Chapter 5: Tariffs and Quotas. An import tariff is a tax on the imported goods, levied as goods pass into the

An import tariff is a tax on the imported goods, levied as goods pass into the domestic country.

An import quota is a physical limit on the amount of the imported goods for a specified period of time.

Both are generally used to protect domestic producers. • Two types of tariffs

Specific tariff: fixed tax per unit (e.g., $/ton of bananas). Import price = export price + per unit tariff

Ad Valorem tariff: percentage tax of the import goods’ price [e.g., (1+t) * price of banana].

Import price = export price * (1+tariff rate)

Small Country Specific Import Tariff Price linkage equation: Import price = export price + per unit tariff

• From the above equation, tariff analysis and the effects are very similar to

transport cost analysis and effects. The only difference is, the transport cost is a real cost (paid for the transport service), but import tariff is an artificial cost imposed by the government.

Mathematical Analysis to show the shift in the ED curve for Specific Import Tariff

Demand QD = a - bP Supply QS = - c + dP

Excess Demand QED = QD – QS = (a + c) - (b + d) P Intervted Excess Demand: a c QED

P -

b d b d

+ =

+ +

So, under free trade, the intercept is a c b d

+

+ and the slope is

1 b d

−

+

After the specific import tariff T, domestic price is world price plus tariff T Price linkage equation: P = PW + T

Substitute the price linkage equation into the excess demand function: ' ED Q = (a + c) - (b + d) (PW + T) ' ED Q = (a + c) – (b+ d) PW – (b + d) T PW = a c QED T b d b d + _{− −} + +

So, after the import tariff policy, the intercept is (a c b d

+

+ - T) and the slope is

1 b d

− +

Comparison of the intercepts and the slopes before and after the import tariff shows that the intercept decreased by T and the slope remains the same

Before Import tariff After the Import tariff Intercept: a c b d + + a c b d + + - T Slope: 1 b d − + 1 b d − +

The free trade equilibrium is at M.

As a result of the import tariff the excess demand shifts down because at each quantity of imports, the importers are willing to pay less as they have to pay for the tariff also. Stated differently, at each price the importers will buy less because the good is more expensive as a result of tariff.

Because of the tariff the domestic price increases (world price + tariff). Domestic production rises, domestic consumption falls, and imports decrease.

The effective supply curve is domestic supply below the new domestic price (world price + tariff) and perfectly elastic supply at the new domestic price.

Welfare Analysis

o Change in producer surplus: ABED (+) o Change in consumer surplus: ACHD (-) o Tariff revenues: BCGF (+) o Change in welfare: EBF (-) + GCH (-)

Production efficiency loss is EBF: This arises as this good is produced at higher cost than the free trade import price. QPQ'_P could have been imported at a cost of

EF ' P

Q QP, but it costs EBQ'_PQP to produce inefficiently in the domestic market. To produce the additional amount of QPQ'_P inefficiently, resources used efficiently in other goods production are drawn to this good. So the production efficiency loss is EBF.

Consumption efficiency loss is GCH: This loss arises as less (QCQ'_C) of this good is consumed. The loss in utility is CHQCQ'_C and the money saved is GHQCQ'_C. The net utility loss, i.e., the consumption efficiency loss is GCH.

Note that, since the world price did not change, the rest of the world welfare is not affected.

The optimal tariff is the tariff that maximizes the welfare gains from trade. Under the free trade, the welfare gain from trade is the triangle between domestic and world prices. Under the tariff scenario, the welfare gain is negative (EBF + GCH). So, what is the optimal tariff?

Prohibitive tariff: Tariffs are so large imports are totally eliminated.

Mathematical Analysis of small country import tariff is as follows: 1) Note excess supply function is a constant function at PW

2) Free trade equilibrium is at the intersection of excess supply function (PW_{) and} excess demand function. That is, substitute PW _{into the excess demand function: Q}

ED = (a + c) - (b + d) PW

3) To compute the free trade domestic supply and demand, substitute PW _{into the} supply and demand functions, respectively.

4) World market equilibrium after the tariff is at the intersection of excess supply and new excess demand. That is, substitute PW _{into the new excess demand function:}

' ED

Q = (a + c) - (b + d) (PW + T)

Note, that the volume of import is less because of T. 5) New domestic price is PW + T.

6) To compute the domestic supply and demand, substitute PW + T into the supply

and demand functions, respectively. 7) Welfare analysis:

To obtain change in producer surplus, integrate the supply function between P and PW + T.

(

)

W w P T _A 0 1 P -α α P dP + +

∫

= W W P T 2 0 1 P P -α P α 2 + +

(

2 W

)

(

W

)

1 1 0 0 α α α T T 2P T T -α 2P T 2 2   = − + + = _ + + _   W 2 0 1 1 -2α T 2α TP α T 2 + + =

To get the change in consumer surplus, integrate the demand function between P and PW + T

∆ in Consumer surplus (loss)

(

)

(

)

W W P _{1 W} 0 1 0 P T β β β P dP T -β 2P T 2 +   = − = _ + + _  

∫

W 2 0 1 1 -2β T+2β TP +β T 2 =

Tariff revenue =

(

)

(

)

(

W 2

)

0 0 1 1

β +α T β α P T T− + + Dead weight loss = ∆in C.S - ∆in P.S – Tariff revenue

(

)

(

)

