Transcript TAX ON ONE PRODUCT (EXCISE TAX)

How will some particular change in public policy ( manily
tax policies) affect the welfare of different groups of citizens
and the overall efficiency of the economy .we are
concerned with questions of positive economics with how
to predict the effect of particular policies , without making
any judgment about whether they are good or bad . It is
worth nothing that we are not dealing with the optimal tax
policies .
Assumptions
We should have full specification of the policy change .
If government expenditure should be increased we should
know how it will happen .
If taxes is to be increased we should know for what
purposes it will be spend . It is meaningless to conclude
that food subsidies will reduce inequality . We should
know how will it be financed .
Walters & Layard CH 3
Application to Public finance
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PURPOSE OF TAXATION
Taxes may be levied for three general purposes .
1- to finance the subsidization of goods subject to
increasing return to scale (including public goods ) .
2- to offset external technological diseconomies , subsidies
being handed out where there are external economies .
3- to correct distribution of income , subsidies being handed
out to deserving .
Except in case 2 the function of tax is to derive an edge
between the value of what a factor produce and what a
factor can consume.
In case 1 government wishes to pay for factor services .
In case 3 the government subsidies the poor so that they
can buy more than they can produce (earn) and taxes the
rich so that they can buy less than they produce (earn).
Walters & Layard CH 3
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PURPOSE OF TAXATION
In case two the aim of tax is to ensure that the private cost
(return) faced by a decision maker are the same as the
social cost (return ) . But even so , the tax release some
resources for the government use .
The aim is to answer the following questions for each of the
main types of taxes available to a government in a closed
economy .
1- How the tax affect the welfare of different groups ,
outside of any benefit citizens may obtain from expenditure
financed by the tax ? This is called the incidence of the tax
2- what is the efficiency cost of the tax ? This is the sum of
welfare losses to taxpayers due to tax minus the benefit it
yields , as measured by the tax yield . This is called the
excess burden of tax .
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THREE GENERAL PRINCIPALS
A- The irrelevance of who pays .
if a market is in competitive equilibrium through out , the
effect of tax upon relative prices and upon quantities is
identical whether the tax is levied on buyers or sellers .
P
S=MC
Demand price =Buyer’s price =P1
AB =Tax rate
A
P*
Supply price=Seller’s price=P2
B
D
P1= P2 + AB
Q
Q
Who is paying the money to tax collector ? This is illustrated in the figure .
Walters & Layard CH 3
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THREE GENERAL PRICIPALS
1-Tax levied on seller’s only ;
The amount the seller’s require the buyers to pay them (P1)
exceed the final amount they want to receive to cover the
marginal costs ( P2) . The seller’s have to pay the tax in
excess of their marginal cost.
2-Tax levied on buyer’s only ;
The amount that the buyers are willing to pay the sellers (P2
) is less than the final amount that they have to pay (P1) to
obtain the commodity . the difference is the amount that
they have to pay to the tax collector as a sale tax .
As is seen the consequence of 1 and 2 is the same . Price
to be paid by buyers is greater than the amount received by
sellers by an amount equal to AB , tax rate .
Walters & Layard CH 3
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THREE GENERAL PRICIPALS
B-Incidence of the tax
A given tax will rise the buyer’s price more and lower the
seller’s price less , the less elastic the demand and the
more elastic the supply curve of the commodity is .
P
D
P
S
S
P1
P1
Pe
D
Pe
p2
P2
Q
Q
Qe
Qe
P2Pe = fall in the seller’s price
Walters & Layard CH 3
P1Pe=Rise in the buyer’s price
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THREE GENERAL PRICIPALS
The same figure could be repeated for different supply
curve elasticity's. now if we are considering a factor
demand and the factor is taxed it will suffer more , the more
inelastic is the supply .
Now suppose that in perfect competition tax is levied on
product market . In the perfect competition analysis this will
be transferred to the factor owners , since the amount of the
tax will be transferred to factor owners by reducing their
wage rate. Because , there will be no excess profit or loss
in the final stage for the firm.
In this kind of analysis a general equilibrium analysis is
needed .
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THREE GENERAL PRICIPALS
C- excess burden of the tax;
We assume that there is no income effect in the demand for
x . In other words MRS is independent of the level of
income ( Y) .
