Transcript Course

FAO - GOVERNMENT OF ITALY COOPERATIVE PROGRAMME
PROJECT GCP/SYR/006/ITA – Phase II
“Assistance for Capacity Building through
Enhancing Operation of the National Agricultural Policy Center”
course in
Partial equilibrium analysis of policy
impacts
Part II, September 21 – October 3, 2002
Piero Conforti
- The National Institute of Agricultural
Economics, Roma, Italy
Aim of this part of the course
Allow the trainees to familiarise with partial
equilibrium analysis of agricultural policies, within
• the single market static frameworks
• (hints on) multi market, dynamic PE frameworks, and on
GE frameworks
Special emphasis on:
– price policy analysis
– welfare analysis
– technical change analysis
Special emphasis on the applications: mostly exercises
in Excel
Content
1. Equilibrium within a single market partial
equilibrium computable model
– isolated markets and regional integration in a closed
economy with transport costs
– the partial equilibrium computable model of an open
economy: the effect of trade on supply demand and
welfare
– price policy analysis: impacts on supply, demand and
welfare
– technical change analysis with MODEXC
Content
2. Beyond the single market model
– relating interdependent markets: hints on multimarket analysis in a partial equilibrium framework
– hints on dynamic partial equilibrium frameworks
– hints on the GE approach: basic structure,
computation, calibration and estimation, applicability
and limitations
Single market PE: introduction
Partial equilibrium: only some parts of the economy (some
markets) are taken into account. What happens in one
sector in terms of demand, supply and price does not
significantly affect what happens in other sectors
it can be applied: to a single market (e.g. wheat) or to a set
of markets (e.g. a set of agricultural products) within a socalled multi-market framework.
In the second case it will take into account the interactions
between e.g the wheat and the barley markets, but it will
not take into account the effects of a change in the cereal
market on fertilizers
Single market PE: isolated markets
Three isolated regional markets with no trade; region 1:
production center
production center
C
D
consumption center
Y
Consumptìon Center Y
Production Centers C & D
Demand function
Supply functions
(1)
(2)
Sc = Sco + Ac*(CPy - Tcy)
(3)
Sd = Sdo + Ad*(CPy -Tdy)
Dy = Dyo+ Ay * CPy
with: Dyo = 3000
Ay = -4
with:
Sco = -500
Ac = 6
Tcy = 19
Sdo = -500
Ad = 4
Tdy = 25
We want ot represent this in a demand-supply graph
inverted demand & supply
1. Demand derived from (1):
1a.
CPy(D) = -Dyo/Ay + Dy/Ay
2. Supply of C derived from (2) (with and without transport)
2a.
CPy = -Sco/Ac + Sc/Ac
(without transport)
2b.
Cpy = (Tcy*Ac - Sco)/Ac + Sc/Ac (with transport)
3. Supply of C and D (with transport)
CPy = [(Tcy*Ac+Tdy*Ad) -(Sco+Sdo)] / (Ac+Ad) +
(Sc+Sd)/(Ac+Ad)
isolated market, graph
800
700
600
CPy
500
Dy
400
Sc
300
Sc+T
(Sc+Sd)+T
200
100
0
0
500
1000
2000
1500
2500
3000
Q
We want to calculate the equilibrium point
3500
equilibrium quantity and price
production center C only
Demand = Supply of C
-Dyo/Ay + Dy/Ay = (Tcy*Ac-Sco)/Ac + Sc/Ac
since Dy = Sc = q
q = [(Tcy*Ac-Sco)/Ac) + (Dyo/Ay)] / (1/Ay - l/Ac)
q= 1554
p = 361
production centers C & D Demand = Supply of C and D
Dy = (Sc+Sd) = q
q = {Dyo/Ay +
+ [(Tcy*Ac+Tdy*Ad) - (Sco+Sdo)] /
(Ac+Ad)} / [(1/Ay) – l/ (Ac+Ad)]
q = 1796
p =301 (from 2a); qc = 1192 qd = 604
deducting transport costs pc = 282 pd = 276
equilibrium quantity and price
Isn’t there a simpler way to calculate the equilibrium point?
Yeeees!!
Take the price first, instead of the quantity; consider the direct
functions and solve directly for the price to get
Cpy = (Dyo-Sco-Sdo+Ac*Tcy+Ad*Tdy)
/ (Ac+Ad-Ay)
isolated market: comments
The equilibrium point is obtained when total production
in the two centers equals the amount demanded by the
consumers at the equilibrium price
To calculate producer prices in the two areas we have to
subtract the transport costs
The inclusion of transport costs causes an upwards shift
of the supply curve, i.e. a fixed increase in the price per
each given quantity
The inclusion of a second production center causes a
shift of the supply curve towards the right, i.e. a change in
the price-quantity relation
other regions
Calculation for region 2
Consumption Center Z
Production Centers B and A
Demand function
Supply functions
(4)
(5)
Sb = Sbo + Ab*(CPz- Tbz)
(6)
Sa = Sao + Aa *(CPz- Taz)
Dz = Dzo + Az*CPz
Dzo = 2000
Az- = -3
with:
Sbo = -1000
Ab = 12
Tbz = 7
Sao = -1200
Aa = 16
Taz = 15
other regions, summary
region 3, all regions
Consumption Center X
Production Center E
Demand function
Supply function
(7)
(8)
Se = Seo + Ae*(CPx-Tex)
with:
Seo = -1000
with:
Dx = Dxo + Ax*CPx
Dxo = 5000
Ax = -5
Ae = 5
Consumption Centers
Production Areas
C
Y
Price
301
Reg 1
Quantity
1796
D
B
Z
Price
146
Reg 2
Quantità
1562
X
Price
604
Reg 3
Quantity
1983
A
E
Tex = 7
Price
282
Quantity
1192
Price
276
Quantity
604
Price
139
Quantity
667
Price
131
Quantity
895
Price
597
Quantity
1983
other regions, graphs
Region 1
Region 3
800
1200
700
1000
600
800
500
400
600
300
400
200
200
100
0
0
0
500
1000
Dy
1500
2000
2500
3000
0
3500
500
1000
Dx
(Sc+Sd)+T
Region 2
700
600
500
400
300
200
100
0
0
500
Dz
1000
1500
2000
(Sb+Sa)+T
2500
3000
3500
1500
2000
2500
Se+T
3000
3500
isolated markets, comments
Prices in the isolated markets are widely different: from 146
of Region 2 to 604 of Region 3.
