• It does not matter for the equilibrium

Microeconomics Consumer Theory

Dr Hamish Low

Lecture 8

Result II

• It does not matter for the equilibrium

whether sellers or buyers are responsible for paying the tax.

• Those who are responsible for paying the tax can pass on a proportion to the other party.

• How much, depends on the elasticity of

demand and supply.

Two special cases

• If supply is perfectly elastic (horizontal), then demanders pay the tax.

• If supply is perfectly inelastic (vertical),

then suppliers pay the tax.

A quantity tax: perfectly elastic supply

q

p

p

P

(q)

P

(q)+t p

E

E

P

(q) q

p

= t

A quantity tax: perfectly inelastic supply

q q p

p₀

P

(q)

p

= E

P

(q) p

t

= q

Dalton’s formula

s p d p

s p d

e e

e t

p

 



Elasticity of demand

Elasticity of supply

The dead weight cost of taxation

q q p

p

P

(q) p

E

E₁

P

(q) q

p

t A

C

D B

Deadweight loss

Tax

revenue

Social Cost of Taxation

• Loss in consumer surplus A+B

• Loss in producer surplus + C+D

• Tax revenue - A+C

• Social loss = B+D

Result III

• Taxation introduces a distortion and creates a deadweight loss.

• Environmental benefits?

Outline of course

• What is rationality?

• What happens as prices change?

• How to measure gains / losses when prices change

• What determines prices?

Rationality

• Economics starts from observed behaviour and infers underlying preferences.

• Are individuals rational?

– are choices consistent

– can we represent choices using utility functions

• Distinguish assumptions which required for

rationality from assumptions required to obtain well- behaved utility functions

• Minimum assumptions for rationality

– transitivity (revealed preference)

• To generate well-behaved indifference curves

– more is better than less (monotonicity) – average is better than extreme (convexity)

B

A A is revealed

preferred to all these points

Concept of Revealed Preference

y

y

x

^x

A  B

y x

p

 p

At given prices, chose A when B is affordable

Only use information on quantities

and prices

B’

A

y

B

B violates WARP

B’ does not violate WARP

Weak Axiom of Revealed Preference

A

B

C

C A

C B

B A

Observe







 ,

:

A C

observe then

We : 

This is not ruled out by WARP (does not say this is inadmissable) This is ruled out by GARP (which requires transitivity)

Revealed Preference

Consumer Choice

• Constraints: determined by prices and income (exogenous)

• Preferences (well-behaved? exogenous)

• Generates consumer choice

Effect of Price Changes

Substitution and income effects:

SE: Good x becomes more expensive relative to good y

IE: Purchasing power has changed.

U

U

A B

C

x y

Hicks substitution effect

Uncompensated: A - C Compensated: A - B

     

m x

m p

p x p

u p

p h p

m p

p

x

x u y x

x y x



 



 



 , , , , , ,

-ve - ve (normal)

+ ve (normal

good)

+ ve

Slutsky Equation

Uncompensated demand:

Compensated demand:

 ^{p p m} 

x

,

,

 ^{p p u} 

h

,

,

Intertemporal Choice

r m m

r c c

to subject

c

c

c

u

c

 

 

 1 1

) ,

max (

2 1

2 1

2 , ₂ 1

1

1 ] [ 1

) ,

(

r c c

r m m

c c

u

L   

 



 

c c u

c c c u

 

 



) ,

(

) ,

(

1 2 1



First order conditions:



    _r

c c c u c

c c

u  







 , , 1

2 2 1

1 2 1

 ^{r m} 

c

,

uncompensated demand for

consumption in t =1 MRS

Price of consumptio

n today

c

c

A

B

m

m

- ( 1 + r )

Increase in interest rate, r

A’

B’

• Person A: S.E. leads to less consumption today, I.E. leads to more consumption today (ambiguous effect on saving)

A’’

B’’

Saver

Borrower

What happens to consumption and

saving of person A and person B?

 

 

  



1

, , ,

c m m

e r c r

u r c

r e r c

u c

 

 



 





- ve

??

+ ve (normal

good)

+ ve (saver) -ve (borrower)

Ambiguous if saver. Unambiguous if borrower

p

p*

P_S(q)

P (q)

p

p

What Determines Prices?

E

Equilibrium

Summary

• Distinction between constraints, preferences and choices

• Comparative statics: manipulate constraints to influence choices

• Requirement of rationality: transitivity as minimum?

• Choices are reflected in demand curves

• Practical uses of consumer theory: want to measure

welfare cost of price change in way which is not sensitive to units used. So, use money measure of utility change