Towards a spatially and socially explicit Chinese agricultural policy

model:A welfare approach

M.A. Keyzer

Lecture 3

Presentation available:www.sow.vu.nl/downloadables.htm

www.ccap.org.cn

1. Introduction

2. Welfare economics, AGE-modeling, CHINAGRO

model

3. New algorithm to solve very large partial

equilibrium welfare program with transportation

4. Conclusion

Overview of the lecture

Part I : Welfare economics, AGE-modeling, CHINAGRO model

2.1 Welfare optimization and competitive equilibrium

(justifies welfare approach)

2.2 CHINAGRO general equilibrium welfare model

Part II : Algorithm to solve spatially explicit partial

equilibrium

Prototype for next generation model

(Check on transport flows and price margins in

CHINAGRO)

1. Introduction

Consumers are indexed

Commodities are indexed

Consumers have concave increasing utility functions

where is consumption vector with elements .

Exchange economy:

Consumers obtain an income from given endowments

2.1 Welfare & competitive equilibrium

i 1,...,m

k 1,...,r

i iu ( x )

ix ikx

i ih p

Competitive exchange equilibrium: Consumption and

prices

Welfare optimization: Consumption solving, given

weights

2.1 Welfare & equilibrium: Definitions

ix 0 i i i i i imax { u ( x )| px h }, for h p , all i

i iik ikx , for all k

i ix 0,all i i i i

i ii i

max u ( x )

subject to

x (p)

i

First Welfare Theorem:

“A competitive equilibrium is Pareto efficient”

(no consumer can be made better off

without making some other consumer worse off)

Second Welfare Theorem:

“Every Pareto efficient allocation, including the welfare

optimum, is a competitive equilibrium with transfers”

(lumpsum transfers are efficient for income redistribution)

2.1 Welfare & equilibrium: Theorems

Negishi Theorem:

“There exist welfare weights such that a welfare

optimum is a competitive equilibrium without

transfers”

The Negishi-weights reflect marginal utilities of income.

A competitive equilibrium without transfers is a welfare

optimum where consumers with a high marginal

utility of income have a low welfare weight.

2.1 Welfare & equilibrium: Theorems (2)

The three basic theorems of welfare economics equally

apply when production takes place and consumers

obtain income from given endowments and from

shares in the profit of producers indexed j :

The welfare program then reads :

2.1 Welfare & equilibrium: Theorems (end)

i j ix 0,all i,y ,all j i i i

i i ji i j

j j

max u ( x )

subject to

x + y (p)

y Y

i i ij jpx p py

Institutional requirements :

1) all goods in the economy are priced (no free use)

2) no one can manipulate prices (no monopoly)

3) all consumers pay the price of what they use, and

receive the price for what they sell (no crime).

4) producers maximize profits independently of

preferences

(shareholder value principle).

2.1 Welfare & equilibrium: Institutions

Point of departure:

Static equilibrium welfare model from the previous

lecture:

2.2 CHINAGRO model: point of departure

j s s s s sv 0;q ;c ,g ,y 0;z ,z 0

gs s S ss s 1 L s s s s s s

s S js j

max

u ( c ) C ( v ,...,v ,q ) ( z z ) p g

subject to

c v q (p )

j s Sj s s s

s s s s s

s s s s

q v ( y z z )

c z y z (p )

y f ( g ,e )

Modifications:

1) Consider all goods simultaneously; linear trade technology.

(variables become vectors; product becomes inner product)

2) Open economy, trading with the outside world at given

prices.

3) Incorporate balance of payments constraint.

4) Conversion from utility to money metric utility through

welfare weights.

5) Detailed component for agricultural production.

2.2 CHINAGRO full model

Implication for modeling:

1) Inputs agriculture subsumed under net supplies of site

s ;

For transport requirements :

2,3)Balance of payments with exports, imports and

world market prices :

where is the total of non-trade transactions.

4) Write for .

5) Write for .