This reflects the different production and consumption
characteristics of the three regions strong production
capacity in region 2 and the strong demand in 3.
Isolated markets do not allow consumers of Region 3 to
benefit from production capacity of Region and its low
prices.
Isolation can be due to natural reasons (e.g. distance, lack of
communication facilities) or to political reasons (e.g.
custom banners or other policies (prohibitive barriers) that
eliminate trade)
market integration
Suppose that region 3 and region 2 are connected by a road
which allows trade
region 2
region 3
A
Z
X
E
B
Region 2
Region 3
Consumption centre
Production centres
Consumption centres
Production centres
Dz = Dzo + Az*CPz
Sb = Sbo + Ab*(CPz- Tbz)
Dx = Dxo + Ax*CPx
Se = Seo + Ae*(CPx-Tex)
with:
with:
Sa = Sao + Aa *(CPz- Taz)
with: Dzo = 2000
Az
= -3
with:
Sbo = -1000
Ab = 12
Tbz = 7
Dxo = 5000
Ax = -5
Seo = -1000
Ae = 5
Tex = 7
Sao = -1200
Aa = 16
Taz = 15
Txz = 65 Transport cost from X to capital Z
Tzx = 65 Transport cost from capital Z to X
market integration
Transport costs are given by
CPz = CPx – Tzx
PPa = CPx – Tzx – Taz
PPb = CPx – Tzx – Tbz
PPe = CPx – Tex
total demand = total supply, i.e. Dx + Dz = Se + Sa + Sb
where:
Dx = Dxo + Ax * CPx
Dz = Dzo + Az * (CPx -Tzx)
Sa = Sao + Aa * (CPx- Taz- Tzx)
Sb = Sbo + Ab * (CPx- Tbz- Tzx)
Se = Seo + Ae * (CPx-Tex)
solving for CPx
market integration
Cpx 
[(Dxo  Dzo - Seo - Sbo - Sao - AzTzx  AeTex  Ab(Tbz  Tzx)  Aa(Taz  Tzx)]
(Ae  Ab  Aa - Ax - Az)
we obtain
(Z and X connected, y isolated)
consumption centers
Production areas
price
301.0
price
Y reg 1
C
quantity
1796.0
D
Z reg 2
price
quantity
241.7
1275.0
B
A
X reg 3
price
quantity
306.7
3466.6
E
282.0
quantity
price
quantity
1192.0
276.0
604.0
price
quantity
price
quantity
234.7
1816.2
226.7
2426.9
price
quantity
299.7
498.4
market isolation and integration, prices
region 1
region 3
Y
X
CP = 301
CP = 604
region 2
Z
CP = 146
region 1
region 3
Y
X
CP = 301
CP = 307
region 2
Z
CP = 242
Tzx =65
market integration, comments
With integration, region 3 consumes 74% more, and region 2
consumes 18% less.
Price decrease by almost 50% in region 3, while it increases
by almost 68% in region 2.
Production increases with integration in region 2, by more
than 170%, while it decreases by almost 75% in region 3.
Altogether there is an increase of 22% in total consumption,
and an 8.7% decrease in production.
With integration, the difference between the two prices is
equal to the transport cost.
market integration, welfare effects
The impact of the integration of the two markets on producers
and consumers can be measured in terms of surplus.
This is a money metric welfare measure
With linear functions welfare changes can be approximated as
(p0 –p1) * (d0 +d1) / 2 (change in consumer surplus)
(p0 –p1) * (s0 +s1) / 2 (change in producer surplus)
where 0 and 1 are referred to time, p is the price, s is supply and
d is demand
The net change in welfare is the difference between the two
above (p0 – p1) * [(d0 + d1) – (s0 + s1)] / 2
(net gain or loss)
market integration, welfare effects
Region 2
Region 3
F
B
A
F
D
C
G
A
E
D
B
G
C
E
In graphical terms,
consumer surplus in region
2 are the areas FCB and
FDE, respectively before
and after market integration.
The difference is CBED,
which represents the losses
of the consumers.
The producer surplus is GCB and GAD in region 2
respectively before and after trade
Since CBAD, gained by producers, is larger than CBDE, lost
by consumers, trade has brought a net benefit to Region 2,
equal to BEA.
market integration, welfare effects
The opposite will happen in Region 3: with integration
consumers will gain and producers will loose.
There will be also
- a transfer of income from Region 3 to Region 2, equal to
the amount of purchases made by the latter in the former,
and
- an increase in the business of the transport sector, equal
to the transport cost.