P = y per x = Px/Py
MRTyx
a
A
P1
b
e
Pe
f
c
P1-T
AB=Tax rate =per unit tax = P↑ , Q↓
B
d
x1
Walters & Layard CH 3
MRSyx
x0
x
Application to Public finance
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THREE GENERAL PRICIPALS
Welfare cost = ∫xo x1 [MRTyx(x) – MRSyx(x)]dx=e+f = -1/2T∆x
The efficiency cost of a per unit tax on a given commodity is
greater the more elastic is the demand and supply of the
tax commodity ( ∆x would be greater in this case ).
So the greater is the possibility of substitution in the
economy , the greater is the welfare cost .
It is possible to use the figure to show the breakdown of the
tax incidence between the households as consumers and
households as income earning factors of production .
The total effect change has three parts .
1- loose to the consumers
2 – loose to the producers
3- gain to the tax payers .
Walters & Layard CH 3
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THREE GENERAL PRICIPALS
1- Loss of consumer surplus
Measured as the difference between the consumer surplus
when x=xo with relative prices equal to (Px / Py)0 and when
x=x1 with relative price equal to (Px/Py )1 . Assuming that the
purchasing power in terms of x is constant or there is no
income effect , demand could be considered as
compensated demand and represented by MRSyx .
Loss=∫0 x1 [MRSyx(x) - (Px/Py)1 ]dx - ∫0 X0 [MRSyx(x)–(Px/Py)o]
dx = a - ( a + b + e ) = - ( b + e)
2- Loss of producer surplus
With the same notion as in the first case , the loss will be
equal to d – (c+d+f) = -( c+f ) . The loss to the producer
[(c+f)] will be transferred to factor owners as a
reduction in their income earned . Because the producers
are operating in the perfect competition conditions with zero
profits .
3- Gain to the to tax payers which is equal to ( b+c )
Walters & Layard CH 3
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THREE GENERAL PRICIPALS
Using the kaldor criteria we should add up the welfare changes
of different parties a find out the result .
∆w= ( b+c) + (- c - f ) + (- b - e) = - ( e + f )
As it was seen , this is the excess burden of the tax . The
consumers and producers taken together loose ( e+f) more
than the paid tax .
Breakdown between consumers and factor owners is very
useful in small corporation since the main effect of the tax
is limited to factor owners previously employed in the
industry.
But in large industries where release of a factor from one
industry affects the workers in other industries , it is not
easy to see which factor owner in which industry is being
affected. In these cases a general equilibrium analysis is
needed .
Walters & Layard CH 3
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GENEREAL TAX
In a two good two factor world and in the context of general equilibrium
we can classify any tax into one of four logically possible categories;
1-General tax on all factors or products , (value added tax )
2- Tax on one factor
3- Tax on one product
4- Tax on one factor when it employed in producing one product only .
General tax on all factors or products .
Suppose a simplest production function ;
Y= aL = YL L = constant return to scale
YL = MPL
supply of labor is given and it is external to the system .
Government wants to consume a fraction equal to [ t/(1+t) ] of what is
produced in the economy and leaving a fraction equal to [ 1/(1+ t) ]
for the workers in the economy . So the government share of the total
product ( Y ) is equal to [ tY/(1+t) ] . How this could happen ?
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GENERAL TAX
(PY Y L )
(1  t )

Walters & Layard CH 3
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GENEREAL TAX
In the first case the government obtain command over
resources by ensuring that national product at market
prices exceeds that at factor cost .
in the second case , it seems that though these two
measures of national product are identical , the factors
can not buy the national product .
“ a general tax levied at an equal proportional rate on
all products has effects identical to a tax at the same
rate on all factors . “
The above statements could be demonstrated for more
than one good and one factor.
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TAX ON ONE FACTOR
W L / PY
(WL/PY )(1+t)=YL
Two factors , and one output , Y = Y ( K , L ) .
Factors are supplied in given quantities , government levies
tax on labor only to allocate some of the output for the use
of government . For this reason government takes away
some of the MPL for this purpose as follows
(WL / Py ) = YL / (1+t) ,
(WK / PY) = YK
The result is illustrated in the following figure ;
Y per L
S
(WL/ PY )(1+t)=real cost of labor = cost of labor after
levying tax = real wage of the labor before levying tax
Real cost of labor to the employer = marginal
product of labor. Before tax a+b is paid to the
labor which is equal to marginal product of
labor.But after tax some of it ( b ) goes to
government as tax payment
Capital
Capitalincome
income
Tax payment
Tax payment
(Real)
b
Labor
income
Labor
share
(Real)
a
Walters & Layard CH 3
L0
L
YL = MPL = YL (L , K0) marginal
product of labor curve
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TAX ON ONE FACTOR
Suppose that we consider two sector model ( X , Y ) .
