MICROECONOMICS THEORY 1 · PDF fileAssumptions •The consumer is rational •Ordinal...

MICROECONOMIC THEORY 1

Lecture 2: Ordinal Utility Approach To Demand Theory

Lecturer: Dr. Priscilla T Baffour; [email protected]

Priscilla T. Baffour (PhD)

Microeconomics 1 1 2017/18

Content

Assumptions

Curvature of indifference curves

Impossible indifference curves

Satiation

Monotonic Preferences

The budget Constraint

Consumer equilibrium

Priscilla T. Baffour (PhD) Microeconomics 1

2 2017/18

Assumptions

• The consumer is rational

• Ordinal utility-the consumer ranks his preferences based on satisfaction derived from each good.

• Total utility depends on quantity consumed

• Consistency and transitivity of choice

• Diminishing marginal rate of substitution

– IC is convex to the origin

– Slope of IC decreases


3 2017/18

Indifference Curve

• IC is the locus of points-bundle of goods- that yield the same level of satisfaction.

• An indifference curve defines the substitution between goods X and Y that is acceptable in the mind of the consumer.

• Indifference map shows all ICs which rank the consumer’s preference.


4 2017/18

Indifference Curve

• IC is convex to the origin. The convex shape indicates as you move towards the southeast along a typical IC, the consumer gives up less and less of Y for an extra unit of X. In other words what is sacrificed for an extra unit of X diminishes.

• The negative of the slope of IC is the marginal rate of substitution.

The rate of substitution declines along an IC (diminishing marginal rate of substitution)


5 2017/18

Indifference Curve


6 2017/18

Second order condition


7 2017/18

• Essentially ensures that the utility curve is convex.

Impossible Indifference Curves

• Lisa is indifferent between e and a, and also between e and b…

– so by transitivity she should also be indifferent between a and b…

– but this is impossible, since b must be preferred to a given it has more of both goods.

B B

urr

ito

s,

p

er

se

me

ste

r

Z , Pizzas per semester

I 1

I 0

a

b

e

2017/18 Priscilla T. Baffour (PhD) Microeconomics 1 8

Impossible Indifference Curves (cont.)

• Lisa is indifferent between b and a since both points are on the same indifference curve…

– But this contradicts the “more is better” assumption. Can you tell why?

– Yes, b has more of both and hence it should be preferred over a.

B ,

Bu

r r ito

s p

er

se

me

ste

r


I

a

b


Figure 4.2 Impossible Indifference

Curves



Curvature of Indifference Curves

• Casual observation suggests that most people’s

indifference curves are convex.

• Special Cases:

– Perfect substitutes - goods that a consumer is

completely indifferent as to which to consume.

– Perfect complements - goods that a consumer is

interested in consuming only in fixed proportions.

2017/18 11

Figure 4.4(a): Perfect Substitutes

• Bill views Coke and Pepsi as perfect substitutes: can you tell how his indifference curves would look like?

– Straight, parallel lines with an MRS (slope) of −1.

– Bill is willing to exchange one can of Coke for one can of Pepsi.

Co

k e

, C

ans p

er w

ee

k

1 2 3 4

P epsi, Cans per w eek

1

0

2

3

4

I 1 I 2 I 3 I 4


Figure 4.4(b): Perfect Complements Ic

e c

ream

, S

coops p

er w

ee

k

1 2 3

Pi e , Slices per w eek

1

2

3

0

I 1

I 2

I 3

a

d

e c

b

If she has only one piece

of pie, she gets as much

pleasure from it and one

scoop of ice cream, a,

as from it and two

scoops, d,

or as from it and

three scoops, e.


Bads

• A commodity the consumer doesn’t like.

Noise

Sleep


Neutrals

• The consumer doesn’t care about it in one way or the other

Noise

Sleep


Satiation

• A situation where there is some overall best bundle (x1, x2) for the consumer, and the closer she is to that bundle, the better off she is in terms of her own preferences.

• In this scenario ICs have a negative slope when the consumer has “too little” or “too much” of both goods and a positive slope when he has “too much” of one of the goods.

