Walters & Layard CH 3Application to Public finance1 How will some particular change in public policy...

Walters & Layard CH 3 Application to Public finance 1

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 .

AssumptionsAssumptions

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 .


PURPOSE OF TAXATION Taxes may be levied for three general purposes .

1-1- to finance the subsidization of goods subject to increasing return to scale (including public goods ) .

2-2- to offset external technological diseconomies , subsidies being handed out where there are external economies .

3-3- to correct distribution of income , subsidies being handed out to deserving .

Except in case 2 the function of tax is to derive an edge edge between the value of what a factor produce and what a between the value of what a factor produce and what a factor can consume.factor can consume.

In case 11 government wishes to pay for factor services .

In case 33 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).


PURPOSE OF TAXATION

PURPOSE OF TAXATION In case twoIn case two the aim of tax is to ensure that the private costprivate cost

(return) faced by a decision maker are the same as the social costsocial 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 ttax affect the welfare of different groupsax 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 incidence of the taxtax

2- what is the efficiency costefficiency 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 taxexcess burden of tax .


THREE GENERAL PRINCIPALS

THREE GENERAL PRINCIPALS A- The irrelevance of who paysA- 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

Q

S=MC

D

P*

Demand price =Buyer’s price =P1

Supply price=Seller’s price=P2

Q

A

B

AB =Tax rate

P1= P2 + AB

Who is paying the money to tax collector ? This is illustrated in the figure .


THREE GENERAL PRICIPALS

THREE GENERAL PRICIPALS

1-Tax levied on seller’s only ;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 ;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 .


THREE GENERAL PRICIPALS THREE GENERAL PRICIPALS B-Incidence of the taxB-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

Q

P

Q

S SD

Pe

Qe

Pe

Qe

DP1

P2

P1

p2

P1Pe=Rise in the buyer’s price P2Pe = fall in the seller’s price


THREE GENERAL PRICIPALS 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 Now suppose that in perfect competition tax is levied on product market . In the perfect competition analysis this will product market . In the perfect competition analysis this will be transferred to the factor owners , since the amount of the be transferred to the factor owners , since the amount of the tax will be transferred to factor owners by reducing their tax will be transferred to factor owners by reducing their wage rate. Because , there will be no excess profit or loss wage rate. Because , there will be no excess profit or loss in the final stage for the firm. in the final stage for the firm.

IIn this kind of analysis a general equilibrium analysis isn this kind of analysis a general equilibrium analysis is neededneeded .


THREE GENERAL PRICIPALS THREE GENERAL PRICIPALS C- excess burden of the tax;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) .

x

P = y per x = Px/Py

Pe

MRTyx

MRSyx

A

BP1-T

P1

AB=Tax rate =per unit tax = P↑ , Q↓

a

b

c

d

e

f

x0x1


THREE GENERAL PRICIPALS 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 .


THREE GENERAL PRICIPALS THREE GENERAL PRICIPALS 1- Loss of consumer surplus 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)- ( b + e)2- Loss of producer surplus2- 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 [(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 )( b+c )


THREE GENERAL PRICIPALSTHREE GENERAL PRICIPALSUsing 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 ownersbetween 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 .


GENEREAL TAX 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 productsGeneral 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 ?


GENERAL TAX GENERAL TAX GENERAL TAX GENERAL TAX

( )

(1 )Y LP Y

t


GENEREAL TAX 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.

Walters & Layard CH 3 15

TAX ON ONE FACTOR

TAX ON ONE FACTOR 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 ;

L

Y per L

YL = MPL = YL (L , K0) marginal product of labor curve

S

L0

Capital income

Tax payment

Labor share

WL /

PY

(WL/P

Y )(

1+

t)=

YL

Capital income

Tax payment

(Real)

Labor income (Real)

(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

a

b


TAX ON ONE FACTOR

TAX ON ONE FACTOR

Suppose that we consider two sector model ( X , Y ) .

Suppose that the supply of labor is givensupply of labor is given , and government government spends the tax proceed at the same way spends the tax proceed at the same way as the as the owners of the factor and demand for labor and capital do owners of the factor and demand for labor and capital do not change. not change. Consequently the marginal productivity ( Y( YLL) )

would not changewould 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 .