Suppose that the supply of labor is given , and
government spends the tax proceed at the same way as the
owners of the factor and demand for labor and capital do
not change. Consequently the marginal productivity ( YL)
would not change and the whole structure of gross price
is unaltered . Gross price of labor in terms of each good (
real wage of labor ) is the same after tax as before . The
allocation of labor does not alter.
If supply of other factor ( except labor ) does vary ,
Then the above analysis would hold if tax do not alter the
supply of other factors ( so that marginal productivity of
labor does not change ) . So there will not be any efficiency
cost .
Walters & Layard CH 3
Application to Public finance
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TAX ON ONE FACTOR
However , even if prices and resource allocation are affected, a tax
on a fixed factor can not involve any efficiency cost , since the
difference between private and social return to the factor does not affect
any choice which the factor owner make about the supply of the labor .
“ a tax on a factor that is in fixed supply will have no efficiency
cost . The allocation of resources will be unaffected , and the tax
will be born entirely by the tax factor , unless the tax alter the relative
demand for the product or supply of the other factors that are in variable
supply “ , in other words ;
If the supply of factor is totally given , the whole factor income is
rent and none of it is needed to induce the factor to become
available . Whenever an income is pure rent , there will be no efficiency
cost in taxing it . Since it’s behavior need not be modified to escape the
tax .
Walters & Layard CH 3
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TAX ON ONE PRODUCT (EXCISE TAX)
Suppose that there are two products; X , Y , neither is in
fixed supply . After tax we will expect an alteration of
resource allocation . There will be one basic assumption ;
“ although taxes redistribute income they do not affect the
relative demand for different goods , because the marginal
propensity to consume on X and Y out of additional income
are the same for consumers and government .
So there would be unique set of community indifference curve
which can be represented by a utility function U(X, Y) which
correctly predict the equilibrium relative prices (Px/PY) for any
particular mix .
In the following we will see how tax on one product will alter
the efficiency conditions and resource allocation .
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TAX ON ONE PRODUCT (EXCISE TAX)
Suppose that ;
Px , Py are prices of X and Y which households will face.
Wk , WL , are factor prices to households ( net of taxes ).
tx , ty = product tax rate as a proportions of net-of-tax price.
tkx , tky = tax rates on capital in X and Y industries , as
proportions of net of tax prices .
tLx , tLy = tax rates on labor in X and Y industries , as
proportions of net of tax prices .
MCx , MCy marginal cost of X and Y to producers .
Each factor will receive the value of it’s marginal
product divided by (1+t) if a tax is levied on that factor.
(t is the tax rate) .
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TAX ON ONE PRODUCT (EXCISE TAX)
Walters & Layard CH 3
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TAX ON ONE PRODUCT (EXCISE TAX)
Now suppose that we levy tax on all commodities ;
MRSxy = ( Px/Py ) = MCx(1+tx) / MCy(1+ty)
-3Kx + Ky = K0
-4Lx + Ly = L0 , if tx = ty , ,
-5if tx = ty , then MRSXY = MCX /MCY , efficiency remains
Since community indifference curve is unambiguously
defined and we do not need to specify the behavior of
different consumers to determine the allocation of
resources , there would be five equations ( 1,2,3,4,5 ) with
five unknowns (Kx , Ky , Lx , Ly , MCx/MCy ) . There will be
unique solutions for the variables .
The above five equations show the relation between
variables when tax is levied on all factors or outputs . Now it
is possible to examine the effect of different tax policies by
the help of above relations .
