AGRICULTURAL PRICES AND MARKETS

AGRICULTURAL PRICES

AND MARKETS

AGRICULTURAL PRICES AND MARKETS

Sponsored by a Grant TÁMOP-4.1.2-08/2/A/KMR-2009-0041 Course Material Developed by Department of Economics,

Faculty of Social Sciences, Eötvös Loránd University Budapest (ELTE) Department of Economics, Eötvös Loránd University Budapest

Institute of Economics, Hungarian Academy of Sciences Balassi Kiadó, Budapest

AGRICULTURAL PRICES AND MARKETS

Author: Imre Fertő

Supervised by Imre Fertő

June 2011

ELTE Faculty of Social Sciences, Department of Economics

AGRICULTURAL PRICES AND MARKETS

Week 3

Agricultural supply

Imre Fertő

Literature

• Tomek, W. G.–Robinson, K. (2003): Agricultural Product Prices. Cornell University Press, Chapter 4

• Hudson (2007): Agricultural Markets and Prices.

Blacwell, Chapter 2

• Ferris. J. N. (1997): Agricultural Prices and Commodity Market Analysis. McGraw-Hill, Chapter 6

• Application:

– Chavas, J. P.–Johnson, S. (1982): Supply dynamics: the case of U.S. broilers and turkeys. American Journal of Agricultural

Economics. 64 558–564

– Bakucs, L. Z., Fertő, I., Fogarasi,J., Latruffe, L. (2010) The impact of EU accession on farms’ technical efficiency in

Hungary. Post-Communist Economies Vol. 22. (2). 165–175

Theory of agricultural supply

• Theory of agricultural supply

• Determining factors of demand

• Price elasticity of demand

• Characteristics of supply

• The methodologies of supply analysis – Distributed lags models

– Introduction to efficiency analysis

Theory of supply

• Demand theory assume that consumers

– Maximise their utility taking into account their budget constraints

• Supply theory assume that producers

– Maximise their profit taking into account their cost constraints

– Usual assumptions,

• Problems of input combinations

• The analysis of firm/farm in terms of revenue and costs

• Can be described in the function of the output

– The problem of the firm is to choose the output which maximize its profit

– Information on cost functions can be obtained from

• Production function

• Cost equations

Theory of supply

• In short run we assume that majority of factors are fix just some factors are changing

• Assume

– q=f(X₁, X₂) and

– C=(r₁*X₁+r₂*X₂+b (fix cost)

– C=g(q)+b

• Total cost=the function of

output+fix cost

• Four cost relationships – ATC=TC/q=g(q)+b/q – AVC=TVC/q=g(q)/q – AFC=FC/q=b/q

– MC=dC/dQ=g’(q)

Theory of supply

• MC always intersects at the minimum of the ATC and AVC curves

• Proof:

– If VC=g(q), then

– MC=g’(q) and AVC=TC/q=g(q)/q – dAVC/dq=(q*g’(q)–g(q))/q²=0

– dAVC/dq=0, if nominator=0 – q*g’(q)–g(q)=0

– g’(q)=g(q)/q

• Similar proof can be applied for ATC-

Theory of supply

• Π=TR–TC=p*q–g(q)–b

– Π partial derivatives for q and it should be equate to zero

– dΠ/dq=p–g’(q)=0 – p=g’(q)

– Price=Marginal costs

– dΠ/dq sometimes we call marginal

revenue because it is partial derivative of TC

– At the profit maximum

• MC=MR=p

Theory of supply

• What happens if the price is changing

– If price increase or decrease the optimal

output, where profit is the maximum increase or decrease, thus MC in the short run is the supply curve of the firm above AVC curve.