Summing up, the total welfare change will be
market integration, summary of welfare effects
Region 2
change in
Consumer Surplus
Producer Surplus
Net change of Region 2
cons value before trade
Values
-135,825
277,922
142,097
227,979
% of cons
59.6
121.9
62.3
100.0
Region 3
change in
Consumer Surplus
Producer Surplus
Net change of Region 3
cons value before trade
Values
808,691
-368,189
440,502
1,063,143
% of cons
76.1
34.6
41.4
100.0
Total
change in
Consumer Surplus
Producer Surplus
Net change of Regions 2 & 3
cons value before the trade
Values
672,866
-90,267
582,599
1,424,418
% of cons
47.2
6.3
40.9
100.0
welfare effects, comments
Altogether both region have benefited from integration,
although region 3 far more than region 2.
The welfare effect is unevenly distributed among social
groups: consumers in region 2 and producers in region 3
suffer a loss, which is smaller than the gain of consumers
in 3 and producer in 2.
The first statement rests upon the hypothesis that the welfare
of all social groups is directly comparable, and equally
weighted.
full market integration
Calculation of the equilibrium price for the three regions: supply
Sc = Sco + Ac CPy – Ac Tcy
Sd = Sdo + Ad CPy – Ad Tdy
Sb = Sbo + Ab CPz – Ab Tbz
Sa = Sao + Aa CPz – Aa Taz
Se = Seo + Ae CPx – Ae Tex
and given that
Cpy = CPz + Tyz
Cpx = CPz + Txz
we have
Sc = Sco + Ac CPz +Ac Tyz - Ac Tcy
Sd = Sdo + Ad CPz +Ad Tyz – Ad Tdy
Sb = Sbo + Ab CPz
– Ab Tbz
Sa = Sao + Aa CPz
– Aa Taz
Se = Seo + Ae CPz +Ae Txz – Ae Tex
full market integration
On the demand side
Dy = Dyo + Ay CPy
Dz = Dzo + Az CPz
Dx = Dxo + Ax CPx
using the relations among regional prices:
Dy = Dyo + Ay CPz + Ay Tyz
Dz = Dzo + Az CPz
Dx = Dxo + Ax CPz + Ax Txz
thus
CPz = [ - (Sco + Sdo + Seo+ Sbo + Sao) + (Dyo +Dxo + Dzo)
+ (Ay Tyz + Ax Txz) +
+ Ac (Tcy – Tyz) + Ad (Tdy – Tyz) + Ae (Tex –
Txz) + Ab Tbz + Aa Taz] /
/ (Ac + Ad + Ae + Ab + Aa – Ay – Ax – Az)
full market integration
Integrated markets
prices
Y
294
Z
244
X
309
C
D
B
A
E
Total
Y
Z
X
Total
demand
1824
1268
3455
prices
production
quantity
275
269
237
229
302
1,150
576
1,845
2,465
510
6,546
production
quantity
regional
trade
1,727
4,310
510
6,546
-97
3,042
-2,944
0
local
transport
cost
21,856
14,405
12,913
36,973
3,572
89,719
regional
transport
cost
4,862
0
191,390
196,251
production value
316,403
155,034
437,284
564,590
154,130
1,627,441
region 3
region 1
Y
X
CP = 294
CP = 309
region 2
Tzy = 50
imports
consumption
value
0
0
0
536,291
309,421
1,067,699
1,913,412
Tzx = 65
Z
CP = 244
full market integration
Considering also consumer prices
region 1
region 3
Y
X
CP = 294
CP = 309
Tcy = 19
Tex = 7
C
PPc = 275
E
PPa = 302
Tdy = 25
Tzy = 50
Tzx = 65
region 2
D
PPd = 269
Z
CP = 244
Taz = 15
A
PPa = 229
Tbz = 7
B
PPa = 237
full market integration
Summary: Integrated and isolated markets
closed
Total consumption expenditure
Imports
Transport
Producer revenue
Producer surplus
Consumer surplus
Net welfare change
open
%
change
1,965,014 1,913,412 -2.6
0
0
0.0
285,971
0.0
1,895,294 1,627,441 -14.1
-91,162
674,214
583,052
-5.6
35.2
30.5
The gains of the consumers are greater than the losses of the
producers and the costs of transport => market integration
is beneficial to the country, although not for everybody.
(small) open economy: production and trade
Even if fully integrated, the previous setting can be
considered as being closed to foreign trade.
The country has only one port of entry, in Region 3. The
import price is 275 (small open).
Consumers of X will prefer the imported good, which is
cheaper than the local, sold at 309, this is sold at the same
price of 275.
Since almost 3000 tons sold in X (region 3) is coming from Z
(region 2), the maximum price in Z is the price in X minus
the transport cost, i.e. 210.
Similarly, the price in region 1, which was also importing
from region 2, will be the price of region 2 (210) plus the
transportation cost of 50, i.e 260.
