genetically modified crops and midwestern farm production: evidence at the state level over...

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Genetically Modified Crops and Genetically Modified Crops and Midwestern Farm Production: Midwestern Farm Production: Evidence at the State Level over Evidence at the State Level over 1960-2004 1960-2004 *The author is C.F. Curtiss Distinguished Professor of Agriculture *The author is C.F. Curtiss Distinguished Professor of Agriculture and Life Sciences and Professor of Economics, Iowa State and Life Sciences and Professor of Economics, Iowa State University. Research is joint with Jessica Schuring and Xing Fan. University. Research is joint with Jessica Schuring and Xing Fan. We thank Eldon Ball for making the data set from the state We thank Eldon Ball for making the data set from the state agricultural production accounts available to us. Funding was agricultural production accounts available to us. Funding was received from the Iowa Agriculture and Home Economics Experiment received from the Iowa Agriculture and Home Economics Experiment Station, Ames, IA. Station, Ames, IA. Wallace E. Huffman*

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Page 1: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Genetically Modified Crops and Genetically Modified Crops and Midwestern Farm Production: Midwestern Farm Production:

Evidence at the State Level over Evidence at the State Level over 1960-20041960-2004

*The author is C.F. Curtiss Distinguished Professor of Agriculture and *The author is C.F. Curtiss Distinguished Professor of Agriculture and Life Sciences and Professor of Economics, Iowa State University. Life Sciences and Professor of Economics, Iowa State University. Research is joint with Jessica Schuring and Xing Fan. We thank Eldon Research is joint with Jessica Schuring and Xing Fan. We thank Eldon Ball for making the data set from the state agricultural production Ball for making the data set from the state agricultural production accounts available to us. Funding was received from the Iowa accounts available to us. Funding was received from the Iowa Agriculture and Home Economics Experiment Station, Ames, IA.Agriculture and Home Economics Experiment Station, Ames, IA.

Wallace E. Huffman*

Page 2: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

I.IntroductionI.Introduction

Ag research in public and private sectors has been shown to impact the Ag research in public and private sectors has been shown to impact the supply of ag outputs, demand for inputs, and TFP supply of ag outputs, demand for inputs, and TFP

Griliches and Evenson were the first to show positive impacts of Griliches and Evenson were the first to show positive impacts of public agpublic ag

research on ag sector output and TFP - 1960sresearch on ag sector output and TFP - 1960s

Public ag research is frequently the foundation for private ag researchPublic ag research is frequently the foundation for private ag research discoveries—hybrid corn of the 1930s; but also GM crop varieties in discoveries—hybrid corn of the 1930s; but also GM crop varieties in

thethe mid-90s (with “input traits”; a biological alternative to common mid-90s (with “input traits”; a biological alternative to common

pesticides). Wheat variety development remains in public sector pesticides). Wheat variety development remains in public sector Improvements in breeding practices for poultry, swine, dairy and beefImprovements in breeding practices for poultry, swine, dairy and beef have largely been under the control of farmershave largely been under the control of farmers

The GM field crop revolution started in 1996 with HT and IR varieties ofThe GM field crop revolution started in 1996 with HT and IR varieties of cotton, corn, and soybean; GM varieties replaced non-GM varieties cotton, corn, and soybean; GM varieties replaced non-GM varieties

roughlyroughly on a seed-for-seed basison a seed-for-seed basis

Page 3: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Objective: To examine the impact of adopting GM corn and soybean Objective: To examine the impact of adopting GM corn and soybean varieties on the structure of farm production in Midwestern varieties on the structure of farm production in Midwestern States over 1960-2004. States over 1960-2004.