– Having too much of one of the goods makes it a bad, reducing the consumption of the bad good moves her closer to the “bliss point”

– If she has too much of both goods, they both become bads, so reducing the consumption of both moves her closer to her “bliss point”


Satiated Preferences


Monotonic Preference

• Premised on the idea that more is better, and that, we are examining conditions before the consumer reaches a satiation point.

• Monotonicity implies that indifference curves have a negative slope.

• Averages are preferred to extremes.


Monotonic Preference

• More of both goods is better for this consumer

X2 Better bundles

Worse bundles

X1


Budget Constraint

• Budget line (or budget constraint) - the bundles of

goods that can be bought if the entire budget is spent

on those goods at given prices.

• Opportunity set - all the bundles a consumer can buy,

including all the bundles inside the budget constraint

and on the budget constraint.


Budget Constraint (cont.)

• If Lisa spends all her budget, Y, on pizza and burgers,

then

pBB + pZZ = Y

– where pBB is the amount she spends on burgers and

pZZ is the amount she spends on pizzas.

• This equation is her budget constraint.

– It shows that her expenditures on burgers and pizza

use up her entire budget.



• How many burgers can Lisa buy?

– To answer solve budget constraint for B (quantity of

burgers):

B

Z

ZB

ZB

P

ZPYB

ZPYBP

YZPBP



• From previous slide we have:

– If pZ = $1, pB = $2, and Y = $50, then:

B

Z

P

ZPYB

$50 ($1 )25 0.5

$2

ZB Z


Figure 4.7: Budget Constraint

From previous slide we have that if:

– pZ = $1, pB = $2, and Y = $50, then the budget constraint, L1, is:

$50 ($1 )25 0.5

$2

ZB Z

B

,

Bu

rge

rs

pe

r se

me

ste

r

Opportunity set

50 = Y / p Z

L 1

25 = Y / p B

20

10

10 0 30


a

b

c

d

Amount of Burgers

consumed if all income

is allocated for Burritos.

Amount of Pizza

consumed if all income

is allocated for Pizza.


Figure 4.8(a) Changes in the Budget

Constraint: Price of Pizza Doubles B

, B

urg

ers

r

per

sem

este

r

Loss

50

L 1 ( p Z = $1)

L2 (pZ = $2)

25

25 0


B = Y PB

- PZ = $1

PB

Z

If the price of pizza doubles, (increases from $1 to $2) the slope of the budget line increases

This area represents

the bundles she can no

longer afford

$2 Slope = -$1/$2 = -0.5

Slope = -$2/$2 = -1


Figure 4.8(b): Changes in the Budget Constraint: Income Doubles

Gain

L 3 ( Y = $100)

L 1 ( Y = $50)

0

B = $50

PB

- PZ

PB

Z

If Lisa’s income increases by $50 the budget line shifts to the right (with the same slope!)

$100

This area represents the

new consumption

bundles she can now

afford!!!

100 50


B, B

urr

itos p

er

sem

este

r

50

25


Consumer equilibrium

• The consumer maximizes utility at a point where the slope of

the indifference curve (MRS) is equal to the slope of the

budget constraint.

• At the chosen point we have tangency of the indifference curve

and the budget constraint,

• px/py = MRS = MUx/MUy, i.e., MUx/px = MUy/py.


The budget constraint and the indifference curve have the same slope at the point e where they touch.

Therefore, at point e:

Slope of I2

Figure 4.9 Consumer Maximization, Interior

Solution (cont.) B

, B

ur r

ito

s p

er

se

me

ste

r

25

50 0


I2

e

MRTP

P

MU

MUMRS

B

Z

B

Z

Slope of BL



30

Corner solution: Boundary-optimal solution with only commodity x2 being consumed

2017/18 Priscilla T. Baffour (PhD) Microeconomics 1

31

Corner solution for perfect substitutes


32

Corner solution with strictly concave preferences


Recap on Taxes, Subsidies & Rationing

Forms of Taxes

1. Quantity (specific) tax

2. Ad valorem (value) tax

3. Lump sum tax

Forms of Subsidies

• Specific subsidy

• Ad valorem

• Lump sum

Rationing


Problem

A government rations water, setting a quota on how much a consumer can purchase. If a consumer can afford to buy 12 thousand gallons a month but the government restricts purchases to no more than 10 thousand gallons a month, how does the consumer’s opportunity set change?


Solved Problem


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