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 multi-
market 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 so-called 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:
C D
Y
consumption center
production centerproduction center
Consumptìon Center Y Production Centers C & D
Demand function Supply functions
(1) Dy = Dyo+ Ay * CPy (2) Sc = Sco + Ac*(CPy - Tcy)
(3) Sd = Sdo + Ad*(CPy -Tdy)
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
We want to calculate the equilibrium point
0
100
200
300
400
500
600
700
800
0 500 1000 1500 2000 2500 3000 3500
Q
CP
y
Dy
Sc
Sc+T
(Sc+Sd)+T
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) Dz = Dzo + Az*CPz (5) Sb = Sbo + Ab*(CPz- Tbz)
(6) Sa = Sao + Aa *(CPz- Taz)
Dzo = 2000
Az- = -3
with: Sbo = -1000
Ab = 12
Tbz = 7
Sao = -1200
Aa = 16
Taz = 15
other regions, summary
region 3, all regionsConsumption Center X Production Center E
Demand function Supply function
(7) Dx = Dxo + Ax*CPx (8) Se = Seo + Ae*(CPx-Tex)
with: Dxo = 5000
Ax = -5
with: Seo = -1000
Ae = 5
Tex = 7Consumption Centers Production Areas
Y
Reg 1
Price
Quantity
301
1796
C
D
Price
Quantity
Price
Quantity
282
1192
276
604
Z
Reg 2
Price
Quantità
146
1562
B
A
Price
Quantity
Price
Quantity
139
667
131
895
X
Reg 3
Price
Quantity
604
1983
E Price
Quantity
597
1983
other regions, graphs
0
100
200
300
400
500
600
700
800
0 500 1000 1500 2000 2500 3000 3500
Dy (Sc+Sd)+T
0
200
400
600
800
1000
1200
0 500 1000 1500 2000 2500 3000 3500
Dx Se+T
0
100
200
300
400
500
600
700
0 500 1000 1500 2000 2500 3000 3500
Dz (Sb+Sa)+T
Region 1 Region 3
Region 2
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
B
A
Z EX
region 3region 2
Region 2 Region 3
Consumption centre Production centres Consumption centres Production centres
Dz = Dzo + Az*CPz
Sb = Sbo + Ab*(CPz- Tbz)
Sa = Sao + Aa *(CPz- Taz)
Dx = Dxo + Ax*CPx Se = Seo + Ae*(CPx-Tex)
with: Dzo = 2000
Az = -3
with: Sbo = -1000
Ab = 12
Tbz = 7
Sao = -1200
Aa = 16
Taz = 15
with: Dxo = 5000
Ax = -5
with: Seo = -1000
Ae = 5
Tex = 7
Txz = 65 Transport cost from X to capital Z Tzx = 65 Transport cost from capital Z to X
market integrationTransport costs are given by
CPz = CPx – TzxPPa = CPx – Tzx – Taz PPb = CPx – Tzx – Tbz PPe = CPx – Tex
total demand = total supply, i.e. Dx + Dz = Se + Sa + Sbwhere:
Dx = Dxo + Ax * CPxDz = 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
we obtainAz) -Ax - Aa Ab (Ae
Tzx)] Aa(Taz Tzx) Ab(Tbz AeTex AzTzx - Sao - Sbo - Seo - Dzo [(DxoCpx
(Z and X connected, y isolated) consumption centers Production areas
Y reg 1 price 301.0 C price 282.0
quantity 1796.0 quantity 1192.0 D price 276.0 quantity 604.0
Z reg 2 price 241.7 B price 234.7 quantity 1275.0 quantity 1816.2 A price 226.7 quantity 2426.9
X reg 3 price 306.7 E price 299.7 quantity 3466.6 quantity 498.4
market isolation and integration, prices
Y
CP = 301
X
CP = 604
Z
CP = 146
region 2
region 3region 1
Y
CP = 301
X
CP = 307
Z
CP = 242
region 2
region 3region 1
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
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.