W 2 W 2 W W 0 1 1 0 1 1 0 0 1 1 -2β T+2β TP +β T -2α T+2α TP +α T +2β T+2α T-2β P +T T-2α P +T T 2 =

(

)

W 2 W 0 1 1 0 1 1 -2β T 2β TP β T 2β T 2β P T T 2   = _ + + + − + _

(

)

W 2 W 0 1 1 0 1 1 -2α T 2α TP α T +2α T 2α P T T 2   + _ + + − + _

(

)

(

) (

)

(

(

)

)

{

W W W W

}

0 1 0 1 0 1 0 1 1 β β P T β β P T β β P β β P T T 2       = _ − + _{ }+ − + −_ − + − + _   

(

W

)

(

(

W

)

)

(

(

W

)

)

(

(

W

)

)

0 1 0 1 1 0 1 0 1 1 -α α P -α α P α T -α α P T -α α P T T 2   + _ + + + + + − + + − + + _  

(

)

{

W W

}

{

W

(

W

)

}

0 1 0 1 0 1 0 1 1 1 β β P T β β P T+ -α α P -α α P T T 2 2   _{   }   = _ − + _ −_ − _{ } + _ −_ + + _

Note that the first expression is the triangular area ( 2

1_{bh) of consumption inefficiency.} The second expression is also triangle area of the production inefficiency.

Large Country Specific Import Tariff

Large importing country faces positively sloped excess supply. This country can depress the world price by decreasing its excess demand, i.e., this country exercises monopsony power in the world market.

The domestic price is the new world price + tariff. The importers will pay the tariff T. The domestic price will not increase as much as in the small country case for a given tariff, because the incidence of the tariff is shared by foreign exporters (who receive lower price) and domestic importers (who pay higher price).

The free trade equilibrium is at M. Because of the tariff, production increases, consumption decreases, and quantity imports decline

Welfare Analysis

Change in producer surplus: ABED (+) Change in consumer surplus: ACHD (-) Tariff revenues: BCJI (+) =B’C’J’I’

Net welfare: BFE(-)+CHG(-)+FGJI(+)=G’C’M(-)+F’G’J’I’(+)

The net welfare could be positive if FGJI (F’G’J’I’) is larger than BFE + CHG

(G’C’M). Or, the net welfare could be negative if FGJI (F’G’J’I’) is smaller than BFE + CHG (G’C’M).

Production efficiency loss is BFE, consumer efficiency loss is CHG, and left over tariff revenue is FGJI

In the exporting country production decreases, consumption increases, and exports decrease. The welfare loss for the exporting country is F’MJ’I’.

The world deadweight loss is C’MJ’

Tariffs imposed by large country has relatively less protective effect for domestic producer than equivalent tariff imposed by a small country. This is because part of the internal price raising impact of a large country is a dissipated in lower world

prices. This effect prevents import volume from falling as much as if no international price decrease occurred. Since imports do not fall as much as in the small country

case, tariff revenues for a given tariff are correspondingly higher in the large country case. The small country is facing more changes in prices and tariff revenues because its excess demand is relatively more inelastic than the excess supply compared to large country’s excess demand and excess supply.

Mathematical analysis for Large Country Import Tariff:

A A S 0 1 Q = −α + α P A A D 0 1 Q = β − β P

(

) (

)

A A ED 0 0 1 1 Q = β + α − β + α P ROW Excess Supply

R R

ES 0 1 Q = c +c P

At Free trade equilibrium, A R P = P

1) Free trade equilibrium price is obtained by equating excess demand and excess supply:

A R 0 0 0 1 1 1 c P P c β + α − = = β + α +

2) To compute the free trade domestic supply and demand, substitute PA _{into the} supply and demand functions, respectively.

3) After tariff, price linkage equation: A R P = P +T The new excess demand function is

(

) (

)

(

)

A R

ED 0 0 1 1

Q = β + α − β + α P +T

4) To obtain the new equilibrium price ( R

P ) in the world market, equate new excess demand and excess supply functions

(

) (

)

(

R

)

R 0 0 1 1 P T c0 c P1 β + α − β + α + = +

(

)

0 0 0 1 1 R 1 1 1 c T P c β + α − − α + β = β + α +

5) To obtain the domestic price, substitute PR _{into the price linkage equation:}

A* R 0 0 0 1 1 1 1 c c T P P T c β + α − + = + = β + α +

6) To compute the domestic supply and demand, substitute new A*

P into the supply and demand functions, respectively.

7) To obtain imports, substitute A*

P into the old excess demand function or PR into the

excess supply function.

A 0 1 0 1 1 0 1 1 1 0 1 1 ED 1 1 1 c c c c T c c T Q c β + α + β − β + α − α = β + α + 8) Welfare analysis:

To obtain change in producer surplus, integrate the supply function between PA _and PA*_.

(

)

A* A P 0 1 P

−α + α

P dP

∫

PA* A 2 1 0 P

P

P

2

α

= − α

+

(

A* A

)

1

( ) ( )

A* 2 A 2 0

P

P

P

P

2

α 



= −α

−

+

_

−

_





(

A* A

) (

1 A* A

)(

A* A

)

0

P

P

P

P

P

P

2

α

= −α

−

+

+

−

(

A* A

) (

A* A

)(

A* A

)

0 1

2

P

P

P

P

P

P

2

− α

−

+ α

+

−

=

To get the change in consumer surplus, integrate the demand function between PA* _and PA

=

(

)

A A A* A* P 2 P ₁ 0 1 0 P P P P dP P 2 β β − β = β −

∫

(

) (

)(

)

A A* A A* A A* 0 1 2 P P P P P P 2 β − − β + − = Tariff Revenue:

(

) (

)

A* A* ED 0 0 1 1 Q *T = β − α − β + α_ P _* T Decompose

(

A* A

) (

A W*

)

T = P −P + P −P

(

) (

)

A* A* A

(

) (

)

A* A W* 0 0 1 1 P P P 0 0 1 1 P P P         = β + α − β + α_{  } − _{ }+ β + α − β + α _{ } − _ This is area (7) and area (8). Area (7) can be shown as equal to area (3).