(small) open economy: production and trade
Thus we have
prices
Y
Z
X
demand
260
210
275
prices
C
D
A
B
E
total
241
235
203
195
268
214
Y
Z
X
total
production
quantity
1,386
3,356
340
5,082
1960
1370
3625
production
quantity
946
440
1436
1920
340
5082
local
transport cost
17,974
11,000
10,052
28,800
35,574
regional trade
regional
transport cost
28,700
0
91,780
120,480
-574
1,986
-1,412
0
production value
227,986
103,400
291,508
374,400
91,120
1,088,414
imports
0
0
1873
1873
consumption
value
509,600
287,700
996,875
1,794,175
closed and open economy, comparison
Comparison: closed (isolated) and open
economy
prices
production
quantities
C
D
B
A
E
total
closed
275
269
237
229
302
open
241
235
203
195
268
prices
Y
Z
X
total
closed
294
244
309
closed
1,150
576
1,845
2,465
510
6,546
open
946
440
1,436
1,920
340
5,082
consumed
quantities
open
260
210
275
closed
1,824
1,268
3,455
6,546
open
1,960
1,370
3,625
6,955
Changes in
producer
surplus
-35,695
-17,303
-55,861
-74,662
-14,478
-197,999
Changes in
consumer
surplus
64,427
44,915
120,548
229,891
production values
closed
316,403
155,034
437,284
564,590
154,130
1,627,441
open
227,986
103,400
291,508
374,400
91,120
1,088,414
consumption values
closed
536,291
309,421
1,067,699
1,913,412
open
509,600
287,700
996,875
1,794,175
closed and open economy, comparison
Summary: closed and open
economy
2500000
2000000
closed
open
% change
1500000
1000000
-18.2
12.8
1.8
-500000
Net welfare change
-197,999
229,891
31,892
0
Consumer surplus
0.0
-28.3
-33.1
Producer surplus
515,075
190,686
1,088,414
500000
Trasport
-6.2
Producer revenue
Producer surplus
Consumer surplus
Net welfare change
1,794,175
Imports
Imports
Transport
Producer revenue
1,913,41
2
0
266,000
1,627,44
1
Total consumption expenditure
Total consumption expenditure
Opening to trade implies a small welfare gain for consumers,
greater than the loss of the producers. The transport sector will be
reduced, while foreign producers will be better off.
closed
open
pan territorial prices
The Government guarantees the same price to all producers
and to all consumers.
It has to be assumed that the Government has a Marketing
Board for enforcing the price regime: this pays producers,
distributes goods to the consumers, and imports.
The Government sets prices equal to the average of the open
market solution: producer price is 275, and consumer price is
214.
The effects on production and trade
pan territorial prices
Y
Z
X
C
D
B
A
E
total
Y
Z
X
total
prices
258
258
258
demand
1968
1226
3710
prices
production
quantity
local
transport cost
214
214
214
214
214
784
356
1,568
2,224
70
5,002
14,896
8,900
10,976
33,360
490
68,622
167,776
76,184
335,552
475,936
14,980
1,070,428
production
quantity
regional trade
regional
transport cost
imports
consumpti
on value
1,140
3,792
70
5,002
-828
2,566
-1,738
0
41,400
0
112,970
154,370
0
0
1902
507,744
316,308
957,180
1,781,232
production value
pan territorial prices
prices
C
D
B
A
E
total
open
241
235
203
195
268
production
quantities
panterrit
214
214
214
214
214
prices
Y
Z
X
total
open
260
210
275
open
946
440
1,436
1,920
340
5,082
panterrit
784
356
1,568
2,224
70
5,002
consumed
quantities
panterrit
258
258
258
open
1,960
1,370
3,625
6,955
panterrit
1,968
1,226
3,710
6,904
Changes
in
producer
surplus
-52,812
-8,358
16,522
39,368
-11,070
-16,350
Changes
in
consumer
surplus
3,928
-62,304
62,348
3,972
production values
open
panterrit
227,986 167,776
103,400
76,184
291,508 335,552
374,400 475,936
91,120
14,980
1,088,414 1,070,428
consumption values
open
panterrit
509,600 507,744
287,700 316,308
996,875 957,180
1,794,175 1,781,232
open ec and pan territorial prices, comparison
-1.5
0.2
-0.7
500,000
0
-500,000
Net Balance of the Marketing Board
-16,350
3,972
-12,379
1,000,000
Net welfare change
1.5
16.9
-1.7
Consumer surplus
515,075 523,050
190,686 222,992
1,088,414 1,070,428
0
35,238
1,500,000
Producer surplus
-0.7
Producer revenue
1,781,232
2,000,000
Trasport
Producer surplus
Consumer surplus
Net welfare
change
1,794,175
% change
Imports
Total consumption
expenditure
Imports
Trasport
Producer revenue
Marketing Board
panterrit
Total consumption expenditure
open
open
panterrit
Pan-territorial prices imply a net welfare loss compared to the open
economy solution, despite prices were set at the same (average)
levels. Moreover, the Marketing Board will suffer from a significant
loss, that, in turn, will be suffered by taxpayers.
pan territorial prices, comments
Administrative costs must be added to the loss of the
Marketing Board, suffered by taxpayers.
The implementation of this policy would not be easy: it will
be difficult to impose the prices to producers and
consumers.
In regions 1 and 3 the it will be more profitable selling
directly to the consumers, because the difference between
producer and consumer price (44) is greater that the local
transport cost.
Similarly consumers of region 2 will find more convenient to
buy the product directly from the farmers.
Implementation difficulties are likely to generate additional
administrative costs.
import parity prices
The Government raises the producer price to the "import
parity” level, e.g. to 275 for all producers in the country.
This kind of provision can be adopted with several aims: e.g.
• to promote an increase in the degree of self-sufficiency of
the country
• to support farmers income, if poor groups are mostly net
food sellers.
• in view of expanding the export capacity of the country.
