Download A numerical example of the effects of an export subsidy

A Numerical Example of the Effects of an Export Subsidy
A partial equilibrium approach similar to that adopted in Chapter 4 for tariffs can be used to analyse
the effects of introducing an export subsidy. For simplicity it is assumed that the country in question
is a small nation, and the usual assumptions are made with regard to linear demand and supply
curves, and no stocks or externalities.
In conditions of free trade it is assumed that the world price (Pw) is 100 euro per tonne and the
initial quantity supplied by the country (Qs) is 2000 tonnes, while the quantity demanded is 1000
tonnes. The price elasticity of demand (Ed) is –0.5 and the price elasticity of supply is Es 1.0. An
export subsidy of 20 euro per tonne is then introduced and competition between exporters will
cause the price on the domestic market to rise from 100 to 120 which is the new domestic price
(Pd) both for producers and consumers.
The formula for supply elasticity can be used to calculate the new quantity supplied Q’s by the
country in question after introduction of the export subsidy:
Es =
Qs
Qs
P
P
Qs
Qs
= Es
P
P
P = 20
P = 100
Es = 1,0
Qs = 2000
Qs = 2000 (1,0 x 20/100)
= 400
Q's = 2000 + 400 = 2400
The formula for price elasticity of demand can also be used to calculate the new quantity
demanded Qd after introduction of the export subsidy:
Ed = Qd
Qd
P
P
Qd
= Qd (Ed
P)
P
Q'd = 1.000 - 100 = 900t
Qd = 1.000 (-0,5 x
100
20 ) = -100
Figure A10.1 The effects of an export subsidy
P
S
Pd=120
a
b
c
Pw=100
D
0
900 1000
2000
2400
Foreign trade without the export subsidy (i.e. net exports) is given by:
Qs - Qd = 2000 - 1.000 = 1000 t
With the export subsidy it becomes:
Q's - Q'd = 2400 – 900 = 500
Before introduction of the export subsidy producer revenue is:
Qs(Pw) = 2000(100) = 200000
With the export subsidy it becomes:
Q’s(Pd) = 2400(120) = 288000
Before the introduction of the export subsidy consumer expenditure is:
Qd(Pw) = 1000(100) = 100000
After the introduction of the export subsidy it becomes:
Q’d (Pd) = 900(120) = 108000
Before the introduction of the export subsidy the trade balance is:
(Qs-Qd)Pw = 100000
With the export subsidy it becomes:
(Q’s-Q’d) Pw = (2400-900)100 = 50000
Q
N.B. It is the world price which is used to calculate the trade balance; the domestic price is used to
calculate producer revenue and consumer expenditure.
The loss in consumer surplus is given by:
- 0,5 (Pd - Pw) (Qd + Q'd) = -0.5(20(1000+900) = -19000
The increase in producer surplus is given by:
0,5 (Pd - Pw) (Qs + Q's) = 0,5 (20(2000+2400)) = +44000
The impact on the government budget (or the income of taxpayers) is the rectangle comprised of
areas a, b and c:
-(Pd-P’w)(Q’s-Q’d) = -20(2400-900) = -30000
The total effect of introducing the export subsidy on welfare is given by:
loss in consumer surplus, plus the increase in producer surplus and the increase in government
revenue:
-19000 + 44000 – 30000 = -5000
Alternatively, the effect of introducing the export subsidy on total welfare can be calculated using
the net welfare effects:
Triangle a is the net loss of welfare on the consumer side:
= - 0,5 (Pd - Pw) (Qd – Q’d)
= - 0,5 (120-100)(1000-900)
= -1000
Triangle c is the net loss of welfare on the production side (reflecting the worsening in the
allocation of resources):
= - 0,5 (Pd -Pw) (Q's - Qs)
= - 0,5(20(2400-2000)
= - 4000
The total effect on welfare is:
-1000-4000 = -5000
In the case of a fall in world prices (because net exports from the country in question increase
following introduction of the export subsidy) there will be a transfer from producers in that country
to consumers in the rest of the world causing a negative effect on total welfare of the country in
question. In the case of a rise in world prices (because net exports from the country decrease after
elimination of the export subsidy) there will be a transfer from consumers in the rest of the world to
producers in that country causing a positive effect on net welfare of the country in question.