ECON 3C03
Public Sector Economics: Taxation
Assignment 1
1. Welfare Economics
a. The First Fundamental Theorem of Welfare Economics mentioned that an economic
equilibrium is always Pareto efficient, in such a way that resources are efficiently
allocated within the market without external help. Every individual, though prioritizing
the maximization of their own utility and/or their own profit, are being guided by an
invisible hand through which it affects the prices accordingly to ensure equilibrium, to
contribute in the society, even though it is beyond their intention. Thus, creating an
equality wherein the Marginal Rate of Substitution of each and every consumer is
equivalent to the Marginal Rate of Transformation of each and every supplier.
b. No. The Second Fundamental Theorem of Welfare Economy dictates that the initial
endowment must be transferred, oftentimes, via lump-sum tax. This, however, is very
difficult to implement in practice as it needs to be based on a factor that is unalterable.
Income Tax can’t be used as an alternative to lump sum tax as it alters the behavior of
producer due to the change in the incentives or gains.
c. The assumption that all Individuals and producers are grounded to the competitive
mechanisms of the market in order to achieve Pareto efficiency. If this assumption will
not hold, then both, FWT and SWT, will not hold as well. The problem is that,
competitive behavior does not really hold in reality, as the real world is filled with
monopolistic behavior. Also, real economy is not always in equilibrium as it some
markets are constantly filled with excess supplies and demands.
2. Consumer Theory
Given:
1
1+
∈
h
U ( c , h )=c−
1
1+
∈
l=24−h
c=consumption p= price of consumption
Y =exogenous income
h=work hours w=wage
M =Income
l=leisure hours τ=ad valorem tax
a. Budget Constraint
τ
c=w ( 1−τ ) h+ Y Note : as τ is∈percent form .
100
c=w ( 1−τ )( 24−l ) +Y
c=w ( 1−τ )( 24−l ) +Y
, b. Consumer’s Utility
1
1+
MRS=
−M U c − p
M Uh
=
w
=
∂
∂
− U
∂c
=
1
−
∂
∂c
( )
c−
h ∈
1+
1
∈
=
−c
1
=
c
1
U 1+ −1 1
( ) ϵ ∈
( )( 1+ h h
∈
∂h ∂ h
c− 1 ϵ
∂h
1+
∈
1 1+
ϵ )
c −p
= note: p=1
1
ϵ
w
h
c −1
=
1
ϵ
w
h
1
ϵ
−h
c=
w
Substitute to Budget Constraint:
c=w ( 1−τ )( 24−l ) +Y
1
ϵ
−h
=w ( 1−τ ) ( 24−l )+Y
w
¿ 2 ϵ
h ( w , 1−τ )=[−w ( 1−τ ) ( 24−l )−wY ]
Substitute: h to c
1
ϵ
−h
c=
w
1
ϵ ϵ
c=
{ 2
− [−w ( 1−τ ) ( 24−l )−wY ] }
w
−[−w2 ( 1−τ ) ( 24−l )−wY ]
c=
w
−−w [ w ( 1−τ )( 24−l ) +Y ]
c=
w
¿
c ( w ,1−τ , Y )=w (1−τ ) ( 24−l ) +Y
Substitute both c and h to Utility Function
1
1+
∈
h
U ( c , h )=c−
1
1+
∈
Public Sector Economics: Taxation
Assignment 1
1. Welfare Economics
a. The First Fundamental Theorem of Welfare Economics mentioned that an economic
equilibrium is always Pareto efficient, in such a way that resources are efficiently
allocated within the market without external help. Every individual, though prioritizing
the maximization of their own utility and/or their own profit, are being guided by an
invisible hand through which it affects the prices accordingly to ensure equilibrium, to
contribute in the society, even though it is beyond their intention. Thus, creating an
equality wherein the Marginal Rate of Substitution of each and every consumer is
equivalent to the Marginal Rate of Transformation of each and every supplier.
b. No. The Second Fundamental Theorem of Welfare Economy dictates that the initial
endowment must be transferred, oftentimes, via lump-sum tax. This, however, is very
difficult to implement in practice as it needs to be based on a factor that is unalterable.
Income Tax can’t be used as an alternative to lump sum tax as it alters the behavior of
producer due to the change in the incentives or gains.
c. The assumption that all Individuals and producers are grounded to the competitive
mechanisms of the market in order to achieve Pareto efficiency. If this assumption will
not hold, then both, FWT and SWT, will not hold as well. The problem is that,
competitive behavior does not really hold in reality, as the real world is filled with
monopolistic behavior. Also, real economy is not always in equilibrium as it some
markets are constantly filled with excess supplies and demands.
2. Consumer Theory
Given:
1
1+
∈
h
U ( c , h )=c−
1
1+
∈
l=24−h
c=consumption p= price of consumption
Y =exogenous income
h=work hours w=wage
M =Income
l=leisure hours τ=ad valorem tax
a. Budget Constraint
τ
c=w ( 1−τ ) h+ Y Note : as τ is∈percent form .
100
c=w ( 1−τ )( 24−l ) +Y
c=w ( 1−τ )( 24−l ) +Y
, b. Consumer’s Utility
1
1+
MRS=
−M U c − p
M Uh
=
w
=
∂
∂
− U
∂c
=
1
−
∂
∂c
( )
c−
h ∈
1+
1
∈
=
−c
1
=
c
1
U 1+ −1 1
( ) ϵ ∈
( )( 1+ h h
∈
∂h ∂ h
c− 1 ϵ
∂h
1+
∈
1 1+
ϵ )
c −p
= note: p=1
1
ϵ
w
h
c −1
=
1
ϵ
w
h
1
ϵ
−h
c=
w
Substitute to Budget Constraint:
c=w ( 1−τ )( 24−l ) +Y
1
ϵ
−h
=w ( 1−τ ) ( 24−l )+Y
w
¿ 2 ϵ
h ( w , 1−τ )=[−w ( 1−τ ) ( 24−l )−wY ]
Substitute: h to c
1
ϵ
−h
c=
w
1
ϵ ϵ
c=
{ 2
− [−w ( 1−τ ) ( 24−l )−wY ] }
w
−[−w2 ( 1−τ ) ( 24−l )−wY ]
c=
w
−−w [ w ( 1−τ )( 24−l ) +Y ]
c=
w
¿
c ( w ,1−τ , Y )=w (1−τ ) ( 24−l ) +Y
Substitute both c and h to Utility Function
1
1+
∈
h
U ( c , h )=c−
1
1+
∈