The effects on production and trade:
import parity prices
Y
Z
X
C
D
B
A
E
total
Y
Z
X
total
prices
275
275
275
275
demand
1700
1175
3300
6175
prices
production
quantity
256
250
268
260
268
261
1,336
700
2,216
2,960
665
7,877
production
quantity
regional
trade
2,036
5,176
665
7,877
336
4,001
-4,337
0
local
transport
cost
25,384
17,500
15,512
44,400
4,655
107,451
regional
transport
cost
-16,800
0
281,905
265,105
production
value
342,016
175,000
593,888
769,600
178,220
2,058,724
imports
0
0
-1702
consumption
value
467,500
323,125
907,500
1,698,125
import parity prices
prices
C
D
B
A
E
total
241
235
203
195
268
production quantities
256
250
268
260
268
prices
Y
Z
X
total
260
210
275
946
440
1,436
1,920
340
5,082
1,336
700
2,216
2,960
665
7,877
consumed quantities
275
275
275
1,960
1,370
3,625
6,955
1,700
1,175
3,300
6,175
Changes in
producer
surplus
17,115
8,550
118,690
158,600
0
302,955
Changes in
consumer
surplus
-27,450
-82,713
0
-110,163
production values
227,986
103,400
291,508
374,400
91,120
1,088,414
342,016
175,000
593,888
769,600
178,220
2,058,724
consumption
values
509,600
287,700
996,875
1,794,175
467,500
323,125
907,500
1,698,125
open ec and import parity prices, comparison
open
Total consumption expenditure
Imports
Trasport
Producer revenue
1,794,175
515,075
190,686
1,088,414
import parity % change
1,698,125
-468,050
372,556
2,058,724
2,500,000
2,000,000
-5.4
-190.9
95.4
89.1
1,500,000
1,000,000
500,000
Change in Producer surplus
Change in Consumer surplus
Net welfare change
302,955
-110,163
192,793
14.7
-6.5
11.4
0
-500,000
lc
on
su
m
pt
io
n
To
ta
107,451
-372,556
0
-265,105
ex
pe
nd
itu
re
Im
po
r ts
T
Pr
r
as
od
po
uc
rt
er
re
Pr
v
od
en
uc
ue
er
C
su
Ne
on
rp
su
tB
lu
m
s
ala
er
N
nc
et
s
ur
eo
we
ft
lfa plus
he
re
M
ch
ar
an
ke
ge
tin
g
Bo
ar
d
-1,000,000
Marketing Board
diff between cons & prod
transports
loss on imports
Net Balance of the Marketing Board
The country becomes an exporter. Gains for producers are larger
than losses for consumers; but the high transport costs imply a
significant loss for the Marketing Board. The transport business
almost doubles its revenue.
open
import parity
import parity prices, comments
The overall welfare effect of the parity import price policy is
negative, since the loss suffered by taxpayers (through the
Marketing Board) are by far higher than the net welfare
balance of producers and consumers.
Consumption decreases by than 5.4% in terms of expenditure,
and by 11% in physical terms. This can indicate that
consumers are in a condition of relative abundance, since
they reduced consumption rather than substituting food
with cheaper alternatives.
production and consumption subsidies
The Government raises the producer price to the highest level
in the country, i.e. to 268 (the level of region 3) for all
producers in the country.
The Government also wishes to support consumers, by fixing
prices at the lowest level in the country, i.e. 210 (that of
region 2).
The country is a price taker, and world price is 275
This provision is adopted with the aim of supporting both
agricultural producers and poor consumers, and to stimulate
the growth of domestic supply.
The effects on production and trade:
production and consumption subsidies
Y
Z
X
C
D
B
A
E
total
Y
Z
X
total
prices
210
210
210
210
demand
2160
1370
3950
7480
prices
production
quantity
local transport
cost
production
value
268
268
268
268
268
268
1,294
672
2,132
2,848
630
7,576
24,586
16,800
14,924
42,720
4,410
103,440
346,792
180,096
571,376
763,264
168,840
2,030,368
production
quantity
regional trade
regional
transport cost
imports
1,966
4,980
630
7,576
-194
3,610
-3,416
0
9,700
0
222,040
231,740
0
0
-96
consumption
value
453,600
287,700
829,500
1,570,800
production and consumption subsidies
prices
C
D
B
A
E
total
open
241
235
203
195
268
production quantities
268
268
268
268
268
prices
Y
Z
X
total
open
260
210
275
open
946
440
1,436
1,920
340
5,082
1,294
672
2,132
2,848
630
7,576
consumed quantities
210
210
210
open
1,960
1,370
3,625
6,955
2,160
1,370
3,950
7,480
Changes in
producer
surplus
30,240
18,348
115,960
174,032
0
338,580
Changes in
consumer
surplus
103,000
0
246,188
349,188
production values
open
227,986
103,400
291,508
374,400
91,120
1,088,414
346,792
180,096
571,376
763,264
168,840
2,030,368
consumption values
open
509,600
287,700
996,875
1,794,175
453,600
287,700
829,500
1,570,800
open ec vs prod&cons subsidies, comparison
open
Total consumption expenditure
Imports
Trasport
Producer revenue
Change in Producer surplus
Change in Consumer surplus
Net welfare change
1,794,175
515,075
190,686
1,088,414
cons&prod subs % change
1,570,800
-26,400
335,180
2,030,368
338,580
349,188
687,768
2,500,000
-12.5
-105.1
75.8
86.5
2,000,000
1,500,000
1,000,000
500,000
16.7
22.2
43.8
0
-500,000
pt
io
n
ex
pe
nd
itu
re
Im
po
rts
Tr
Pr
as
od
po
uc
rt
er
re
Pr
v
od
en
ue
uc
e
rs
Co
ur
N
ns
pl
et
um
us
Ba
er
N
la
et
su
nc
w
rp
eo
elf
lu
ft
s
ar
he
ec
M
h
an
ar
ge
ke
tin
g
Bo
ar
d
-1,000,000
tal
co
ns
um
-439,408
-335,180
672
-773,916
-86,149
To
Marketing Board
diff between cons & prod
transports
loss on imports
Net Balance of the Marketing Board
Total net balance
open
cons&prod subs
Also in this case the country becomes an exporter, there are welfare
gains for both producers and consumers; but the high transport costs
and the price subsidies for both producers and consumers imply a
significant loss for the Marketing Board.
production and consumption subsidies, comments
The overall balance of the policy is negative: the loss suffered
by taxpayers (financing the Marketing Board) is greater
than the net welfare gains of producers and consumers.