2.2 CHINAGRO full model (2)

j s Sj j s s s sg v z z

j s s, ,

p p

w ,w

(p w p w ) B

B

s s su ( c )s s s su ( c )

s s sF ( y ,e ) 0 s s s sy F ( g ,e )

Full CHINAGRO general equilibrium welfare model :

2.2 CHINAGRO full model (end)

j s s s ss s s sv 0;g 0;c ,y 0;z ,z 0;w ,w 0

+s S j j s Ss j j s s s

j s Sj j s s s s

s s s s

max u ( c )

subject to

c g v w v ( y z z ) w (p )

g v z z

(p w p w ) B

c z y z

s

s s s

(p )

F ( y ,e ) 0

CHINAGRO model is suited to represent a complex

economic system in a transparent way.

Nonetheless, it assumes that all transportation cost within

counties are truly incurred. As explained in the

previous lecture, this assumption would need to be

relaxed.

Therefore, as a background check on transport flows and

price margins in CHINAGRO, and as a prototype for next

generation models, consider again the single-

commodity partial equilibrium approach.

3. Partial equilibrium with transportation

3. Spatially explicit equilibrium model

Recall, from lecture 2, the model that maximized

the sum of money-metric utilities minus transport costs

subject to commodity balance at every site.

Demand + Outflow = Production + Inflow

Outflow from site s to r = Inflow into site r from s

sr s s s sv 0;q ,c 0 s s s s1 sS s

rs sr s s

rs rs s

max u ( c ) C ( v ,...,v ,q )

subject to c v q (p )

q v e

3. Spatial model: transport cost

Work focused on transport cost along main highways,

railways, and waterways, and along secondary

roads.

Spatially explicit data were collected for rice and

wheat.

The resulting map of transport costs per ton-kilometer

is shown on the next sheet.

3. Spatial model: transport cost

3. Spatial model: solution

Objective : Find equilibrium

supply, demand, flows and price on a map

Tool : A new algorithm to solve a large scale,

spatially explicit welfare program

Advantage : Integration between disciplines

3. Spatial model: what are the costs?

Costs over formal infrastructure(waterways, railways and highways) relatively low:

But these are only a small fraction of the consumer price.

We must also allow for storage cost, cost of changing from the informal mode of transportation to the formal and cost at both ends of the chain: collection and retail distribution

Spatial equilibrium models Connect districts, or nodes in a network Not spatially explicit

3. Spatial equilibrium models

3. Spatially explicit model

Allow for all possible flows on the Union Jack grid

3. Partial equilibrium: new algorithm

Key algorithmic principle: gravity driven flow Gravity : water does not flow uphill Transport : goods never flow to lower price

Low price

High price

3. Partial equilibrium: new algorithm (2)

Two step algorithm:Step 1 Solve gravity constrained welfare program

Impose gravity rule: exclude flows from high to low prices

Per site from low to high price:

(a) update availability = production + inflow

(b) maximize utility of site + value of sales

subject to

consumption + outflow = given availability Per site from high to low price:

update sales price on basis of customer’s value

3. Partial equilibrium: new algorithm (3)

Step 2 Improvement achieved?

Yes:

Update gravity ordering on basis of prices of gravity-constrained program and go to Step 1

No:

Otherwise, end (optimum is found)

3. Partial equilibrium: new algorithm (4)

Application to spatially explicit welfare model for China

Exogenous variables production map cereals population map tariffs and world market prices cereals freight costs per ton

Study world market price penetration

Grid of cells of 10-by-10 km = 93125 cells (markets)

3. New algorithm: zoom in on results

Preliminary results for rice

Price

Preliminary results for rice

Flow

Preliminary results for rice

Production

Preliminary results for rice

Consumption

Preliminary results for rice

JointPrice Flow

Production Consumption

Preliminary results for wheat

Price

Preliminary results for wheat

Flow

Preliminary results for wheat

Production

Preliminary results for wheat

Consumption

Preliminary results for wheat

JointPrice Flow

Production Consumption

4. Conclusion

CHINAGRO: Multicommodity general equilibrium welfare model with spatially explicit partial equilibrium models in the background.

General equilibrium model: work in progress to be discussed further tomorrow.

Partial equilibrium model: preliminary results show that it is possible to generate meaningful spatially explicit equilibrium, with “very large” number of geographical units to represent transport flows and price margins in China.

A next, challenging partial equilibrium application will be the pork industry considering the meat and feed markets simultaneously