Outputs groups are: corn, soybean, wheat and livestockOutputs groups are: corn, soybean, wheat and livestock

Variable inputs: farm capital services, labor, energy, chemicals Variable inputs: farm capital services, labor, energy, chemicals and and

other materialsother materials

Quasi-fixed factors: land, adoption rate for GM corn and Quasi-fixed factors: land, adoption rate for GM corn and soybean varieties, public agricultural research, pre-season soybean varieties, public agricultural research, pre-season precipitation precipitation

Method: Aggregate restricted-expected profit function and Method: Aggregate restricted-expected profit function and associated output supply and input demand functions; shadow-associated output supply and input demand functions; shadow-price functions; biases associated with quasi-fixed factorsprice functions; biases associated with quasi-fixed factors

an econometric model with a system of equationsan econometric model with a system of equations

Data: State aggregate data for Midwest agriculture (Corn Belt Data: State aggregate data for Midwest agriculture (Corn Belt and Lake States), 1960-2004 and Lake States), 1960-2004

Page 4: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

II. Genetically Engineered Crops in the U.S.II. Genetically Engineered Crops in the U.S.

Commercial pesticides: insecticides use starting in 1940s and Commercial pesticides: insecticides use starting in 1940s and herbicides, herbicides,

starting in 1950s have been used as an aid in crop productionstarting in 1950s have been used as an aid in crop production

However, target pests adapt over time and become However, target pests adapt over time and become

resistant – never ending problem resistant – never ending problem

Biotech revolution has enabled private sector development of Biotech revolution has enabled private sector development of

herbicide tolerant and insect resistant crop varieties herbicide tolerant and insect resistant crop varieties

IP by soil bacteria: IP by soil bacteria: Bacillus thuringiensisBacillus thuringiensis & others & others

HT by bacteria that are resistant to selective herbicides (Round Up) HT by bacteria that are resistant to selective herbicides (Round Up) Fernandez-Cornjo and McBride 2002Fernandez-Cornjo and McBride 2002

RR soybean varieties, which are not sensitive to application RR soybean varieties, which are not sensitive to application date, weed infestation, or rainy weather have been widely date, weed infestation, or rainy weather have been widely accepted by farmers, despite USDA finding little expected accepted by farmers, despite USDA finding little expected

payoffpayoff

IP corn varieties: Bt resistant primarily to European Corn BorerIP corn varieties: Bt resistant primarily to European Corn Borer

and later protection against corn rootworm, successful and later protection against corn rootworm, successful

with Midwestern farmerswith Midwestern farmers

GM corn with double and triple stacksGM corn with double and triple stacks

Hence, new biological alternatives to commercial pesticides have Hence, new biological alternatives to commercial pesticides have beenbeen

developed as HT and IP crop varieties developed as HT and IP crop varieties

Page 5: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor
Page 6: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Figure 1

Source: Fernandez-Cornejo 2010

Page 7: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Ht Soybean Adoption Rates: U.S. and Eight Midwestern States, 1996-2007

0

20

40

60

80

100

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

IL

IN

IA

MI

MN

MO

OH

WI

U.S.

Figure 2

Source: ERS (2008) for 2000-2007; our estimates for 1996-1999.

Page 8: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Combined Bt and Ht Corn Adoption Rates: U.S. and Eight Midwestern States, 1996-2007

0

10

20

30

40

50

60

70

80

90

100

1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

IL

IN

IA

MI

MN

MO

OH

WI

U.S.

Figure 3

Source: ERS (2008) for 2000-2007; our estimates for 1996-1999.

Page 9: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

III. An Aggregate Model of ProductionIII. An Aggregate Model of Production Contributions of technology examined by production/transformation fn Contributions of technology examined by production/transformation fn oror as a profit function; profit function has appealing propertiesas a profit function; profit function has appealing properties

Huffman and Evenson (1989), Shumway et al. (1988) and Bairam (1989), Huffman and Evenson (1989), Shumway et al. (1988) and Bairam (1989), found it fruitful to examine the structure of ag production in state data found it fruitful to examine the structure of ag production in state data using a flexible aggregate multi-output multi-input profit functionusing a flexible aggregate multi-output multi-input profit function

Define Define yyi i > > 0 as outputs, 0 as outputs, i i = 0,1, .., n, and < 0 as variable inputs, = 0,1, .., n, and < 0 as variable inputs, ii = n+1, = n+1, …,n+m; z…,n+m; zkk > 0 is quasi-fixed factors, k = 1,…,K, which are not freely> 0 is quasi-fixed factors, k = 1,…,K, which are not freely

variable.variable.