=

(

β − β_{0 1}PA*

) (

− −α + α_{0 1}PA*

)

 _PA* −PA_{ } + β + α − β + α

(

_{0 0}

) (

_{1 1}

)

PA* _{ }PA −PW*_

 

This is area (3) +area (8).

Consumer loss + Producer gain is

(

) (

)(

)

(

) (

)(

)

A A* A A* A A* 0 1 A* A A* A A* A 0 1 1 2 P P P P P P 2 1 2 P P P P P P 2   = _ β − − β + − _   + _− α − + α + − _

(

A A*

) (

A A*

)

A*

(

A A*

)

A

(

A A*

)

0 0 1 1 1 P P P P P P P P P P 2   = _β − + β − − β − − β − _

(

A* A

) (

A* A

)

A*

(

A* A

)

A

(

A* A

)

0 0 1 1 1 P P P P P P P P P P 2   + _−α − − α − + α − + α − _

(

)(

) (

)(

)

(

)(

) (

)(

)

A* A A* A A A* 0 1 0 1 A* A* A A A* A 0 1 0 1 1 P P P P P P 2 1 P P P P P P 2   = _ β − β − + β − β − _   + _ −α + α − + −α + α − _

(

)(

) (

)(

)

(

)(

) (

)(

)

A A A* A* A A* 0 1 0 1 A* A A* A* A A* 0 1 0 1 1 P P P P P P 2 1 P P P P P P 2   = _ β − β − − β − β − _   + _ β − β − + β − β − _

(

)(

) (

)(

)

(

)(

) (

)(

)

A A* A A* A* A 0 1 0 1 A* A* A A* A* A 0 1 0 1 1 P P P P P P 2 1 P P P P P P 2   + _ −α + α − − −α + α − _   + _ −α + α − + −α + α − _

(

A

) (

A*

)

A* A

(

A*

) (

A

)

A* A 0 1 0 1 0 1 0 1 1 1 P P P P P P P P 2 2       = − _ β − β − β − β _ − _ − _ −α + α − −α + α _ − _

(

A*

) (

A*

)

A* A 0 1P 0 1P P P  _{  } + β − β_ − −α + α _ − _

This is consumption inefficiency (area 4) + production inefficiency (area 2) + part of tariff revenue (area 3).

(

) (

)

(

)

(

(

) (

)

)

(

) (

)

A* A A A* 0 0 1 1 0 0 1 1 A* A* A 0 0 1 1 1 P P P P 2 P P P     = − _ − _{ } β + α − β + α − β + α − β + α _     + β + α − β + α_{  } − _

Net welfare loss/gain = C.S loss + P.S gain + Tariff Revenue = area (4) + area (2) + area (8)

(

A

) (

A*

)

A* A

(

A*

) (

A

)

A* A 0 1 0 1 0 1 0 1 1 1 P P P P P P P P 2 2       − _ β − β − β − β _ − _− _ −α + α − −α + α _ − _

(

) (

)

A* A W* 0 0 1 1 P P P     + β + α − β + α_{  } − _

The net welfare loss/gain can be written as area (6) + area (8)

(

) (

)

(

)

(

(

) (

)

)

A* A A A* 0 0 1 1 0 0 1 1 1 P P P P 2     = − _ − _{ } β + α − β + α − β + α − β + α _

(

) (

)

A* A W* 0 0 1 1 P P P     + β + α − β + α_{  } − _ Incidence of Specific Tariff

We can analyze whether the exporter’s price declines more than the importer’s price rises due to a specific import tariff. Suppose country A is the exporting country B is the importing country.

( )

B B T q = ED P

( )

A A T q = ES P B A A B P = P +T, or P = P −T A B dP =dP −dT

( )

B

( )

A ED P = ES P B A B A ED ES dP dP P P ∂ ₌ ∂ ∂ ∂

(

)

B A B B A A ED ES ES dP dP dP dT P P P ∂ ∂ ∂ = = − ∂ ∂ ∂ B B B A A ED ES ES dP dP dT P P P ∂ ∂ ∂ = − ∂ ∂ ∂ B B A B A ES ED ES dP dP dT P P P ∂ ∂ ∂ − = ∂ ∂ ∂ B A B A ES ED ES dP dT P P P ∂ ∂ ∂  ₋  ₌  _{∂ ∂}  _∂   B A A B ES dP _P ES ED dT P P ∂ ∂ = _{∂ ∂} − ∂ ∂ A B A B T T

Note at the initial free trade equilibrium, q =q and P =P

A B A A ES T A B ES ED A A B B T T ES P dP P q e ES P ED P dT e e P q P q ∂ ∂ = _{∂ ∂} = − − ∂ ∂ A B dP dP 1 dT = dT − A ES ES ES ED e dP e 1 dT = e −e − = ES e − _ED ED ES ED ES ED e _e e e e e + = − − B ES ES ED dP e 0 dT = e −e ≥

ES

If e is perfectly elastic, the import tariff is fully paid by the importers.