Region 2 Region 3
A
BC
D
G
E
F
BA
D
G
C E
F
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 Values % of cons Consumer Surplus -135,825 59.6 Producer Surplus 277,922 121.9 Net change of Region 2 142,097 62.3 cons value before trade 227,979 100.0
Region 3 change in Values % of cons Consumer Surplus 808,691 76.1 Producer Surplus -368,189 34.6 Net change of Region 3 440,502 41.4 cons value before trade 1,063,143 100.0
Total change in Values % of cons Consumer Surplus 672,866 47.2 Producer Surplus -90,267 6.3 Net change of Regions 2 & 3 582,599 40.9 cons value before the trade 1,424,418 100.0
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 integrationCalculation 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 haveSc = 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 sideDy = 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
Y
CP = 294
X
CP = 309
Z
CP = 244
region 2
region 3region 1
Tzx = 65Tzy = 50
Integrated markets prices demand Y 294 1824 Z 244 1268 X 309 3455
prices production
quantity local
transport cost
production value
C 275 1,150 21,856 316,403 D 269 576 14,405 155,034 B 237 1,845 12,913 437,284 A 229 2,465 36,973 564,590 E 302 510 3,572 154,130 Total 6,546 89,719 1,627,441
production
quantity regional
trade regional transport
cost
imports consumption value
Y 1,727 -97 4,862 0 536,291 Z 4,310 3,042 0 0 309,421 X 510 -2,944 191,390 0 1,067,699 Total 6,546 0 196,251 1,913,412
full market integration
Considering also consumer prices
Y
CP = 294
X
CP = 309
Z
CP = 244
region 2
region 3region 1
Tzx = 65Tzy = 50
APPa = 229
BPPa = 237
Taz = 15 Tbz = 7
EPPa = 302
Tex = 7
Tdy = 25
DPPd = 269
CPPc = 275
Tcy = 19
full market integration
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.
Summary: Integrated and isolated markets
closed open %change
Total consumption expenditure 1,965,014 1,913,412 -2.6Imports 0 0 0.0Transport 285,971 0.0Producer revenue 1,895,294 1,627,441 -14.1
Producer surplus -91,162 -5.6Consumer surplus 674,214 35.2Net welfare change 583,052 30.5
(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 haveprices demand
Y 260 1960Z 210 1370X 275 3625
prices productionquantity
localtransport cost
production value
C 241 946 17,974 227,986D 235 440 11,000 103,400A 203 1436 10,052 291,508B 195 1920 28,800 374,400E 268 340 35,574 91,120total 214 5082 1,088,414
productionquantity
regional trade regionaltransport cost
imports consumptionvalue
Y 1,386 -574 28,700 0 509,600Z 3,356 1,986 0 0 287,700X 340 -1,412 91,780 1873 996,875total 5,082 0 120,480 1873 1,794,175
closed and open economy, comparisonComparison: closed (isolated) and openeconomy
prices productionquantities
Changes inproducersurplus
production values
closed open closed open closed openC 275 241 1,150 946 -35,695 316,403 227,986D 269 235 576 440 -17,303 155,034 103,400B 237 203 1,845 1,436 -55,861 437,284 291,508A 229 195 2,465 1,920 -74,662 564,590 374,400E 302 268 510 340 -14,478 154,130 91,120total 6,546 5,082 -197,999 1,627,441 1,088,414
prices consumedquantities
Changes inconsumersurplus
consumption values
closed open closed open closed openY 294 260 1,824 1,960 64,427 536,291 509,600Z 244 210 1,268 1,370 44,915 309,421 287,700X 309 275 3,455 3,625 120,548 1,067,699 996,875total 6,546 6,955 229,891 1,913,412 1,794,175
closed and open economy, comparison
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.
Summary: closed and openeconomy
closed open % change
Total consumption expenditure 1,913,412
1,794,175 -6.2
Imports 0 515,075 0.0Transport 266,000 190,686 -28.3Producer revenue 1,627,44
11,088,414 -33.1
Producer surplus -197,999 -18.2Consumer surplus 229,891 12.8Net welfare change 31,892 1.8
-500000
0
500000
1000000
1500000
2000000
2500000
To
tal c
on
sum
pti
on
exp
end
itu
re
Imp
ort
s
Tra
spo
rt
Pro
du
cer
rev
enu
e
Pro
du
cer
surp
lus
Co
nsu
mer
su
rplu
s
Net
wel
fare
ch
ang
e
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
prices demand Y 258 1968 Z 258 1226 X 258 3710
prices production
quantity local
transport cost production value
C 214 784 14,896 167,776 D 214 356 8,900 76,184 B 214 1,568 10,976 335,552 A 214 2,224 33,360 475,936 E 214 70 490 14,980 total 5,002 68,622 1,070,428
production
quantity regional trade regional
transport cost imports consumpti
on value
Y 1,140 -828 41,400 0 507,744 Z 3,792 2,566 0 0 316,308 X 70 -1,738 112,970 1902 957,180 total 5,002 0 154,370 1,781,232
pan territorial prices
prices production quantities
Changes in
producer surplus
production values
open panterrit open panterrit open panterrit C 241 214 946 784 -52,812 227,986 167,776 D 235 214 440 356 -8,358 103,400 76,184 B 203 214 1,436 1,568 16,522 291,508 335,552 A 195 214 1,920 2,224 39,368 374,400 475,936 E 268 214 340 70 -11,070 91,120 14,980 total 5,082 5,002 -16,350 1,088,414 1,070,428
prices consumed quantities
Changes in
consumer surplus
consumption values
open panterrit open panterrit open panterrit Y 260 258 1,960 1,968 3,928 509,600 507,744 Z 210 258 1,370 1,226 -62,304 287,700 316,308 X 275 258 3,625 3,710 62,348 996,875 957,180 total 6,955 6,904 3,972 1,794,175 1,781,232
open ec and pan territorial prices, comparison
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.