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TAX ON ONE PRODUCT (EXCISE TAX)
a- equal tax on all products ( tx =ty=t )
MRSxy = ( Px/Py ) = MCx(1+t) / MCy(1+t)=MCx/MCy
Tax will not alter the resource allocation , the same result
will be obtained . This is the same as tax on all factors of
production ;
b- Equal tax on all factors of production ( tLx=tLy=tKx=tKy)
Tax will not alter the resource allocation , the same result
will be obtained . This is the same as as tax on all products;
(YK / XK) (1+tKx )/(1+tKy )= (Px/PY)=MCx/MCy
(YL / XL ) (1+tLx )/(1+tLy)= (Px/PY)=MCx/MCy →
(YK / XK) = (Px/PY)=MCx/MCy
(YL / XL ) = (Px/PY)=MCx/MCy
as it is seen none of the equations 1 through 5 will change
before and after tax both in case a and b. . So the resource
allocation would not change either .
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TAX ON ONE PRODUCT (EXCISE TAX)
so we can conclude that a tax levied at an equal
proportional rate on all products has effect identical to a tax
at the same rate on all factors .
c- equal tax on labor only , ( tLx=tLy=t).
As it is clear this will not change any of the equations 1 to 5
. Again this will not change the resource allocation .
d- Tax on output X only , tx=t
As it is seen , this will alter the equilibrium conditions and
resource allocation. As it is clear output remains on the
transformation curve ; RTSKLx = RTS KLY , but the product
mix will change , that is ;
MRS = Px / Py = MCx ( 1 + t)/ Py > ( MCx / MCy ) = RPTxy
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TAX ON ONE PRODUCT (EXCISE TAX)
After tax , MRS > MRT
Optimal point
Y
Transformation curve
Y2
O
Y1
X2
X
X1
Incidence of the tax
As it is shown in the figure , tax on output x will
reduce the production and consumption of labor
intensive output (X), and increase the production and
consumption of capital intensive output Y.
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As a result , capital intensity in production of both outputs will
fall (slide 37 CH 2 ). That is ;( K/L )x and ( K/L )y decrease .
So marginal productivity of capital would increase and
marginal productivity of labor would decrease
Since x is taxed and price of x is increased , non of the factors
factor could buy its marginal product in x industry .
As marginal productivity of labor decrease in both industries X
, and Y , WL/Px and WL/Py will decrease and this will
unambiguously worsen the labor welfare , since
[
UL ( WL/Px , WL/ Py ) ] will decrease .
But for the welfare of capital owners this is not clear , because
when capital productivity increase , Direction of change for
(WK/Px ) is not known . It is under two effects ;
Walters & Layard CH 3
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TAX ON ONE PRODUCT (EXCISE TAX)
The first effect is increase in the marginal productivity of
capital in x industry which will increase (WK / Px) . The
second effect is decrease in ( WK /Px ) , because of
increase in price of X ,since tax is levied on output x .
Consequently the direction of change in Uk ( Wk/Px , WK/Py )
is not known. It should be noted that the welfare gain from
the increased spending is not included .
Could the output of x increase as a result of increase in price
of x because of tax policy ?
In order to answer the question we should see what
happens to excess demand for output X .
1-If marginal propensity to spend on x be the same for
private and governmental sector , transfer of fund from
private to government sector does not affect total demand .
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TAX ON ONE PRODUCT (EXCISE TAX)
2- If government has higher marginal propensity to spend
on x than the private sector , even if government spends all
the tax proceeds on x , production of x must fall if
community consumes more y than before . In this case ,
the price elasticity of demand for x exceeds unity .
Px ↑= %1→Qx↓ > %1 →( Px Qx ) ↓
income is constant
( Py Qy ) 
Y
So , as long as E>1 , an excise tax on a labor intensive
good will normally make labor worse off and may or may
not make capital worse off . The policy is efficient since
economy will remain on the P.P.F. .
Walters & Layard CH 3
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TAX ON ONE FACTOR IN ONE INDUSTRY
suppose that tax is levied on labor in a labor intensive
industry X . Perfect competitive condition is prevailing .
Two distortions will result ;
1- production does not occur on the efficient transformation
curve . Since ; (XL/XK) = (WL)(1+tLx) / WK > (WL/WK)=(YL/YK)
RTSx LK > RTSy LK
Production does not occur on the efficiency locus (contract
curve ). The production does occur on the new locus which
is not efficient and lies inside the efficient one .the same is
true for the transformation curve . Because the
transformation curve is derived from the contract curve.
The new transformation curve which is not efficient lies
inside the old one which is efficient .