(Below AVC curve firm does not produce, because VC is not already covered)

– If TR=p*q, then

• AR=TR/q=p*q/q=p

• MR=dTR/dq=p

• AR=MR=p

• Thus D curve is the market price for the firm

Determining factors of supply

• Supply function

• Q_s=f(P_i, P_s, P_c, I_n, N, T, R, O), where – Q_s: quantity of supply

– P_i: price of product

– P_s: price of substitute product

– P_c: price of complementary product – I_n: price of inputs

– N: number of producers – T: technology

– R: distribution of producers – O: goal of the producers

How can various factors affect on supply quantity

– P_i: increase or decrease – P_s: increase or decrease – P_c: increase or decrease – I_n: increase

– N: increase or decrease – T: improve

– R: change – O: change

Supply elasticity

• Own price elasticity

– If E_p<1 elastic

– If E_p=1 unit elasticity – If E_p>1 inelastic

– If E_p=0 perfectly inelastic – If E_p=∞ perfectly elastic

) /

/(

) /

(

p

dQ dP P Q

E 

) /(

) (

) /(

)

(

p

Q Q Q Q P P P P

E      

Supply elasticities

• Cross price elasticities

– If E

>0, then i and j substitute

– If E

<0, then i and j complementary – If E

=0, then i and j independent

• Input price elasticity

) /

/(

) /

( ^{i j j i}

ij dQ dP P Q

E 

) /

/(

) /

( dQ dI I Q

E



Characteristics of supply

• Dependence on nature

• Production fluctuation due to wheather

• Durability of the products

• Long production cycle

• The large share of immobil production factors

• Limited use of economies of scale

• Consequences:

– Price inelastic supply – Risk aversion

– Inverse supply curve – “overproduction trap”

Approaches of supply analysis

• Data:

– Time series

• Aggregate macro data – Cross-sectional data

• Households surve – Panel data

• Combination of time series and cross- sectional data

• Approaches

– Single equation models

Single equation models

Model Function Elasticity

Linear Y=α+βX β(X/Y)

Log-log logY=α+βlogX β

Log-lin logY=α+βX βX

Lin-log Y=α+βlogX β(1/Y) Reciprocal Y=α+β(1/X) –β(1/XY)

Distributed lag

• Dynamic effects

– Policy takes time to have an effect

– The size and nature of the effect can vary over time

– Permanent vs. Temporary effects

• Effect is distributed through time

– consumption function: effect of income through time

– effect of income taxes on GDP happens with a lag

– effect of monetary policy on output through time

The distributed lag effect

Economic action at time t

Effect at time t

Effect at time t+1

Effect at time t+2

The distributed lag effect

Effect at time t

Economic action at time t

Economic action at time t-1

Economic action at time t-2

Two questions

• How far back?

– what is the length of the lag?

– finite or infinite

• Should the coefficients be restricted?

– e.g. smooth adjustment

– let the data decide

Unrestricted finite distributed lag

• Finite: change in variable has an effect on another only for a fixed period

– e.g. monetary policy affects GDP for 18 months

– the interval is assumed known with certainty

• Unrestricted (unstructured)

– the effect in period t+1 is not related

to the effect in period t

y

=  + 

x

+ 

x

+ 

x

+ . . . +

x

+ e

n unstructured lags

no systematic structure imposed on the ’s

the ’s are unrestricted

OLS will work

i.e. will produce consistent and

unbiased estimates

Problems

1. n observations are lost with n-lag setup.

• data from 1960, 5 lags in model implies earliest point in regression is 1965

• use up degrees of freedom (n-k)

2. high degree of multicollinearity among x_t-j’s

• x_t is very similar to x_t-1 – little independent information

• imprecise estimates

• large stn errors, low t-tests

• hypothesis tests uncertain.

3. Several LHS variables

• many degrees of freedom used for large n.

4. Could get greater precision using structure

Arithmetic lag

• Still finite: the effect of X eventually goes to zero

• The coefficients are not independent of each other

– The effect of each lag will be less than previous one

– E. g. monetary policy in 1995 will have

less of an effect on GDP in 1998 than will monetary policy in 1996

• Note how this is different to the capital exp example

Arithmetic lag structure

(impulse response function)

i

_i

₀ = (n+1)

₁ = n

₂ = (n-1)

_n = 

. . .

0 1 2

.

. .

. .

. .

. .

linear

lag

structure

The arithmetic lag structure

Imposing the relationship :

_ii = (n - i+ 1) 

₀ = (n+1) 

₁ = n 

₂ = (n–1) 

₃ = (n–2) 





_n-2 = 3 

_n-1 = 2 

_n = 

only need to estimate one coefficient, , instead of n+1 coefficients, 0 , ... , n .

y_t =  + ₀ x_t + ₁ x_t-1 + ₂ x_t-2 + . . . +_n x_t-n + e_t

Polynomial distributed lag

. . . .