ES

If e is perfectly inelastic, the import tariff is fully paid by the exporters.

A ED ES ED dP e 0 dT = e −e ≤ ED

If e is perfectly elastic, the import tariff is fully paid by the exporters.

ED

If e is perfectly inelastic, the import tariff is fully paid by the importers.

A ED B ES dP / dT e dP / dT e − = −

(

)

This shows that the country with less elastic response in absolute values will incur the larger share of the import tariff.

Ad Valorem Tariff

Let us examine how the Ad Valorem tariff affects the excess demand function. Price linkage equation: P = PW (1 + T)

Mathematical Analysis to show the change in the ED curve for Ad Valorem Tariff Demand QD = a - bP

Excess Demand QED = QD – QS = (a + c) - (b + d) P P = a c QED b d b d + − + +

So, under free trade, the intercept is a c b d

+

+ and the slope is

1 b d

−

+ . Note that the

quantity intercept is (a+c). After the ad valorem import tariff T,

Domestic price = world price * (1+ T) Price linkage equation: P = PW (1 + T)

Substitute the price linkage equation into the excess demand function: QED = (a + c) - (b + d) PW (1 + T) QED - (a + c) = - (b+ d) PW (1 +T) PW = a c (b d)(1 T) + + + - ED Q (b+d)(1 T)+

So, after the import tariff policy, the intercept is a c (b d)(1 T) + + + and the slope is 1 (b d)(1 T) −

Comparison of the intercepts and the slopes before and after the ad valorem tariff shows that the intercept and the slope have decreased.

Before ad valorem tariff After ad valorem tariff Intercept: a c b d + + a c (b d)(1 T) + + + Slope: 1 b d − + 1 (b d)(1 T) − + +

Once we know the rotation of the excess demand function, the rest of the analysis are similar to specific tariff analysis.

Incidence of Ad Valorem Tariff

We can analyze whether the exporter’s price declines more than the importer’s price rises due to an ad valorem import tariff. Suppose country A is the exporting country B is the importing country.

( )

B B T q = ED P

( )

A A T q = ES P

(

)

B A P = P 1 T+

(

)

B A A dP = +1 T dP +P dT

( )

B

( )

A ED P = ES P B A B A ED ES dP dP P P ∂ ₌ ∂ ∂ ∂

(

)

B A B A B A A ED ES ES dP P dT dP dP P P P 1 T   ∂ ₌ ∂ ₌ ∂ −   ∂ ∂ ∂ _ + _

(

)

(

)

B A B B A A ED ES dP ES P dT dP P P 1 T P 1 T ∂ ∂ ∂ = − ∂ ∂ + ∂ +

(

)

(

)

B A B B A A ED ES dP ES P dT dP P P 1 T P 1 T ∂ ₋ ∂ _{= −}∂ ∂ ∂ + ∂ +

(

)

B A A B A 1 T ED ES dP ES P dT P P (1 T) P (1 T) + ∂ ∂ ₋  ₌ ∂  _{∂ ∂}  _{+ ∂ +}  

(

)

A B A A B ES P dP _P ES ED dT _{1 T} P P ∂ ∂ = _{∂ ∂} − + ∂ ∂ A B A B T T

Note at the initial free trade equilibrium,T=0, q =q and P =P

A B A A ES T A B B ES ED A A B B T T ES P dP 1 P q e ES P ED P dT P e e P q P q ∂ ∂ = _{∂ ∂} = − − ∂ ∂

(

)

(

)

A B A dP dP P dT = 1 T dT+ − 1 T+

At the initial equilibrium A B

P = P and T =0. Thus, A B A dP dP P dT = dT − A B A B dP 1 dP 1 1 dT P = dT P − A ES ES A ES ED e dP 1 e 1 dT P = e −e − = ES e − _ED ED ES ED ES ED e _e e e e e + = − −

B ES B ES ED dP 1 e 0 dT P = e −e ≥ ES

If e is perfectly elastic, the import tariff is fully paid by the importers.

ES

If e is perfectly inelastic, the import tariff is fully paid by the exporters.

A ED A ES ED dP 1 e 0 dT P = e −e ≤ ED

If e is perfectly elastic, the import tariff is fully paid by the exporters.

ED

If e is perfectly inelastic, the import tariff is fully paid by the importers.

A ED B ES dP / dT e dP / dT e − = −

(

)

This shows that the country with less elastic response in absolute values will incur the larger share of the import tariff.

Small Country Import Quota

The import quota restricts the amount of imports that can enter into the country. These import quotas are usually given to the importers either freely or for some charges through licensing. Technically the import license could be auctioned off through bidding process.

Free trade equilibrium is at M. Import quota limits the amount of imports to q. If the quota is less than the free trade volume of imports, it’s a binding quota. If the quota is above the free trade volume of imports, it’s a non-binding quota. The domestic price increases.

If import quotas are auctioned off, the per unit quota rent will be ST. This rent is identical to tariff if imports are equal under quota and tariff. Then, ceteris paribus, the analysis and the welfare implications under the quota scenario are same as those under the tariff scenario.

Welfare Analysis:

Change in producer surplus = +1

Change in consumer surplus=-(1+2+3+4) Quota revenues =+3

Net welfare change = -(2+4)

Some differences between tariff and quota cases arise if domestic demand and supply fluctuates.