Walters & Layard CH 3
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TAX ON ONE FACTOR IN ONE INDUSTRY
oy
K0
New curves
X0
RTSLKx > RTSLKy
P’
(K/L)X0
y1
R
p
X
ox
P
P’
L0
(K/L)yo
Y
Walters & Layard CH 3
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TAX ON ONE FACTOR IN ONE INDUSTRY
as it is seen from the figure the relative product price does not
correctly reflect the rate of transformation along the new
transformation curve .
if price elasticity of demand for X is greater than one ,
production of X will decrease as the result of tax policy (
assuming marginal propensity to spend on x is identical ) .
As it is shown in the figure point P moves to a point between
ox and P’ , for example a point like R on the new contract
curve .
As it is shown in the figure , (K/L)y will decrease and cause
labor productivity decrease and capital productivity increase
which led , Wk/PY to increase and WL/ Py to decrease .
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TAX ON ONE FACTOR IN ONE INDUSTRY
(K/L)y will fall unambiguously , but the same is not true for
(K/L)x .
1-Suppose that X falls a little and production of x occur at a
point near to P’ at a point between R and P’ . In this
case (K/L)x will increase which cause XL to increase and
XK to decrease .
There would be two effects on ( WL/px ) ;
First - ( WL/px ) will increase because XL has increased .
Second - ( WL/px ) will decrease because tax is levied on
labor and ( WL/px ) has decreased to [ WL/px )=(XL/ (1+tLx) ]
But we know that ( WL/px ) ↓ = (WL/Py)↓ (Py/Px)↓ . (both
(WL/Py) and (Py/Px) will decrease . So WL/Px will decrease
too ).
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TAX ON ONE FACTOR IN ONE INDUSTRY
But it is not known what will happen to( Wk/Px) , since the
direction of change of WK is not known . Because ;
WK = ( XK )↓ ( Px )↑ , ( Px will increase while XK will
decrease ). [ (Wk /Px ) ? = (Wk /Py ) (Py/Px)↓ ]
2- production of x falls a great deal and production occur at
a point between Ox and R near to Ox. In this case (K/L)x
will decrease and XL will decrease and XK will increase .
Since WK ↑ = ( XK ) ↑ (Px ) ↑ , so WK will increase and
capital will gain (since both XK and YK will increase ).
labor will be worse off unambiguously ;
( WL/px ) = (WL/Py)↓ (Py/Px)↓
Capital gains due to the greatly increased quantity of capital
intensity commodity y which is demanded .
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Factor tax with variable factor supply
Factor tax with variable factor supply
So far we have assumed that factors are in given supply.
But if the supply of the factors of production are variable ,
there will be efficiency cost involved in levying tax .
Because the factors are responding to changes in prices
when tax is levied . We will examine two kind of tax , first
tax on earned income , second tax on capital .
1- tax on earned income ,
Suppose that in the following figure Y=goods , X= lesiure
Tax on earned income → tax on L →
tax on goods purchased → potential consumption falls
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Factor tax with variable factor supply
Y
Before tax → MRS=MRT
C
After tax → MRS < MRT
MRS + T = MRT
C’
X
X’
MRS = (Px/Py)= the rate at
which people would like to
increase their personal income
(consumption) by sacrificing
leisure (working more)
Walters & Layard CH 3
After tax people would
like to work less and
have more leisure and
less earned income .
MRT =( MCx/MCy) the rate at which
production sector can actually produced
goods by sacrificing leisure .
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Factor tax with variable factor supply
2- tax on capital
Now suppose that X is consumption today and Y is
consumption in the future .
MRS= the rate at which consumers would like to increase
their personal future consumption by decreasing from
present consumption .
MRT = the rate at which society future consumption can
actually increase by sacrificing from present consumption
(through investment by saving today )
Before tax MRS = MRT ;
After tax MRS < MRT ( MRS + T=MRT ) ; by levying tax on
capital income ( on interest rate or on return from capital) ,
saving is discouraged ( MRS decrease ), and present
consumption will increase , X increase to X’ .
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Interpersonal distribution
To evaluate any change of budgetary scale in the real world
, we want to know how it would affect the interpersonal
distribution of income and the level of output . This requires
three extension ;
1- we should include the distribution of the benefits from
any government expenditure between individuals .
2- we should recognize that there are more than two
factors of production .
3- we should note that individuals often own both labor and
capital .
