Part 4 The Theory of Demand We have drawn all our demand curves downward sloping Why do economists...

Part 4The Theory of Demand

• We have drawn all our demand curves downward sloping

• Why do economists think demand curves normally slope downward?

• Market demand curves are aggregations of individual (or household) demand curves

• What factors will affect a household’s demand for a good?

Household Consumption Choices

• Households buy a variety of goods (a “bundle” of goods)

• Different households buy different bundles of goods

• Household choice will depend on:- income- relative prices of goods- preferences

• Income and prices can be shown in a budget constraint

• What shapes preferences?• How can a given set of preferences be

represented?

Budget Constraint

Qy

Qx

Affordable

Unaffordable

Budget constraint with given income = Iand given prices Px and Py:I = PxQx + PyQy

Preferences and Utility

• Which of the affordable combinations will a household choose to purchase?

• The intuitive answer is that the household will choose the bundle of goods that it “likes the best” or provides the most satisfaction of all the affordable bundles

• More formally, if the degree of satisfaction of all wants and desires can be measured on a single “utility” scale, the household will choose the bundle of goods that maximizes utility

Cardinal Utility Theory

• When the idea of a utility measure was first proposed in economics it was sometimes assumed that one could think of units of utility in the same way as units of weight or temperature

• Such a measure has a defined unit that can be added, multiplied, & etc

• Many possible units of measure but they are all linear transformations of each other (eg: deg F = 32 + 9/5 C)

Total and Marginal Utility

• More goods give more total utility• More of any particular good will

tend to give less additional total utility with each increment

• Diminishing marginal utility• Diminishing marginal utility and the

“paradox of value”• What is the rule for maximizing total

utility out of a given budget when each good has diminishing marginal utility?

Maximizing Utility

Quantity MUx MUy

1 20 16

2 18 15

3 14 14

4 8 13

5 0 12

Example of two goods x and y

Utility maximizing bundle with an incomeOf $6 and Px and Py= $1?Utility maximizing bundle with an income$16 and Px=$3 and Py=$2

Maximizing Utility

• The total utility gained from a given budget will be maximized where the budget is all spent and marginal utility per dollar spent is equalized across all goods

• Rules for a utility maximum:

I=PxQx+PyQy and

MUx/Px = MUy/Py or

MUx/MUy = Px/Py

Implications

• Maximization is where

I=PxQx+PyQy and

MUx/Px = MUy/Py

• Fall in Px will increase ability to purchase X and Y. If X is normal Qx increases.

• Fall in Px leads to a substitution of X for Y

• Increase in Qx decreases MUx

• Decrease in Qy increases MUy

Individual and Market Demand

• Market demand curves are the horizontal summation of the demand curves of all individuals or households

Ordinal Utility Theory

• The idea of utility as measurable in a cardinal way was subject to much criticism

• The idea of a utility measure as a rank ordering replaced the idea of cardinal measurement

• An “ordinal” measure is a ranking only.

• No unit of measurement• Higher numbers imply only

more preferred

Preferences

Qy

Qx

DefinitelyLess preferred

to A: U<5

DefinitelyPreferred to

A: U>5

Bundle A: X’,Y’U=5

If both X and Y provide utility

X’

Y’

Indifference Curves

A locus of all bundles with the sameutility ranking. The consumer is indifferentbetween them

U=5

U>5 (preferred toAny point on U=5)

U<5(any point on U=5 preferred)

Indifferent between any point on U=5Qy

Qx

A Preference Map

U=5

U=6

Qy

Qx

a

b

c

d

Preference Maps

• In order to draw a preference map at all we are assuming:

• goods are infinitely divisible (indifference curves are continuous)

• Every combination of goods can be ranked (preferences are complete)

• Preferences are consistent (indifference curve cannot intersect or touch)

The Shape of Indifference curves

• Negative slope (more is preferred to less)

• Marginal rate of substitution (MRS)

• Convex to the origin (diminishing marginal rate of substitution)

• MRS=ΔQy/ΔQx keeping utility constant—slope of the indifference curve

Maximizing Utility Once Again

• In the ordinal utility context maximizing utility means choosing that bundle of goods that is on the highest indifference curve achievable with given income and prices

• Budget line: I = PyQy+PxQx

PyQy = I- PxQx

Qy = I/Py – (Px/Py)Qx

I/Py is the Y intercept

Px/Py is the slope of the budget line

Budget line

I/Px Qx

Qy

I/Py

I = PyQy+PxQx

Px/Py is the slope of the budget line

Utility Maximization:Indifference Curves

U=5

Qx

Qy

Qy*

Qx*

Highest indifference curveachievable

U=4

U=6

Budget line and indifference curve are tangent.On budget line and highest indifference curvewhere MRS=Px/Py

Changes in Income

• Changes in income with constant prices will shift the budget line outwards in a parallel fashion

• Normal goods will show increased consumption with higher income

• Inferior goods will show decreased consumption with higher income

• Consumer preferences determine if a good is normal or inferior (shape of indifference curves)

Income Effect

Qy

QxQx’ Qx”

U”

U’

I’

I”

Income consumption line

X and Y normal

Qy

Qx

I”I’

U’

U”

Qx” Qx’

X inferior, Y normal

Changes in Price

• Change in the price of X changes the slope of the budget line by changing the X intercept

Qy

QxI/Px’ I/Px”

Px’>Px”I/Py

Price Effect and Demand Curves

Qy

Qx

Qx

Px

U’

U”

Qx’ Qx”

Qx’ Qx”

Budget linewith Px”

Px”

Budget linewith Px’

Px’

Demand curve for X

Income and Substitution Effects of a Price

Change• The effect of a price change on

the demand for a good can be decomposed into two effects

• The substitution effect is the effect of the change in relative prices keeping real income (utility) constant

• The income effect is the effect on real purchasing power of the price change

Income and Substitution Effects of a Price

ChangeQy

QxQx’ Qxs Qx”

Sub Inc

a b

s

Overall effect (a to b) can be broken down into a substitutionand income effect

Income and Substitution Effects of a Price

Change• Income effects of a price change are

usually small--unless the good accounts for a high proportion of expenditure

• For normal goods the income effect works to reinforce substitution effect and a price decline must increase quantity demanded

• For inferior goods the income effect works against the substitution effect, but the substitution effect is usually larger

Income and Substitution Effects of a Price

Change• What does it take to get an

upward sloping demand curve? The “Giffen” good case

• Giffen goods must be both inferior and important in the budget

• Very unlikely to come across a Giffen good

• Policy uses of income and substitution effects--carbon taxes and income tax rebates