Tariff scenario Quota scenario Demand shifts No change in prices

Qty of imports change No change in qty of imports Price changes Supply shifts No change in prices

for binding quota World price

fluctuates Qty of imports change Price changes No change in qty of imports No change in price

Under import tariff, world price signals are transmitted to the domestic market. Under import quota, world price signals are not transmitted to the domestic market and the importing country has shielded itself from world price fluctuations.

If the domestic demand and supply is more volatile than the world market,

importing country will experience more domestic price fluctuations under the quota than under the tariff.

Mathematical Analysis for small country quota,

A A S 0 1 A A D 0 1 q P q P = −α + α = β − β

The excess demand is: A A

ED 0 0 1 1

q = β + α − β + α( ) ( )P Invert the excess demand function

A A 0 0 ED 1 1 1 1 q P = β + α − β + α β + α

So, under free trade, the intercept is 0 0 1 1 α + β

α + β and the slope is _{1 1} 1 −

α + β Free trade equilibrium before quota is obtained by substituting ROW price PR _{into the} excess demand function. Note that under free trade

PA _{= P}R_.

A R

ED 0 0 1 1

q = β + α − β + α( ) ( )P

Introduce quota

( )

q . After the import quota q , the new excess demand function will be A A 0 0 ED 1 1 1 1 q P = β + α − β + α β + α for A ED q ≤q q Otherwise

After quota, the above excess demand function is not used to determine the volume of imports. The excess demand function is used only to determine price in A. The world price will be still PR_{. The price in the importing country is obtained by} equating

A

0 0 1 1

q = β + α − β + α( ) ( )P Solve the above equation for PA_:

A 0 0

1 1 1 1

q P = β + α −

β + α β + α

Note this price is function of the quota

( )

q . Also note that if

( )

q is equal to tariff

imposed-imports, then, PA _{under the quota and the tariff will be equal.}

To do the welfare analysis, integrate the supply function between free trade PA _and new PA _{to get the change in producer surplus. Integrate the demand function between} free trade PA _{and new P}A _{to get the change in consumer surplus. Obtain the quota} revenues as per unit quota rent * quota. Net welfare is sum of change in producer surplus (+), consumer surplus (-), and quota revenues.

Large Country Import Quota

The analysis of large country import quota is similar to that of large country import tariff, once we impose the quota and determine the world price and domestic price and as long as the quota rent is collected by the government.

Welfare Analysis:

Change in producer surplus = +1

Change in consumer surplus=-(1+2+3+4) Quota revenues =+(3+5)=+(7+8) Net welfare change = -(2+4)+5=-6+8

Mathematically, A A S 0 1 Q = −α + α P A A D 0 1 Q = β − β P

(

) (

)

A A

ED 0 0 1 1

Q = β + α − β + α P ROW Excess Supply

R R

ES 0 1 Q = c +c P

At Free trade equilibrium, A R P = P

1) Free trade equilibrium price is obtained by equating excess demand and excess supply: A R 0 0 0 1 1 1 c P P c β + α − = = β + α +

2) To compute the free trade domestic supply and demand, substitute PA _{into the} supply and demand functions, respectively.

3) After quota, the new excess demand function is A A 0 0 ED 1 1 1 1 q P = β + α − β + α β + α for A ED q ≤q q Otherwise

After quota, the above excess demand function is not used to determine the volume of imports. The excess demand function is used only to determine price in A.

4) To obtain the new equilibrium world price ( R

P ), equate q to excess supply function.

R 0 1 q =c +c P R 0 1 q c P c − =

5) The price in the importing country is obtained by equating A

0 0 1 1

q = β + α − β + α( ) ( )P Solve the above equation for PA_:

A 0 0

1 1 1 1

q P = β + α −

β + α β + α

Note this price is function of the quota

( )

q . Also note that if

( )

q is equal to tariff

imposed-imports, then PA _{under the quota and the tariff will be equal.}

6) To compute the domestic supply and demand, substitute new PA _{into the supply and} demand functions, respectively.

7) To do the welfare analysis, integrate the supply function between free trade PA _and new PA _{to get the change in producer surplus. Integrate the demand function between} free trade PA _{and new P}A _{to get the change in consumer surplus. Obtain the quota} revenues as per unit quota rent * quota. Net welfare is sum of change in producer surplus (+), consumer surplus (-), and quota revenues.

A TRQ imposes a smaller (or zero) tariff for a certain amount of imports and a larger tariff above this amount

TRQ was introduced in the Uruguay Round as part of the tariffication process, which converts the wedge between the domestic price and the world price arising from non-tariff barriers (quota) into an equivalent non-tariff. Tariffication brings more

transparencies and avoids red-tapism.