TAX ON ONE FACTOR

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 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 cost . The allocation of resources will be unaffected , and the tax will be born entirely by the tax factorwill 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 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 rent and none of it is needed to induce the factor to become availableavailable . 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 .


TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) TAX ON ONE PRODUCT (EXCISE TAX)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 .


TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) TAX ON ONE PRODUCT (EXCISE TAX)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) .


TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX)


TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) Now suppose that we levy tax on all commodities ;

MRSxy = ( Px/Py ) = MCx(1+tx) / MCy(1+ty) - 3 -

Kx + Ky = K0 - 4 -

Lx + Ly = L0 , if tx = ty , , - 5 -

if 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 .


TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) a- equal tax on all products a- equal tax on all products ( t( tx x =t=tyy=t )=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 b- Equal tax on all factors of production ( t( tLxLx=t=tLyLy=t=tKxKx=t=tKyKy))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 .


TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) TAX ON ONE PRODUCT (EXCISE TAX)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 ,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 , d- Tax on output X only , ttxx=t=t

As it is seen , this will alter the equilibrium conditions and resource allocation. As it is clear output remains on the transformation curve ; RTSKL

x = RTS KLY , but the product

mix will change , that is ;

MRS = Px / Py = MCx ( 1 + t)/ Py > ( MCx / MCy ) = RPTxy


TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) Y

X

Transformation curve

O

Optimal pointAfter tax , MRS > MRT

X1X2

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.

Y1

Y2


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 Direction of change for (W(WKK/P/Pxx ) is not known . It is under two effects ) is not known . It is under two effects ;


TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) TAX ON ONE PRODUCT (EXCISE TAX)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 Could the output of x increase as a result of increase in price of x because of tax policy ?of x because of tax policy ?

In order to answer the question we should see what In order to answer the question we should see what happens to excess demand for output Xhappens 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 .


TAX ON ONE PRODUCT (EXCISE TAX)TAX ON ONE PRODUCT (EXCISE TAX) TAX ON ONE PRODUCT (EXCISE TAX)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 So , as long as E>1 , an excise tax on a labor intensive good will normally make labor worse off and may or may good will normally make labor worse off and may or may not make capital worse offnot make capital worse off . The policy is efficient since . The policy is efficient since economy will remain on the P.P.F.economy will remain on the P.P.F. .


TAX ON ONE FACTOR IN ONE INDUSTRYTAX 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 The production does occur on the new locus which is not efficient and lies inside the efficient one .the same is is not efficient and lies inside the efficient one .the same is true for the transformation curve . Because the true for the transformation curve . Because the transformation curve is derived from the contract curvetransformation curve is derived from the contract curve. The new transformation curve which is not efficient lies inside the old one which is efficient .


TAX ON ONE FACTOR IN ONE INDUSTRY TAX ON ONE FACTOR IN ONE INDUSTRY

XX

YY

New curves

(K/L)X0

(K/L)yo

pR

RTSLKx > RTSLK

y

ox

oy

P’K0

L0

X0

y1

PP’



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 .



(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 1-Suppose that X falls a little and production of x occur at a point near to P’ at a point point near to P’ at a point between R and P’ 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 ).


TAX ON ONE FACTOR IN ONE INDUSTRY TAX ON ONE FACTOR IN ONE INDUSTRY But it is not known what will happen to( Wknown what will happen to( Wkk/P/Pxx) ) , since the direction of change of WK is not known . Because ;

WWKK = ( X = ( XK K )↓ ( P)↓ ( Px x )↑ )↑ , ( 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 2- production of x falls a great deal and production occur at a point between Oa point between Ox x and R and R near to Onear to Oxx.. 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 .


Factor tax with variable factor supplyFactor 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= lesiureY=goods , X= lesiure

Tax on earned income → tax on L →

tax on goods purchased → potential consumption falls



Y

C

C’

X’X

Before tax → MRS=MRT

After tax → MRS < MRT

MRS + T = MRT

MRT =( MCx/MCy) the rate at which production sector can actually produced goods by sacrificing leisure .