Knowing all the above , we should know that whether the
policy is equalizing (progressive ) or dis-equalizing
(regressive) . For this we need to calculate a pre and post
policy income measure.
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Interpersonal distribution
With income rise, if net benefit rise the policy is dis-qualizing
or it is regressive .With income rise if net benefit fall ,the
policy is equalizing or it is progressive.
The sufficient condition for progressively is as following ;
d(B-C)/dy = dB/dY - dC/dY < 0
B = benefit from policy
C = cost of the policy
A policy can already be progressive even if it benefits the
rich more than the poor , provided that it imposes even
greater differential cost on rich .
EBY = elasticity of benefit with respect to income .
ECY = elasticity of cost with respect to income .
If EBY > ECY , , the policy is regressive .
If EBY < ECY , , the policy is progressive .
Thus a subsidy on a normal good (like food) financed by a
poll tax ( equal tax on every one ) is regressive. Because the
size of the subsidy rises with income while the tax does not .
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PROBLEMS
Q3-1 ; Suppose a tax of $T per unit is imposed on labor . Market price are
sticky and do not adjust fully to produce a new equilibrium. Compare the
welfare of the workers when
i- The tax is levied on employers
ii- The tax is levied on workers.
W
W1
SL
a
Tax=ab
W*
W2
Walters & Layard CH 3
b
L1
DL = VMPL
L*
L
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PROBLEMS
Solution ;
i- W2 = wage paid to workers = the minimum amount which they want to
receive to stay at work .(market price)
W1 = cost of labor to employer= the minimum amount which the workers
should receive to stay at work + tax which they have to pay per worker.
L* L1 = unemployment level .
ii- W1 = wage paid to workers by employers . The workers will pay ab
amount of this wage to government for tax and receive the remaining which
is W2 , the minimum amount which they need to receive to stay at work.
L* L1 = unemployment level .
Q3-2 ; Suppose a small tax of $T per unit were levied in the US on the
following commodities; Salt , Hotel rooms in Miami , Yellow shirts . Suppose
also that equilibrium price and quantity were the same for all there
commodities. In which case would the buyer’s price per unit rise most and
in which case least ?
Solution ; Buyer’s price will rise more , the more inelastic is the demand
curve and the more elastic is the supply curve.
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PROBLEMS
Q3-3 ;
(i) suppose that the equilibrium price and quantity per annum were the
same for yellow shirts and hotel room booking in Miami. Which on efficiency
grounds , would it be better to tax to get a given revenue?
(ii) – Develop a formula which expresses the welfare cost of a small per-unit
tax T as a function of T , x , p , and the elasticity of supply and demand .
Then show that this cost , as a function of tax yield , depends only on the
elasticities of Supply and demand and the proportional tax rate T/p .
(iii) – check that you understanding the relation of figures 3-2 and 3-3 .
After the tax is imposed and its proceeds back in lump-sum form to
consumers , What distances in Figure 3-3 (measure in terms of y )
(a) – the value of national income to consumers ?
(b) – the national income in market price .
( c) – the national income in factor cost (i.e., the amount of y which can
be purchased by factor incomes) .
Walters & Layard CH 3
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PROBLEMS
Solution ;
Suppose that demand and supply are both quite elastic for yellow shirts ,
and demand for holidays in Miami is fairly elastic while supply is inelastic .
Miami Hotels
Yellow Shirts
S
ab=tax=cd
D
c
S
a
D
P*
b
d
Q2
Q’2
Q’1
Q1
Equal per unit tax on both goods result in less efficiency in terms of
decreasing the output in Miami hotels . Tax revenue is equal to t ( Q’) .
The greater is Q’ the smaller amount of per unit tax is necessary to get a
given
amount
. to Public finance
Walters
& Layard
CH 3 of tax reveneiw
Application
41
PROBLEMS
ii- we know that
PD = PS + T → Demand price = Supply price + Tax
dp D
dp S
x 
x  T
dx
dx
T
Tx
1
x 

S
D
1
dp
dp
P 1 

So ;
S

D
dx
dx

2
1
T x
1
T x 
2
2P 1  1
S
D


T 


P
2
xp
1
2 1  1
S
D


We can see that the excess burden of the tax depends on the proportional
tax rate , expenditure o the good, and demand and supply elasticity, we
could also find that ;
1 T x
T
1

That is ;
Walters & Layard CH 3
2
Tx

2P
Application to Public finance
1
S

1
D
42
PROBLEMS
For a given T/P , excess burden per dollar of tax revenue is larger , the
larger is supply elasticity and absolute value of demand elasticity.