TRQ guarantees the exporting countries to export at least as much as in the previous years, but also possibly to export more at a higher tariff

The trade liberalization occurs by increasing the import quota and reducing the tariff

Two possible cases for setting the tariff 1) Maximize tariff revenue

2) Optimal tariff Small country case:

Mathematically,

Tariff revenue A

(

)

(

)

(

W

)

ED 0 0 1 1

T * Q T P T T

= = β + α − β + α +

Maximize tariff revenue with respect to T

(

)

W

(

)

0 0 1 1 1 1 TR P 2T 0 T ∂ = β + α − β + α − β + α = ∂

(

) (

)

(

)

W 0 0 1 1 1 1 P T 2 β + α − β + α = β + α W W A W 1 1 0 0 1 1 1 1 W 1 1 _{0 0 1 1} 2( )P ( ) ( )P 2( ) P P T T T 2( ) ( ) ( )P β + α + β + α − β + α β + α + = = β + α _{β + α − β + α} W 0 0 1 1 W 0 0 1 1 ( ) ( )P ( ) ( )P β + α + β + α = β + α − β + α

Price elasticity of the importing country’s excess demand function: A ED 1 1 A q ( ) P ∂ = − β + α ∂

A ED A q P ∂ ∂ A A ED P q = A 1 1 A 0 0 1 1 ( )P ( ) ( )P − β + α β + α − β + α After tariff, PA ₌ W P +T= W W 1 1 0 0 1 1 1 1 2( )P ( ) ( )P 2( ) β + α + β + α − β + α β + α

Substitute the above equation into the elasticity of ED function.

ED e

(

)

W W 1 1 1 1 0 0 1 1 1 1 W W 1 1 1 1 0 0 1 1 0 0 1 1 ( ) 2( )P ( ) ( )P 2( ) 2( )P ( ) ( )P ( ) 2( )   β + α _ β + α + β + α − β + α _ β + α = −   β + α _ β + α + β + α − β + α _ β − α − β + α = W W 1 1 0 0 1 1 W W 0 0 1 1 0 0 1 1 2( )P ( ) ( )P 2 2( ) 2( )P ( ) ( )P 2 β + α + β + α − β + α − β + α − β + α − β + α + β + α = W 0 0 1 1 W 0 0 1 1 ( ) ( )P ( ) ( )P β + α + β + α − β + α − β + α W 0 0 1 1 ED _W 0 0 1 1 ( ) ( )P e ( ) ( )P β + α + β + α = β + α − β + α

Thus for small country case, the maximum tariff revenue occurs when the ratio of domestic price to revenue tariff is exactly equal to the absolute value of the price elasticity of the importing country’s excess demand function.

Large Country

Now let us examine the tariff that maximizes the tariff revenue in the large country case.

Maximize the revenue (T.R) with respect to T.

A 0 1 0 1 1 0 1 1 1 0 1 1 ED 1 1 1 T( c c c c T c c T) T.R. T * Q c β + α + β − β + α − α = = β + α + 0 1 0 1 1 0 1 1 1 0 1 1 1 1 1 c c c 2 c T c 2 c T T.R. 0 T c β + α + β − β + α − α ∂ = = ∂ β + α +

[

]

0 1 0 1 1 0 1 0 1 0 0 0 1 1 1 1 1 1 1 1 1 c c c c c ( ) c ( ) T 2( c c ) c 2( ) β + α + β + α β + α + β + α = = β + α β + α Substituting T in A ED q we get, 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 1 1 1 1 1 A ED 1 1 1 c c c c c c c c ( c c ) 2( c c ) q ( c ) β + α + β − α  β + α + β + α − β + α _{ } β + α   = β + α + 0 1 0 1 1 0 1 0 0 1 0 1 1 0 1 0 1 1 1 2( c c c c ( c c c c ) 2( c ) β + α + β + α − β + α + β − α = β + α +

0 1 0 1 1 0 1 0 1 1 1 c c c c 2( c ) β + α + β + α = β + α +

Free trade imports: Substituting A

P =PR in qA_ED A 0 0 0 ED 0 0 1 1 1 1 1 c q ( ) ( ) ( c ) β − α − = β +α − β + α β + α + A 0 1 0 1 1 0 1 0 ED 1 1 1 c c c c q c β + α + β + α = β + α +

Thus under linear demand and supply function tariff revenue maximizing imports is half of the free trade imports.

Optimal tariff:

Optimal tariff is obtained by minimizing the welfare loss (C.S loss + P.S. gain + T.R.).

The Small Country Case:

In the small country case (C.S loss + P.S. gain + T.R.) can be at its maximum (=0) only when T=0.

Net welfare loss

(

)

{

W W

}

{

W

(

W

)

}

0 1 0 1 0 1 0 1 1 1 β β P T β β P T+ -α α P -α α P T T 2 2         = _ − + _ −_ − _{ } + _ −_ + + _

{

W W

}

0 1 0 1 1

(Net Welfare Loss) 1

[ (P T)] [ P ] T T 2 ∂ _{= + β − β + − β − β − β} ∂

{

W W

}

0 1 0 1 1 1 [ P ] [ (P T)] T 0 2 + −α + α − −α + α + − α = 1 1 1 1 1 1 [ T] T [ T] T 0 2 2 = − β − β − α − α = 1 1 3 3 T T 0 2 2     = β _{ }+ α _{ }=     1 1 3 T( ) 0 2 β + α = , T 0 ∴ =

The Large country case: The net welfare loss/gain

(

) (

)

(

)

(

(

) (

)

)

A* A A A* 0 0 1 1 0 0 1 1 1 P P P P 2     = − _ − _{ } β + α − β + α − β + α − β + α _

(

) (

)

A* A W* 0 0 1 1 P P P     + β + α − β + α_{  } − _ A* A A* A A* A W* 1 1 0 0 1 1 1 [P P ][P P ][ ] [( ) ( )P ][P P ] 2 = − − − β + α + β + α − β + α −

Minimize the net welfare loss/gain with respect to T. But, first express

(

A* A

)

P −P

and

(

A w*

)

P −P in terms of T.