There is a deadweight loss arising from resource
misallocation.
Both poduction and consumption increase significantly; in the
long run this may give rise to investment in agriculture, and
to further supply increases, while demand may slow down,
as the population approaches satiety.
adverse weather
The same simplified model can be used to analyse other
phenomena, like, e.g. supply or demand shocks.
An example is that of weather condition, that affect
agricultural supply.
Bad weather affecting production can be represented through
a supply shift.
The effects on production and trade:
adverse weather
Y
Z
X
C
D
B
A
E
total
Y
Z
X
total
prices
260
210
275
258
demand
1960
1370
3625
6955
prices
production
quantity
local transport
cost
production
value
241
235
203
195
268
212
696
190
936
1,320
90
3,232
13,224
4,750
6,552
19,800
630
44,956
167,736
44,650
190,008
257,400
24,120
683,914
production
quantity
regional trade
regional
transport cost
imports
886
2,256
90
3,232
-1,074
886
188
0
53,700
0
-12,220
41,480
0
0
3723
consumption
value
509,600
287,700
996,875
1,794,175
adverse weather
prices
C
D
B
A
E
total
open
241
235
203
195
268
adverse weather
241
235
203
195
268
prices
Y
Z
X
total
open
260
210
275
adverse weather
260
210
275
production quantities
open
946
440
1,436
1,920
340
5,082
adverse weather
696
190
936
1,320
90
3,232
consumed quantities
open
1,960
1,370
3,625
6,955
adverse weather
1,960
1,370
3,625
6,955
Changes in
producer
surplus
-34,208
-19,688
-49,417
-60,750
-10,750
-174,813
Changes in
consumer
surplus
0
0
0
0
production values
open adverse weather
227,986 167,736
103,400 44,650
291,508 190,008
374,400 257,400
91,120
24,120
1,088,414 683,914
consumption values
open adverse weather
509,600 509,600
287,700 287,700
996,875 996,875
1,794,175 1,794,175
open ec vs adverse weather, comparison
2,000,000
open
Total consumption expenditure
Imports
Trasport
Producer revenue
1,794,175
515,075
190,686
1,088,414
1,500,000
adverse weather % change
1,794,175
1,023,825
86,436
683,914
1,000,000
0.0
98.8
-54.7
-37.2
500,000
0
-25.6
0.0
-9.7
-500,000
ex
pe
nd
itu
re
Im
po
rts
Tr
Pr
as
od
po
uc
rt
er
r
ev
Pr
od
en
ue
uc
er
Co
s
u
N
ns
rp
et
lu
um
Ba
s
er
N
la
et
su
nc
w
rp
eo
elf
lu
ft
s
ar
he
ec
M
h
an
ar
ge
ke
tin
g
Bo
ar
d
-174,813
0
-174,813
To
tal
c
on
su
m
pt
io
n
Change in Producer surplus
Change in Consumer surplus
Net welfare change
open
adverse weather
In this case there is only a change in producer surplus, since
consumers remain in the same position, thanks to increased imports
adverse weather, comments
The small open economy hypothesis allows for prices to
remain unchanged after the adverse weather: imports
substitute for domestic production, thus consumer surplus
does not change.
technical change
In this simplified model technical change can be introduced
as a supply shift, i.e. just as the opposite of the previous
example of adverse weather.
The effects on production and trade:
technical change
Y
Z
X
C
D
B
A
E
to tal
Y
Z
X
to tal
p rices
260
210
275
258
d eman d
1960
1370
3625
6955
p rices
p ro d u ctio n
q u an tity
241
235
203
195
268
216
1,071
565
1,686
2,220
590
6,132
p ro d u ctio n
q u an tity
reg io n al
trad e
1,636
3,906
590
6,132
-324
2,536
-2,212
0
lo cal
tran s p o rt
co s t
20,349
14,125
11,802
33,300
4,130
83,706
reg io n al
tran s p o rt
co s t
16,200
0
143,780
159,980
p ro d u ctio n
v alu e
258,111
132,775
342,258
432,900
158,120
1,324,164
imp o rts
0
0
823
co n s u mp tio n
v alu e
509,600
287,700
996,875
1,794,175
technical change
prices
C
D
B
A
E
total
open
241
235
203
195
268
technical change
241
235
203
195
268
prices
Y
Z
X
total
open
260
210
275
technical change
260
210
275
production quantities
open
946
440
1,436
1,920
340
5,082
technical change
1,071
565
1,686
2,220
590
6,132
consumed quantities
open
1,960
1,370
3,625
6,955
technical change
1,960
1,370
3,625
6,955
Changes in
producer
surplus
21,010
15,703
32,521
38,813
23,250
131,297
Changes in
consumer
surplus
0
0
0
0
production values
open technical change
227,986 258,111
103,400 132,775
291,508 342,258
374,400 432,900
91,120
158,120
1,088,414 1,324,164
consumption values
open technical change
509,600 509,600
287,700 287,700
996,875 996,875
1,794,175 1,794,175
open ec vs technical change, comparison
2,000,000
1,800,000
1,600,000
open
Total consumption expenditure
Imports
Trasport
Producer revenue
1,794,175
515,075
190,686
1,088,414
technical change % change
1,794,175
226,325
243,686
1,324,164
1,400,000
1,200,000
0.0
-56.1
27.8
21.7
1,000,000
800,000
600,000
400,000
9.9
0.0
7.3
200,000
0
itu
po
Im
pe
nd
ex
pt
io
n
su
m
tal
co
n
To
rts
T
Pr
ra
sp
od
or
uc
t
er
r
ev
Pr
en
od
ue
uc
er
Co
s
ur
N
ns
pl
et
um
us
Ba
e
N
la
rs
et
nc
ur
w
eo
pl
elf
us
ft
a
r
he
ec
M
ha
ar
ng
ke
e
tin
g
Bo
ar
d
131,297
0
131,297
re
Change in Producer surplus
Change in Consumer surplus
Net welfare change
open
technical change
Imports in this case decreases, since more domestic production is
available at the same price
technical change, comments
Also in this case, the small open economy hypothesis allows
for prices to remain unchanged after the technical change
injection, thus consumer surplus does not change, as they
substitute one to one domestically produced goods for
imported ones.