iiiY
e+f
a) – the value of national income to
consumers = being calculated from CIC
after tax in terms of Y =
Ymax = d + b + c + a
a
b+c
Slope = - MCX / MCY (1+t)
d
Slope = - MCX / MCY
b – the value of national income in
market price = being calculated from
relative market prices after tax =
Ymax = d + b + c
a) – the value of national
income in factor cost = being
calculated from slope of MRT
after tax in terms of Y =
Ymax = d
Y Max
CIC0
CIC1
X1
Walters & Layard CH 3
X0
X
Application to Public finance
43
PROBLEMS
Q1-4 Suppose government wants to buy one-tenth of the national product .
Y= K1/4 L3/4 and factor supplies are K0 and L0 . What tax rate (computed
on the net of tax price ) would it use in the following cases ;
i- the tax is a product tax
ii- the tax is tax on capital
iii- the tax is at an equal rate on labor and capital.
Solution ;
i- PY = buyer’s price = [ WL / YL ] (1+t) , PY YL = WL (1+t)
WL = (PY YL ) / (1+t)
government share = (PY YL ) [ t / (1+t) ] = (1/10) (PY YL )
government share of national product = t/(1+t) = 1/10 ,
t = 1/9
ii- ( WK / Py ) = YK / ( 1+t)
( WK / Py )(t) ( K0 ) = Tax revenue from capital income = (1/10) Y
(WK / Py )(t) ( K0 ) =YK /(1+t)( K0 ) = (1/4 ) (Y/ K0 ) ( 1/ (1 + t) (K0 )=(1/10) Y
(1/4 ) Y ( 1/ (1 + t)=(1/10) Y , t = 2/3
iii - the same as in i, t= 1/9
Walters & Layard CH 3
Application to Public finance
44
PROBLEMS
Q3-5 , a subsidy to capital will encourage the use of capital intensive methods of
production , even if the supply of capital is fixed. True or False.
S= subsidy to capital .
(WK / Py )=YK (1+S) ,Capital income will increase.Tax will also increase to finance the subsidy .
Y
SK
Y per L
(K/L)y
K
P
YK *
subsidy
DK
(K/L)x
(K/L)*
K/L
X
L
Solution -Use of capita intensive methods of production means moving P to the left
on contract curve . This means producing more Y and less X . If Y is capital
intensive good , the production of Y will increase if there is a shift in demand towards
more Y . The shift in demands will result from increased income from subsidy or any
other change like shift in the supply of L or K .
Walters & Layard CH 3
Application to Public finance
45
PROBLEMS
Q3-6 , Suppose there is small increase in local property taxes and that
these are levied on tenants. Who will bear this tax , landlords or tenants.
i- If market rents are market-determined
ii- if market rents are regulated well below the equilibrium level.
P
SH
i- if market rent is P* , the
Assumption ; market
consumers will not pay any
supply are perfectly
amount more than this level.
inelastic
Since they are paying this
P*
level of rent , all the tax
0
P
should be born by landlords.
DH Q
That is tenants pay P0 to
Q1 Q2
landlords and the rest to
government for tax ( tax
amount equal to P*P0 ) .
ii- If market rent is regulated at P0 , the real cost of housing for tenants is
P0 plus tax . So the tenants will bear a tax at most equal to P0 P* for Q1
level of housing supply.
Walters & Layard CH 3
Application to Public finance
46
PROBLEMS
Q3-7 X and Y are produced at constant rate of returns by K and L in fixed supply .
Y is labor intensive . Labor has a relatively strong preference for x . What are the
probable effects on the welfare of labor ( L) and capital ( K) of an excise tax on Y ,
The proceeds of which are spent on government purchases of X ? Does Labor
necessarily loose
Solution - ( K/L)y < (K/L)x , Y is labor intensive , X is capital intensive
Excise tax on Y → ( Px / Py )  → sub. Effect → private spending on X 
Government spends the whole income of tax from Y on X , so the total effect of
these two is rising the production of X from P to P’ ( since demand for X has risen
). Moving from P to P’ will result into fall in the capital intensity of production in both
X and Y .