-500,000
0
500,000
1,000,000
1,500,000
2,000,000
To
tal
con
sum
ptio
n e
xpe
ndit
ure
Impo
rts
Tra
spo
rt
Pro
duc
er r
even
ue
Pro
du
cer
surp
lus
Con
sum
er s
urpl
us
Net
wel
fare
ch
ang
e
Net
Bal
ance
of
the
Mar
ket
ing
Bo
ard
open
panterrit
open panterrit % change
Total consumption expenditure
1,794,175 1,781,232 -0.7
Imports 515,075 523,050 1.5 Trasport 190,686 222,992 16.9 Producer revenue 1,088,414 1,070,428 -1.7 Marketing Board 0 35,238
Producer surplus -16,350 -1.5 Consumer surplus 3,972 0.2 Net welfare change
-12,379 -0.7
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
prices demand Y 275 1700 Z 275 1175 X 275 3300
275 6175
pricesproduction
quantity
local transport
cost
production value
C 256 1,336 25,384 342,016D 250 700 17,500 175,000B 268 2,216 15,512 593,888A 260 2,960 44,400 769,600E 268 665 4,655 178,220total 261 7,877 107,451 2,058,724
production
quantityregional
trade
regional transport
costimports
consumption value
Y 2,036 336 -16,800 0 467,500Z 5,176 4,001 0 0 323,125X 665 -4,337 281,905 -1702 907,500total 7,877 0 265,105 1,698,125
import parity pricesChanges in producer surplus
C 241 256 946 1,336 17,115 227,986 342,016D 235 250 440 700 8,550 103,400 175,000B 203 268 1,436 2,216 118,690 291,508 593,888A 195 260 1,920 2,960 158,600 374,400 769,600E 268 268 340 665 0 91,120 178,220total 5,082 7,877 302,955 1,088,414 2,058,724
Changes in consumer surplus
Y 260 275 1,960 1,700 -27,450 509,600 467,500Z 210 275 1,370 1,175 -82,713 287,700 323,125X 275 275 3,625 3,300 0 996,875 907,500total 6,955 6,175 -110,163 1,794,175 1,698,125
prices production quantities production values
prices consumed quantitiesconsumption
values
open ec and import parity prices, comparison
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.
-1,000,000
-500,000
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
Total c
onsum
ption e
xpen
diture
Impor
ts
Trasport
Produc
er rev
enue
Produ
cer s
urplus
Consu
mer su
rplus
Net welf
are ch
ange
Net Bala
nce o
f the
Mark
eting B
oard
open
import parity
open import parity % change
Total consumption expenditure 1,794,175 1,698,125 -5.4Imports 515,075 -468,050 -190.9Trasport 190,686 372,556 95.4Producer revenue 1,088,414 2,058,724 89.1
Change in Producer surplus 302,955 14.7Change in Consumer surplus -110,163 -6.5Net welfare change 192,793 11.4
Marketing Boarddiff between cons & prod 107,451transports -372,556loss on imports 0Net Balance of the Marketing Board -265,105
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 prices demand Y 210 2160 Z 210 1370 X 210 3950
210 7480
pricesproduction
quantitylocal transport
costproduction
value
C 268 1,294 24,586 346,792D 268 672 16,800 180,096B 268 2,132 14,924 571,376A 268 2,848 42,720 763,264E 268 630 4,410 168,840total 268 7,576 103,440 2,030,368
production
quantityregional trade
regional transport cost
importsconsumption
value
Y 1,966 -194 9,700 0 453,600Z 4,980 3,610 0 0 287,700X 630 -3,416 222,040 -96 829,500total 7,576 0 231,740 1,570,800
production and consumption subsidiesChanges in producer surplus
open open openC 241 268 946 1,294 30,240 227,986 346,792D 235 268 440 672 18,348 103,400 180,096B 203 268 1,436 2,132 115,960 291,508 571,376A 195 268 1,920 2,848 174,032 374,400 763,264E 268 268 340 630 0 91,120 168,840total 5,082 7,576 338,580 1,088,414 2,030,368
Changes in consumer
surplusopen open open
Y 260 210 1,960 2,160 103,000 509,600 453,600Z 210 210 1,370 1,370 0 287,700 287,700X 275 210 3,625 3,950 246,188 996,875 829,500total 6,955 7,480 349,188 1,794,175 1,570,800
prices production quantities production values
prices consumed quantities consumption values
open ec vs prod&cons subsidies, comparison
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.