This means that producers get the entire benefit arising from
technical change.
As it will be shown, this is a very simplified representation.
beyond the static single market model
Aim: providing hints on more sophisticated
equilibrium modeling frameworks
• MODEXC, dynamic model for the analysis of technical
change
• large multi market multi country frameworks employed in
the analysis of agricultural policies
•the functioning and the scope of general equilibrium models
and CGEs
MODEXC
A more sophisticated treatment compared to what was shown
up to now. MODEXC:
• calculates and analyzes the effects of technological change,
measured as surplus of producers and consumers
• allows for the treatment of different types of technical
change, other than a parallel supply shift
• has a slightly more sophisticated functional form
• is a recursive dynamic model
• assumes free market conditions and the absence of policies.
It can be used for modelling both closed and (small) open
economy conditions
• distinguishes technical change from other supply shifters
MODEXC functional form
supply
s0  c( p  pm )
demand
d0  b p
with
pm = minimum bid price
p = price
c, g, b = constants
 = own price elasticity
g
MODEXC dynamics
Expected prices are defined according to Nerlove (1958)
under a scheme of distributed lags as:
pt*  1 pt 1   2 pt 2  3 pt 3   4 pt 4  5 pt 5
where:
pt*
= expected price in period "t",
pt-1...pt-n = lagged prices from period "t-1" to
period "t-n", and
1….n = weighted factors of lagged prices.
MODEXC and tech change
• The model considers technical change as a horizontal
supply shift, i.e. as a percentage increase of production
• if k is expressed as a percentage change of production costs
(kc), it can be converted to its equivalent in terms of
production expansion (kp) through supply elasticity
(fp = price elasticity of supply) and
k p  kc f p
with Dq = increase in
q0  q1  q0  q0  Dq
k

production due to the new
q0
q0
technology
MODEXC and tech change
Three types of supply shift depending on the position k takes
within the original function.
• pivotal shift:
s1  ck ( p  pm )
• divergent shift:
s1  c(kp  pm )
• convergent shift: s1  c( p0 
g
g
pm g
)
k
The general form of shifted supply is:
pm g
s1  k1c( k2 p 
)
k3
Priceper unit of output
MODEXC and tech change: surplus
S1
E0
p0
F
p1
E1
d0
pm
p
q
S
q1
q
Quantity of output
• The area p0p1E0E1 represents this gain of consumers
• producers are affected by lower marginal costs (pmFE1) and
by price reduction p0E0Fp1; thus total producer surplus
change is pmFE1 – p0E0Fp1.
• pmE0E1 represents the net social surplus
• the final effect depends on elasticities; particularly, if
demand elasticity is low producers gains are most probably
small, if not negative
MODEXC and tech change
The model assumes that the rate of adoption of technical
change is
• slow the initial stages,
• then increases as the technology is more widely adopted and
its performance and benefits are better known,
• hen decreases in advanced stages of the adoption process,
• and finally becomes stabilized
This is represented assuming that the supply shift
factor, k, obeys a logistic-type pattern
MODEXC and tech change
The model allows to consider both supply and demand shifters,
independent of thecnical change. These are
kdt  (1  AGRD)t
demand shifter (e.g. population, income)
k 0t  (1  q )t
supply shifter (tech change in other sectors)
If q differs from zero, the annual k value is adjusted because q is
applied on a greater base than that used to estimate the final value
of k.
hints on large multi market PE
Reference to AGLINK, FAPRI frameworks employed in
agricultural policy analysis and ag market projections.
A typical large PE model consists of sets of
behavioral equations,
equilibrium relations, and
identities
Equations can be grouped into a supply component, a demand
or utilisation component, and a foreign trade component;
This pattern is repeated for each region and product included in
the models.
Moreover there are price transmission equations, linking world
to domestic prices, and
world market equilibrium conditions that close the models.