.

0 1 2 3 4 i



₀

₁ ₂

₃

₄

where i = 1, . . . , n p = 2 és n = 4

For example, a quadratic polynomial : _

0 = ₀

₁ = ₀ + ₁ + ₂

₂ = ₀ + 2₁ + 4₂

₃ = ₀ + 3₁ + 9₂

₄ = ₀ + 4₁ + 16₂

n = the length of the lag p = degree of polynomial

ahol i = 1, . . . , n



= 

+ 

i + 

i

+...+ 

i



= 

⁺ 

^{i +} 

ⁱ

Polynomial distributed lag

Geometric lag model

(impulse response function)



.

. .

. .

0 1 2 3 4 i

₁ = 

₂ = ²

₃ = ³

₄ = ⁴

₀ = 

geometrically declining weights

y_t =  + ₀ x_t + ₁ x_t-1 + ₂ x_t-2 + ₃ x_t-3 + . . . + e_t

y_t =  + x_t +  x_t-1 + ^ x_t-2 + ^ x_t-3 + . . .) + e_t infinite unstructured lag ^:

infinite geometric lag:

Substitute _i = ⁱ

₀ = 

₁ = 

₂ = ²

₃ = ³

.

. .

Alternative lag models

• Adaptive expectations model

– A version of the geometric lag model

– If we assume that individuals have “adaptive

expectation” then the geometric lag model will emerge – Assume expectations

• Formed on the basis of past experience

• Expectations are updated in the light of errors

– AE is not always consistent with “rational expectations”

• Partial Adjustment Model

– Another version of the geometric lag model

– Assume individuals adjust to the ideal gradually

• Cost of adjusting, so don’t adjust quickly

Agricultural production

• Production function:

– Physical total product, TPP= Y=f(X)

– Physical average product : APP=Y/X=f(X)/X – Physical marginal product:

• MPP=dTPP/dX=dY/dX=df(X)/dX=f’(X) – Factor elasticity

• E=(dY/Y)/(dX/X)=(dY/dX)/(X/Y)=MPP/APP

Production and cost functions

• Estimation of production functions – Cobb–Douglas

– CES

– Translog etc.

• Estimation of cost functions

• Estimation of technical development

Types of economies of scale

Sources of economies of scale

• Sources of increasing economic of scale – Fix costs

– Division of labour

– Price advantage buying inputs

• Sources of decreasing economic of scale – Limitations of efficient management

– Limitation to control agroclimatic conditions

– Changing nature of risk

Efficiency and productivity

• Definition of efficiency and productivity

• Methodologies

–Index numbers –DEA

–SFA

Technical efficency

TE=OQ/OP AE=OR/OQ CE=OR/OP

TE=OA/OB AE=OB/OC RE=OA/OC

SFA

A Hungarian example

Variable Coeff. SE robust-SE

Trend 0,19^** 0,194 0,255

EU2004 –1,364^*** 0,372 0,428

EU2005 –2,197^*** 0,593 0,743

Company dummy –1,812^** 0,526 0,733

Region 1 dummy –0,868^*** 0,290 0,297

Region 2 dummy –0,543^** 0,220 0,251

Land to Labour Ratio 4,825^*** 1,608 1,102 Subsidies to Output Ratio 0,138^*** 0,014 0,013 Subsidies 2004 to Output Ratio 0,006 0,024 0,014 Subsidies 2005 to Output Ratio 0,808^*** 0,114 0,257 Livestock Output to Total Output Ratio –2,912^*** 1,128 0,969 Livestock Output to Total Output Ratio² 2,997^*** 1,229 1,054 Soil Quality Index –1,578^*** 0,244 0,303

Conclusions

• Economic theory is useful for analysing of

agricultural supply, but it should be taken into

account the characteristics of agricultural supply

• Dependence on nature

• Production fluctuation due to wheather

• Durability of the products

• Long production cycle

• The large share of immobile production factors

• Limited use of economies of scale

• Consequences:

– Price inelastic supply – Risk aversion