Consumer Demand Theory II Session 3, EA 4 th July, 2007 Prof. Samar K. Datta.

Consumer Consumer Demand Theory IIDemand Theory II

Consumer Consumer Demand Theory IIDemand Theory II

Session 3, EASession 3, EA44thth July, 2007 July, 2007

Prof. Samar K. DattaProf. Samar K. Datta

Overview of items intended to be covered in this session

• Consumer Choice

– Interpretation of consumer equilibrium: Equi-marginal principle

– Corner solution

• Diminishing MU & diminishing MRS• Income effect and distinction between normal and

inferior goods• Engel curve• Price consumption curve and demand curve• Substitutes and complements • Examples /Food for thought

Two conditions for optimal consumer

choice1) Must be located on the budget line.

2) Must give the consumer the most preferred combination of goods and services (i.e., maximum satisfaction).

U2

Consumer ChoicePc = $2 Pf = $1 I = $80

Budget Line

A

At market basket A the budget line and theindifference curve aretangent and no higherlevel of satisfaction

can be attained.

At A:MRS =Pf/Pc = .5

Food (units per week)

Clothing(units per

week)

40 8020

20

30

40

0

• When consumers maximize satisfaction:

CF/P PMRS

CFC F /P P /MUMU

Marginal utility andconsumer choice

• Since MRS is also equal to the ratio of the marginal utilities of consuming F and C:

• The equation for utility maximization can be alternatively expressed as:

CCFF PMUPMU //

Marginal utility andconsumer choice

• Total utility is maximized when the budget is allocated so that the marginal utility per dollar of expenditure is the same for each good.

• This is referred to as the equal marginal principle.

Marginal utility andconsumer choice

A Corner Solution

Ice Cream (cup/month)

FrozenYogurt

(cupsmonthly)

B

A

U2 U3U1

A corner solutionexists at point B.

Condition for corner solution

•MUX/PX > MUY/PY

•Implications of corner solution:

brand loyalty at any price?

Questions on diminishing MU & diminishing MRS

• Does diminishing MRS necessarily imply diminishing MUs?

• Does diminishing MUs necessarily imply diminishing MRS?

Income Changes, Income Consumption Curve, and Shift in Demand Curve

• Income Changes– An increase in income shifts the

budget line to the right, increasing consumption along the income-consumption curve.

– Thus, increase in income shifts the demand curve to the right.

Income Consumption Curve

Food (units per month)

Clothing(units per

month)

An increase in income,with the prices fixed,

causes consumers to altertheir choice ofmarket basket.

Income-Consumption Curve

3

4

A U1

5

10

B

U2

D7

16

U3

Assume: Pf = $1 Pc = $2

I = $10, $20, $30

Income Changes & Shifts in the Demand

Curve

Food (units per month)

Priceof

food

An increase in income,from $10 to $20 to $30,with the prices fixed,shifts the consumer’sdemand curve to the right.

$1.00

4

D1

E

10

D2

G

16

D3

H

Normal vs. Inferior Good

• Normal Good - The income-consumption curve has a positive slope:

• The quantity demanded increases with income.

• The income elasticity of demand is positive.• Inferior Good - The income-consumption

curve has a negative slope:• The quantity demanded decreases with

income.• The income elasticity of demand is

negative.

An Inferior Good

Hamburger (units per month)

Steak(units per

month)

15

30

U3

C

Income-ConsumptionCurve

…but hamburgerbecomes an inferior

good when the incomeconsumption curvebends backward between B and C.

105 20

5

10

AU1

B

U2

Both hamburgerand steak behaveas a normal good, between A and B...

Individual Demand

• Engel Curves– Engel curves relate the quantity of

good consumed to income.– If the good is a normal good, the

Engel curve is upward sloping.– If the good is an inferior good, the

Engel curve is downward sloping.

Engel Curves

Engel curve isbackward bending for inferior goods.

Inferior

Normal

Food (unitsper month)

30

4 8 12

10

Income($ per

month)

20

160

Price-Consumption Curve

Price Consumption Curve

Food (units per month)

Clothing(units per

month)

4

5

6

U2

U3

A

BDU1

4 12 20

The price-consumptioncurve traces out theutility maximizing

market basket for thevarious prices for food.

Individual Demand Curve

Demand Curve

Individual Demand relatesthe quantity of a good thata consumer will buy to theprice of that good.

Food (units per month)

Priceof Food

H

E

G

$2.00

4 12 20

$1.00

$.50

Derivation of Demand Curve from Price

Consumption Curve

Clothing (units per month)

Price of food

Substitutes and Complements

1. Two goods are considered substitutes if an increase (decrease) in the price of one leads to an increase (decrease) in the quantity demanded of the other.

• e.g. movie tickets and video rentals

2. Two goods are considered complements if an increase (decrease) in the price of one leads to a decrease (increase) in the quantity demanded of the other.

• e.g. petrol and motor oil

3. Two goods are independent when a change in the price of one good has no effect on the quantity demanded of the other.

Substitutes and Complements

• Substitutes and Complements– If the price consumption curve is

downward-sloping, the two goods are considered substitutes.

– If the price consumption curve is upward-sloping, the two goods are considered complements.

The trust fund shifts the budget line

Example: College Trust Fund

P

Q Education ($)

OtherConsumption

($)

U2A

U1

A: Consumption before the trust fund

B

B: Requirement that the trust fund must be spent on education

C

U3 C: If the trust could be spent on other goods – i.e., unconstrained

B

20,000

A

Gasoline(gallons per year)

Spendingon othergoods ($) 20,000

5,000

U1

C15,000

2,000

D

With a limit of2,000 gallons,

the consumer movesto a lower

indifference curve(lower level of utility).

18,000

U2

Example: Gasoline Rationing

Will the consumer be necessarily worseoff at D?

Food for thought

• How would you display effect of income tax (proportional or progressive) with or without certain exemptions (e.g., on medical insurance)?

• How will commodity taxation change consumer equilibrium?

• How will income taxation influence labor supply?• How will consumer indifference curves look like

if one good is a bad, or both goods are bad?• Is it possible to display exchange between two

people having fixed endowments of two goods and no income, when there are no formal markets or prices to facilitate exchange?