From the previous analysis,

A W 0 0 0 1 1 1 c P P c β + α − = = β + α + W* 0 0 0 1 1 1 1 1 c ( )T P c β + α − − β + α = β + α + A* 0 0 0 1 1 1 1 c c T P c β + α − + = β + α +

(

)

A* A 1 1 1 1 c T P P c − = β + α + ;

(

)

A w* 1 1 1 1 1 ( )T P P c β + α − = β + α + After substituting

(

A* A

)

P −P ,

(

PA −Pw*

)

, and PA*into the net welfare loss/gain, we

get 2 2 1 1 0 0 0 1 1 1 1 1 1 0 0 2 1 1 1 1 1 1 1 1 1 ( )( c c T) c T 1 ( ) ( ) T 2 _{( c )} c c    β + α β + α − +  β + α  = − _ _ β + α + β + α −_{  } β + α + β + α + β + α + _{  }  

Differentiate the above equation with respect to T and set it zero:

(

)

(

)

(

)

2 2 2 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 1 2 2 1 1 1 1 1 1 1 1 1 1 1 1 c T ( )( ) ( ) ( c c T) c ( ) T 0 c c ( c ) ( c ) β + α β + α β + α β + α β + α − + β + α = − + − − = β + α + β + α + β + α + β + α +

(

)

(

)

(

)

2 1 1 1 0 0 1 1 1 1 0 0 0 1 1 1 2 1 1 1 1 1 1 1 1 1 c T ( )( ) ( ) ( c ) [c 2( )] 0 c c ( c ) β + α β + α β + α β + α β + α − = − + β + α + − = β + α + β + α + β + α + 2 1 1 1 1 1 1 1 1 1 0 0 1 1 1 1 0 0 0 c T(β + α )[c + β + α2( )]= β + α +( c )(β −c )(β + α − β + α) ( ) (β + α −c ) 1 1 1 0 0 1 1 0 0 0 1 1 1 1 ( c ) ( ) ( )( c ) T c [c 2( )] β + α + β + α − β + α β + α − = + β + α 0 1 0 1 0 1 0 1 0 1 0 1 1 0 1 0 1 0 1 0 1 0 1 0 1 1 1 1 c c c c T c [c 2( )] β β + β α + β + α β + α α + α − β β − β α + β − α β − α α + α = + β + α O 1 0 0 o 1 1 1 1 1 1 c ( ) c ( ) T c [c 2( )] β + α + β + α = + β + α

Compare this with revenue maximizing tariff R 1 0 0 0 1 1

1 1 1 c ( ) c ( ) T c [2( )] β + α + β + α = β + α TO _{< T}R _{because of extra} 1 2

c in the denominator of TO expression.

The more inelastic is the excess supply relative to the absolute price elasticity of excess demand, the more likely optimal tariff can be pursued. If excess supply is perfectly elastic, as with small country, price cannot be depressed down by the importing country, then the optimal tariff is zero.

Thought the good is priced competitively in the domestic market, a large importing country has market power in the world market, and it can use monopsony pricing rule to find the optimal import tariff.

A W p q p (q)q π = − q is quantity traded pW is world price pA is domestic price π is profit

This country acts as a price taker at home but exercise monopsony power in the world market. W A W d dq dp p p q 0 dq dq dq π _{= − − =} W A W W q dp p p 1 0 dq p   = − _ + _=   pA pW 1 1 0 e   = − _ + _=   where W dq p e

dp q = = elasticity of export supply

MFC or MCI

MCI > import price (pW) because importing country being large, its decision to import another unit would raise the import price, increasing the cost on all units of imports. Thus, full marginal cost of imports consists of the price of another unit of imports plus the extra inframarginal generated on existing imports.

Then, optimal tariff is pA – pW , i.e., for ad valorem tariff tpW = pA – pW = W p e . Thus, 1 t e = .

Hence, the optimal ad valorem tariff is equal to the inverse elasticity of export supply. The more inelastic export supply is, the larger the optimal tariff will be.

Illustration of

( )

OE 1

HE = foreign elasticity of demand for imports η −1

The elasticity of demand for imports ( ) dM P , dP M

η = −

where M is imports and P is S O

P .

P At any point on the offer curve

S O

P E

P = Mbecause of the trade balance

condition: P MS =P E.O However, the trade balance equation should not be misconstrued as the

equilibrium condition at this point. It merely suggests that a country is willing to import in return for some exports at certain terms of trade. The equation becomes an equilibrium condition only when one country’s import demand is exactly matched by the other country’s export supply at the

equilibrium terms of trade.

Since S O P E P , P M = = dM P dM E₂ E dP M M d M η = − = −       2 2 E _{MdE EdM dE} d _{M E} M _{M dM} Note dM dM M   − ₋     − = − =

Taking the inverse of the above equation:

2 dM M dE E M E d dM M − = −   ₋     2 2 dM E M E M d M ∴η = − = −       2 E dE _M M E dM − dM E EdM _dE dE _{MdE EdM} M dM M E dM E dE = − = − = − − − − Note that dM

dE gives the slope of the offer curve at any point, such as B. Thus,

dM HB

. dE = HE

Also note that M HB.

dM HB 1 OH OH OH dE HE M dM HB HB HE _{HE OH OH HE OE} 1 E dE OH HE OH ∴η = − = − = − = − = = − − − − − OE 1 1 1 1 t* . HE OH OE OH HE 1 1 OE OE OE = = = = = − ₋ η − ( ) 1 1 Thus, t*

1 foreign elasticity of demand for imports 1

= =

η − − .