-1,000,000
-500,000
0
500,000
1,000,000
1,500,000
2,000,000
2,500,000
open
cons&prod subs
open cons&prod subs % change
Total consumption expenditure 1,794,175 1,570,800 -12.5Imports 515,075 -26,400 -105.1Trasport 190,686 335,180 75.8Producer revenue 1,088,414 2,030,368 86.5
Change in Producer surplus 338,580 16.7Change in Consumer surplus 349,188 22.2Net welfare change 687,768 43.8
Marketing Boarddiff between cons & prod -439,408transports -335,180loss on imports 672Net Balance of the Marketing Board -773,916Total net balance -86,149
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 prices demand Y 260 1960 Z 210 1370 X 275 3625
258 6955
pricesproduction
quantitylocal transport
costproduction
value
C 241 696 13,224 167,736D 235 190 4,750 44,650B 203 936 6,552 190,008A 195 1,320 19,800 257,400E 268 90 630 24,120total 212 3,232 44,956 683,914
production
quantityregional trade
regional transport cost
importsconsumption
value
Y 886 -1,074 53,700 0 509,600Z 2,256 886 0 0 287,700X 90 188 -12,220 3723 996,875total 3,232 0 41,480 1,794,175
adverse weather
Changes in producer surplus
open adverse weather open adverse weather open adverse weatherC 241 241 946 696 -34,208 227,986 167,736D 235 235 440 190 -19,688 103,400 44,650B 203 203 1,436 936 -49,417 291,508 190,008A 195 195 1,920 1,320 -60,750 374,400 257,400E 268 268 340 90 -10,750 91,120 24,120total 5,082 3,232 -174,813 1,088,414 683,914
Changes in consumer
surplusopen adverse weather open adverse weather open adverse weather
Y 260 260 1,960 1,960 0 509,600 509,600Z 210 210 1,370 1,370 0 287,700 287,700X 275 275 3,625 3,625 0 996,875 996,875total 6,955 6,955 0 1,794,175 1,794,175
prices production quantities production values
prices consumed quantities consumption values
open ec vs adverse weather, comparison
In this case there is only a change in producer surplus, since consumers remain in the same position, thanks to increased imports
-500,000
0
500,000
1,000,000
1,500,000
2,000,000
Total c
onsu
mpti
on ex
pend
iture
Impo
rts
Traspo
rt
Produ
cer r
even
ue
Produ
cer s
urpl
us
Consu
mer su
rplu
s
Net welf
are ch
ange
Net Bala
nce o
f the
Mark
eting
Boa
rd
open
adverse weather
open adverse weather % change
Total consumption expenditure 1,794,175 1,794,175 0.0Imports 515,075 1,023,825 98.8Trasport 190,686 86,436 -54.7Producer revenue 1,088,414 683,914 -37.2
Change in Producer surplus -174,813 -25.6Change in Consumer surplus 0 0.0Net welfare change -174,813 -9.7
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 p rices demand Y 260 1960 Z 210 1370 X 275 3625
258 6955
p ricesp roductio n
qu an tity
local trans po rt
cos t
p roduction v alue
C 241 1,071 20,349 258,111D 235 565 14,125 132,775B 203 1,686 11,802 342,258A 195 2,220 33,300 432,900E 268 590 4,130 158,120to tal 216 6,132 83,706 1,324,164
p roductio n
qu an tityreg ional
trade
reg io nal trans po rt
cos timports
cons umption value
Y 1,636 -324 16,200 0 509,600Z 3,906 2,536 0 0 287,700X 590 -2,212 143,780 823 996,875to tal 6,132 0 159,980 1,794,175
technical change
Changes in producer surplus
open technical change open technical change open technical changeC 241 241 946 1,071 21,010 227,986 258,111D 235 235 440 565 15,703 103,400 132,775B 203 203 1,436 1,686 32,521 291,508 342,258A 195 195 1,920 2,220 38,813 374,400 432,900E 268 268 340 590 23,250 91,120 158,120total 5,082 6,132 131,297 1,088,414 1,324,164
Changes in consumer
surplusopen technical change open technical change open technical change
Y 260 260 1,960 1,960 0 509,600 509,600Z 210 210 1,370 1,370 0 287,700 287,700X 275 275 3,625 3,625 0 996,875 996,875total 6,955 6,955 0 1,794,175 1,794,175
prices production quantities production values