MRS = (Px/Py)= the rate at which people would like to increase their personal income (consumption) by sacrificing leisure (working more)

After tax people would like to work less and have more leisure and less earned income .



2- tax on capital2- tax on capital Now suppose that X is consumption today and Y is X is consumption today and Y is consumption in the future . 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’ .


Interpersonal distributionInterpersonal distribution To evaluateTo evaluate any change of budgetary scale in the real world , we want to know how it would affect the interpersonal affect the interpersonal distribution of income and the level of outputdistribution 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 whether the policy is equalizing (progressive ) or dis-equalizing policy is equalizing (progressive ) or dis-equalizing (regressive)(regressive) . For this we need to calculate a pre and post policy income measure.


Interpersonal distribution 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 < 0B = benefit from policyC = cost of the policyA 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 .

PROBLEMSPROBLEMSQ3-1Q3-1 ; 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

L

DL = VMPL

SL

W*

L*

a

b

Tax=abW1

W2

L1

PROBLEMSPROBLEMSSolution ; Solution ;

i- 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- 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 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 ; Solution ; Buyer’s price will rise more , the more inelastic is the demand curve and the more elastic is the supply curve.


PROBLEMSPROBLEMSQ3-3 ; Q3-3 ;

(i) (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) – (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) – (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) .


PROBLEMSPROBLEMSSolution ;

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 .


Yellow Shirts

DS

DS

Miami Hotels

ab=tax=cd

a

b

c

d

Q1

Q2

Q’1 Q’2

P*

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 of tax reveneiw .

PROBLEMSPROBLEMSii- we know that

PD = PS + T → Demand price = Supply price + Tax

So ;

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 ;

That is ; Walters & Layard CH 3 Application to Public finance 42

D Sdp dpx x T

dx dx

11 1S D

S D

T Txx

dp dp Pdx dx

221 1 11 1 1 12 2 2S SD D

T x T xpT x

P P

1 11 12 2S D

T x T

Tx P

PROBLEMSPROBLEMSFor a given T/P , excess burden per dollar of tax revenue is larger , the larger is supply elasticity and absolute value of demand elasticity.

iii-


Y

X

Y Max

CIC1

CIC0

X0 X1

Slope = - MCX / MCY

Slope = - MCX / MCY (1+t)

d

b+c

a

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

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

PROBLEMSPROBLEMSQ1-4 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 ;Solution ; i- 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- 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 iii - the same as in i, t= 1/9 Walters & Layard CH 3 Application to Public finance 44

PROBLEMSPROBLEMSQ3-5 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 .


K/L

Y per L

DK

SK

)K/L(*

YK*

K

LX

Y

P

(K/L)x

(K/L)y

Solution 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 .

subsidy

PROBLEMSPROBLEMSQ3-6 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.


Q

P

P*

P0

DH

SHAssumption ; market supply are perfectly inelastic

i- if market rent is P* , the consumers will not pay any amount more than this level. Since they are paying this level of rent , all the tax should be born by landlords. That is tenants pay P0 to 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.

Q1 Q2

PROBLEMSPROBLEMSQ3-7Q3-7 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 - 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 .

Walters & Layard CH 3 Application to Public finance 47X

Y

K

L

PP’

PROBLEMSPROBLEMS(K/L)x (K/L)y → MPL

x , 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) - 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) – (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


PROBLEMSPROBLEMS


F

M Land

PLabor

(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 .

P’

PROBLEMSPROBLEMS (ii) -


P

q

DS

P*

W

L

SL

DL

P*

a

Tax = P* a

aS’

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.

PROBLEMSPROBLEMSQ3-9 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).

Walters & Layard CH 3 51

Ox

Oy K

L

P

P’

R

(K/L)x

(K/L)y

Old efficiency locus

New Locus

XL /XK = WL / WK (1+tkx ) < WL / WK = YL / YK RTSLK x < RTSLK

y 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.

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 clear2- 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 .

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Walters & Layard CH 3Application to Public finance1 How will some particular change in public policy...

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