Y
P’
K
X
Walters & Layard CH 3
P
L
Application to Public finance
47
PROBLEMS
(K/L)x  (K/L)y  → MPLx  , Mply  . → UL ( WL /Px , WL /Py ) .
Labor can not buy its marginal product in Y since Py has risen .
So labor necessarily worse off even though the price of x for which labor
has strong preference has fallen .
Q3-8 (i) - Suppose closed economy has as factors only land and labor ,
with agriculture more land intensive than manufacturing. A food subsidy is
introduced that is financed by a proportional tax on all factor incomes. Must
labor necessarily loose ?
(ii) – The British government publishes an annual analysis the incidence of
taxes and subsidies . This assumes that Product taxes are passed on to the
consumers and factor taxes are born by the factor being taxed. This
assumption are criticized on the ground that it implies the supply of factor is
perfectly inelastic and the supply of products perfectly elastic , and that
these two effects are incompatible propositions. Evaluate the logic of this
preposition
Walters & Layard CH 3
Application to Public finance
48
PROBLEMS
Labor
F
P
P’
M
Land
(i) A tax on all factor incomes is equivalent to an equi-proportional tax on both
goods . So if this is combined with a subsidy on food, the total package is
equivalent to a tax on manufactures and a smaller subsidy on food. Assuming that
Food production will increase , point P moves to point P’ . Since the ratio of
labor to Land decrease in Food sector, so MPL will decrease as well. But a
subsidy on food rises the purchasing power of labor in food. The total effect
depends on the relative strength of the elastic ties. If Labor spends a large share
of his income on food he may gain .
Walters & Layard CH 3
Application to Public finance
49
PROBLEMS
(ii) P
Tax =
P*
W
a
S’
a
SL
P*
a
P*
S
DL
D
L
q
Two assumptions are not necessarily inconsistent. If factor intensities are the
same in both industries, the transformation curve is a straight line . And MRT is
constant along the transformation curve (since MRT equals to relative marginal
cost of q in terms of other commodity, supply curve of q which is its MC is
perfectly elastic) . In this case product tax will not alter the relative factor prices ,
since MRT or relative marginal cost is constant and so the relative factor prices
will not change . So all the tax will pass to the consumers . But for the tax on
factors this is not the case as it shown in the figure.
Walters & Layard CH 3
Application to Public finance
50
PROBLEMS
Q3-9 complete table 3-1 .
( in a two commodities and two factors world , when x is labor intensive and Y is capital
intensive , what will be the effect of tax on capital in X industry).
Oy
K
Old efficiency locus
New Locus
(K/L)x
P
P’
R
Ox
(K/L)y
L
XL /XK = WL / WK (1+tkx ) < WL / WK = YL / YK
RTSLK x < RTSLKy at point P’ , Qx  so
production should occur on the Ox P section of the
new locus . Either on Ox R section or on RP section.
51
Walters & Layard CH 3
1- production lies on RP section
or X decrease a little bit . (K/L)y
will increase , YK falls , YL rise.
(K/L)x will decrease , XL falls
and XK rise . But
(WK /Px)=(Py /Px )(WK/Py) 
Both marginal productivities of
capital in X and Y will fall so
capital is unambiguously worse
off . But labor welfare is not clear
2- production lies on Ox R
section of the curve . . (K/L)y will
fall YK rise and YL falls . ( K/L)x
falls , XL fall and Xk rise . But
(WK /Px)=(Py /Px )(WK/Py) 
, so direction of the XK is not
clear . So by tax on labor
intensive good and large
decrease in labor will loose
definitely but capital welfare is
not clear .
PROBLEMS
Walters & Layard CH 3
Application to Public finance
52
PROBLEMS
Walters & Layard CH 3
Application to Public finance
53
PROBLEMS
Walters & Layard CH 3
Application to Public finance
54
PROBLEMS
Walters & Layard CH 3
Application to Public finance
55
PROBLEMS
Walters & Layard CH 3
Application to Public finance
56
PROBLEMS
Walters & Layard CH 3
Application to Public finance
57
PROBLEMS
Walters & Layard CH 3
Application to Public finance
58
PROBLEMS
Walters & Layard CH 3
Application to Public finance
59
PROBLEMS
Walters & Layard CH 3
Application to Public finance
60