prices consumed quantities consumption values
open ec vs technical change, comparison
Imports in this case decreases, since more domestic production is available at the same price
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
1,600,000
1,800,000
2,000,000
Total c
onsu
mpti
on ex
pend
iture
Impo
rts
Traspo
rt
Produ
cer r
even
ue
Produ
cer s
urpl
us
Consu
mer su
rplu
s
Net welf
are ch
ange
Net Bala
nce o
f the
Mark
eting
Boa
rd
open
technical change
open technical change % change
Total consumption expenditure 1,794,175 1,794,175 0.0Imports 515,075 226,325 -56.1Trasport 190,686 243,686 27.8Producer revenue 1,088,414 1,324,164 21.7
Change in Producer surplus 131,297 9.9Change in Consumer surplus 0 0.0Net welfare change 131,297 7.3
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
demand
gppcs m )(0
pbd 0
withpm = minimum bid pricep = pricec, g, b = constants = own price elasticity
MODEXC dynamics
Expected prices are defined according to Nerlove (1958) under a scheme of distributed lags as:
where:
= 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.
5544332211*
tttttt pppppp
*tp
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
(p = price elasticity of supply) and
with q = increase in production due to the new
technology
pcp kk
0
0
0
010
q
q
qqqk
MODEXC and tech change
Three types of supply shift depending on the position k takes within the original function.
• pivotal shift:
• divergent shift:
• convergent shift:
The general form of shifted supply is:
gppcks m )(1
gpkpcs m )(1
gk
ppcs m )( 01
gk
ppkcks m )(
3211
MODEXC and tech change: surplus
• 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
F
S p
of output
qq q1
E1
d0
S1
Priceper unit
E0
p0
p1
pm
Quantity of output
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
demand shifter (e.g. population, income)
supply shifter (tech change in other sectors)
If differs from zero, the annual k value is adjusted because is applied on a greater base than that used to estimate the final value of k.
td AGRDk
t)1(
t
tk )1(0
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) si,n = s(pv,i,n, pv,j,n, Pols) (8) ci,n = c(pz,i,n, pz,j,n, Polc) (2) rv,i,n =r(pv,i,n, PR) (9) AL = al(pv,i,n, pv,j,n) (3) Qov,i,n = si,n rv,i,n (10) rz,i,n = r(pz,i,n, AL, PR) (11) Qoz,i,n = ci,n rz,i,n demand (4) Cuv,i,n = cu(pv,i,n, Yn, POPn) (12) Qd z,i,n = qd(pz,i,n, Yn, POPn) (5) AAv,i,n = aa(Qoz,i,n) (6) SEv,i,n = se(sv,i,n) (7) 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; E = exports Pols = policies based on land; v = crops; I = imports; Polc = policies based on livestock heads; z = livestock; tc = exchange rate Qo = supply; n = country; PR = yield trend; pn = price in country n; and Y = GDP; pw= world price; s = land (hectares); POP = population; Cu = demand for human consumption; c = heads (number); AA = demand for feed; SE = demand for seeds; AL = index of feed cost; Qd = total demand. r = yield (per hectare or per head); Polp = policies directly affecting prices;
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 modelsAll 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 modelsEquations of the basic model
real flows expenditure
XSi = f(DLi, DKi) supply of good i hXD
i = ahi (Yh / pi) demand for i
w = (
XSi /
DLi) pi labour demand
r = (
XSi /
DKi) pi capital demand equilibrium conditions
XSi =
h
hXDi demand equal supply
i
DLi =
h
LSh demand for labour
equals labour endowement
income flows
Yh = w LSh + r KS
h
i
DKi =
h
KSh Demand for capital
equals capital endowement
identities
Pi XS
i = DLi w + DKi r
Yh =
i
hXDi pi
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 approachNo 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