts of the demandcurve).

So we have Q DX = g(PX, Psubst, Pcomp, Income, Expectation)

A particular demand curve Q DX = g(PX) shows the relation

between the quantity demanded of a product and its pricewhen we hold all the factors constant. This is alsosometimes written as P= f(Q).

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8/14/2019 Session 4, 5 ME


Total Revenue (TR)

- TR = Price x Q uantity

Average Revenue (AR)

- total revenue per unit of output

- AR = TR / Q

Marginal Revenue

- The additional revenue associated with

an additional unit of output

- MR = dTR / dQ

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Example: Horizontal Demand Curve

8/14/2019 Session 4, 5 ME


Example: Horizontal Demand Curve

(price is a constant function)P

Q

10D

P

TR

slope = MR = 10

= AR =MR

P = f(Q) = 10

AR = P = 10

TR = PQ = 10 Q

MR = dTR / dQ = 10

So D, AR, & MR are the same

horizontal function.

TR is an upward sloping line with a

constant slope.Implications for revenue:

Every time you sell another unit of

output, revenue increases by the

session 4, 5 me

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