Crop products
livestock product
supply
(1)
(2)
(3)
si,n = s(pv,i,n, pv,j,n, Pols)
rv,i,n =r(pv,i,n, PR)
Qov,i,n = si,n rv,i,n
(8)
(9)
(10)
(11)
ci,n = c(pz,i,n, pz,j,n, Polc)
AL = al(pv,i,n, pv,j,n)
rz,i,n = r(pz,i,n, AL, PR)
Qoz,i,n = ci,n rz,i,n
(12)
Qd z,i,n = qd(pz,i,n, Yn, POPn)
demand
(4)
(5)
(6)
(7)
Cuv,i,n = cu(pv,i,n, Yn, POPn)
AAv,i,n = aa(Qoz,i,n)
SEv,i,n = se(sv,i,n)
Qdv,i,n = Cuv,i,n + AAv,i,n + SEv,i,n
price transmission
(13)
pi,n = p(pi,w, tc, Polp)
trade
(14)
(E i,n - Ii,n) = Qoi,n - Qd i,n
closure
(15)
 (E i,n - Ii,n) = 0
where:
i, j = products;
v = crops;
z = livestock;
n = country;
and
s = land (hectares);
c = heads (number);
AL = index of feed cost;
Polp = policies directly affecting prices;
E = exports
I = imports;
tc = exchange rate
PR = yield trend;
Y = GDP;
POP = population;
AA = demand for feed;
Qd = total demand.
Pols = policies based on land;
Polc = policies based on livestock heads;
Qo = supply;
pn = price in country n;
pw= world price;
Cu = demand for human consumption;
SE = demand for seeds;
r = yield (per hectare or per head);
hints on large multi market PE
modeling is simplified in several respects:
• production is entirely deterministic (no uncertainty factors
farmers’ attitude toward risk)
• input demand only for land, herds, and where primary
products are employed as inputs in the production of other
goods included in the model, (feed crops, oilseeds, dairy)
• land use and herd depends solely on the price obtained for
agricultural products.
• technical change is a trend variable (rather poor
representation)
hints on large multi market PE
• goods produced in different countries are be perfectly
homogeneous (only net trade position, no inra-industry trade)
• price changes occurring in one market are always transmitted
to all the other
• the closure rule is defined by excess supplies, that must add
up to zero in all markets
• the PE assumption implies that feedbacks from agriculture to
the other sectors are not described. The effects on agriculture
of what happens in other sectors (and in macroeconomic
variables) is usually included as exogenous shocks.
hints on large multi market PE
The typical model is comparative static: it compares the two
equilibrium solutions under the hypothesis that adjustment of
endogenous variables is complete
However, large size multi country multi commodity models
often include some elements of dynamics
This is modelled simply by including lagged variables in the
equations, according to a recursive criteria: equilibrium
solutions are based on the forecast of exogenous variables, and
on the value of the endogenous variables obtained in the
previous period.
This implies that agents’ behaviour is optimal with reference to
each single period, but not through time.
hints on GE models
All productive sectors of the economy are represented.
Blocks of relations dealing with production, consumption and
factor use
The simplest example is a setting including 2 good, 2 factors
and 2 consumers
production
Goods - sectors
Production function
agriculture
XSagr = f (L, K)
textiles
XStex = f (L, K)
consumption
Agents
Utility function
rural
Urur = f (Xagr, Xtex)
urban
Uurr = f (Xagr, Xtex)
Factors of production
endow ments
labour
L=L
capital
K=K
hints on GE models
Equations of the basic model
 
 
real flows
supply of 
good
i
h
X Si = f(DLi, DK i)
w = ( X Si /
r = ( X Si /
D Li)
D K i)
expenditure
pi
pi
D
hX i
i demand
h
labour


capital demand
i
= ahi (Y h / pi)
demand for i
equilibrium conditions
h
X Si =
income flows
D Li =
Y h = w LSh + r 
K Sih
DK i =
identities
P i X Si = D Li w + D K i r
Yh =
D
hX i
pi
D
hX i
LSh
demand equal supply
demand for labour
equals labour
endowement
K Sh Demand for capital
equals capital
endowement
hints on GE models
Equilibrium conditions allow to “close” the model, and a set of
identities ensure that income does not exceed expenditure, and
that it equals that of the factors of production.
In this simplified model only the initial factor endowments and
the utility function parameter are exogenous, while all the rest
is calculated by the model
This can be solved by by imposing equilibrium conditions on
all markets:
supply (from the production functions) equals demand
of the two consumers (from their utility maximisation).
GE and CGE models
In order to be "computable" a general equilibrium model
requires
a database describing the flows of resources in the
economy at the level of aggregation considered in the
model;
a set of parameters for the behavioral relations of the
model
The database for a CGE model is knonw as Social Accounting
Matrix (a set of accounts describing resource flows between
consumers producers, the government and foreign economies
Parameters can be obtained through calibration or estimation
calibration vs estimation
calibration = deterministic procedure normally used to
estimate some or all parameters; the base year database is used
to determine the values of the parameters that are compatible
with the exogenous and the endogenous variables
This does not allow a statistical control of the parameters
Econometric estimation (especially through symultaneous
equations) is unfeasible most of the times, due to models’ size
and limited number of observations
Block econometric estimation and sensitivity analysis are
frequent alternatives.
advantages and drawbacks of GE vs PE approach
No approach is “better” in absolute terms: all depends on the
problem to be analysed
Compared to the PE, the GE approach removes a simplifying
hypothesis: that what happens the sector that are considered in
the model do not affect demand and supply in sectors that are
not considered, and vice versa.
Thus the GE approach can be effective
to highlight the effects of a general budget constraint
in the economy
to consider the feedback from (e.g.) agriculture to other
sectors, and the second round effects
the importance of feedback effects is related to (i) the relative
size of agriculture compared to the other sectors; (ii) the degree
of integration between (e.g.) agriculture and the rest of the
economy
advantages and drawbacks of GE vs PE approach
...specifying a GE instead of a PE model appear to be
worthwhile when the benefits in terms of additional information
compared to the treatment of the same problem within a PE
framework is greater than the increase in the “costs” associated
with the time spent in data processing and the more complex
specification of the mode