The relationship between import demand elasticity( )η and export supply elasticity( )ε

Let us define E = exports, M = imports, P1 = world price of good 1, P2 = world price of good 2, and 2

1

P

P = relative world price = P.

The trade balance is the value of exports equal to the value of imports.

2 2 1 1 2 1 P E =P M ⇒PE =M 2 1 2 dE dP dM P E dP + dP = dP 2 1 2 dE dM P E dP + = dP 2 1 2 1 Ex.Sy. Ely. dE dM P P 1 E dP M dP ε= η + =   1 2 1 2 Ex.Sy. Ely. dM dE P P 1 M dP E dP η ε= − =   1 1 . 1 ∴ = η − ε

Derivation of the Optimal Tariff in a General Equilibrium Framework

Consider an economy which produces n traded goods in quantities X ,..., X1 n and

consumes them in quantities C ,...,C .1 n The economy wishes to choose the i

C and the Xiand, if it is a large country the world prices of these goods, * * *

1 2 n

p , p ,..., p ,to maximize the community utility function ( 1 2 n)

u C ,C ,...,C (1)

subject to a number of constraints. These are the following:

i. The economy’s balance-of-trade constraint:

( ) n * i i i i 1 p C X 0 = − = ∑ (2)

ii. The economy’s transformation function:

(X , X ,..., X1 2 n) 0

φ = (3)

iii. A market-clearing condition for each good:

(

)

i * * *

i i 1 2 n

C −X =R p , p ,..., p (4)

where i

R is the rest of the world’s net export function for good i. Note that if

the home country is small, it can buy or sell as much as it likes at the given world prices * * *

1 2 n

p , p ,..., p (i.e. Riis perfectly elastic), so equation (4) is redundant

and therefore drops out of the problem for the small-country case. The Lagrangean for the general problem is

( ) n ( ) ( ) n

(

)

* j * * 1 n 1 i i i 2 1 n j j j 1 n i 1 j 1 L u C ,...,C p C X X ,..., X C X R p ,...p = =   _{ } = + λ _∑ − _+ λ φ + ω∑ _ − − _  

And the first-order conditions are that for all i,

* i 1 i i i L u p 0 C ∂ _{= + λ + ω =} ∂ (5) * 2 i 1 i i i L p 0 X ∂ _{= λ φ − λ − ω =} ∂ (6) ( ) n j 1 i i j i * j 1 i L C X R 0 p = ∂ _{= λ − − ω =} ∑ ∂ (7) where j j i * i i i i i R u R , u , p C X ∂ ∂ ∂φ ≡ ≡ φ ≡ ∂ ∂ ∂ .

From equation (5) and (6), we have the following equations involving marginal rates of substitution in consumption i

j u u      

  and marginal rates of

transformation in production i j :  _φ    _φ   * i i i * j j j u p T u p T + = + (8) * i i i * j j j p T p T φ + = φ + (9) where i i 1 T ≡ω . λ

We shall now use equation (8) and (9) to derive optimal policies in different situations. It is instructive to consider the small- and large-country cases separately.

(a) Small-country case

When the home country is small, it cannot treat the world prices as variables. Thus, the constraint (4) and equation (7) are dropped. In particular, this

implies that ωi can be set equal to zero; hence Ti disappears from equations (8)

and (9) which can now be written in the simpler form:

* i i * j j u p u =p (8a) * i i * j j p p φ ₌ φ (9a)

Thus, (8a) and (9a) imply that the MRS in consumption and the MRT in production are equal to relative world prices for each pair of goods; that is,

* i i i * j j j u p u p φ = = φ

so no taxes or subsidies are optimal in such a case.

(b) Large-country case

When the home country is large, it will also be able to employ policy instruments to affect the value of the world prices * * *

1 2 n

world’s goods markets [equation (4)]. In this case, the more general

optimality conditions, equations (8) and (9), apply. Note that these equations extend the basic principle previously established that the instruments chosen should be those which directly affect the target variables, i.e., the cure should be directed to where the malady is. Instrument T 'si affect domestic consumer

and producer prices equally – they are therefore trade taxes (tariffs or export taxes). Clearly, they are used to exploit the country’s ability to determine its terms of trade [they were absent from equations (8a) and (9a)]. Rearrange equation (7) to obtain ( ) n j 1 i i j i j 1 C X R = λ − = ω∑ n i j 1 j i j 1 R R = λ = ω∑ n _j i j i j 1 ₁ R R = ω = ∑ λ j j 1 Since Tω = λ n i j j i j 1 R T R = = ∑ By setting * j j j

T =t p , we see that the optimal set of trade taxes must satisfy

n * j i j j i j 1 t p R R = = ∑ (10)

where * j j j

t ≡T / p is the ad valorem tariff (or the tariff equivalent of an export

tax) applied to good j. For the simple case of two goods with a tariff on the importable (say, good i), equation (10) can be rearranged to yield the

following simple formula for the optimal tariff expressed in terms of the elasticity of the foreign supply curve:

i i i * * i i R R t p p ∂ ₌ ∂ * i i * i i i p 1 R t p R ∂ = ∂ so that ti =1 /εi, where

(

)(

)

* i i * i p / Ri R / pi

ε ≡ ∂ ∂ is the elasticity of supply of imports. From (8) and (9), we can see

MRS = MRT = Domestic Price Ratio i i j p T p * *  ₊  >    