PPii > 0 are prices of outputs and inputs, and normalized prices are> 0 are prices of outputs and inputs, and normalized prices are

denote denote ppii = P = Pii / P / P00

Normalized restricted-expected profit function includes quasi-fixed factors Normalized restricted-expected profit function includes quasi-fixed factors and and

expected prices, eq (1)expected prices, eq (1)

Applying Hotelling’s Lemma to (1) yields a set of output supply and Applying Hotelling’s Lemma to (1) yields a set of output supply and variable input demand functions (2) for n+m choices and supply variable input demand functions (2) for n+m choices and supply equation for theequation for the

numeraire commodity is derived residually from (1) and (2), or (2’).numeraire commodity is derived residually from (1) and (2), or (2’).

Page 10: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

The exact algebraic form of the normalized quadratic profit function is given by:

01 1 1 1 1 1 1 1

1 1

2 2

n m K n m n m K K n m K

i i k k ij i j kl k l ik i ki k i j k l i k

p z p p z z p z

(1)

Given the normalized quadratic profit function (1), the set of net output equations for the n + m choices can be obtained by applying Hotelling’s lemmas:

k

K

kikj

mn

jijii zpy

11

* , i = 1, , n + m. (2)

Then, the supply equation for the numeraire output can be obtained residually:

K

k

K

llkkl

mn

i

mn

jjiij

K

kkk zzppzy

1 11 110

*0 2

1

2

1 . (2’)

Page 11: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

i, j = 1,…, n + m**

/ln

lnijij

j

iij yp

p

y

j

mn

jij

i

ii p

yp

y

1

*0

*

0

1

ln

ln

i

mn

iij

j

jj p

y

p

p

y

1

*0

*0

0 ln

ln

mn

i

mn

jjiij pp

yp

y

1 1*00

*0

00

1

ln

ln

i = 1,…, n + m (3)

j = 1,…, n + m

Page 12: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

1 1

K n m

k k kl l ik il ik

z pz

k = 1,…, K, (4)

The shadow-value of the fixed factors associated with the normalized-quadratic profit function are

which can be evaluated at the sample means of p’s and z’s once given the coefficient estimates for demand and supply equations.

If ≠ then the use of the quasi-fixed factor is not at a profit max rate of use

k kzp

Page 13: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

,0*

1

*0

i

n

iiR ypy (5)

Total revenue is denoted by

.0*

1

i

mn

niiC yp

and the total variable cost is denoted by

(6)

,0*

R

iiRi

yps

(7)

Then the i-th revenue share is denoted by

and the i-th factor’s cost share is denoted by

.0

*

C

iici

yps

(8)

Page 14: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

The bias effect for the i-th output is:

.,...,1,1 1

*ni

zp

yz

z

s

s

zB

R

n

i

K

llkliikk

i

ikk

k

Ri

Ri

kRik

(9) We obtain the bias for the numeraire output as

Rik

n

i

RiR

Rk Bs

sB

10

0

1. (10)

The bias effect for a variable input i is

.,...,1,1*

mnnip

yz

z

s

s

zB

C

mn

niiik

i

ikk

k

Ci

Ci

kCik

(11)

Page 15: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

IV. The Data, Variables and ResultsIV. The Data, Variables and ResultsData for 8 midwestern states: IA, IL, IN, MI, MN, MO, OH and WIData for 8 midwestern states: IA, IL, IN, MI, MN, MO, OH and WI

OutputsOutputs

Crop: Corn for grain, soybeans, wheat (NASS)Crop: Corn for grain, soybeans, wheat (NASS)Livestock: Livestock and livestock products (Ball)Livestock: Livestock and livestock products (Ball)

Inputs (Ball)Inputs (Ball) Capital services: Implicit rental on farm equipment and inventories Capital services: Implicit rental on farm equipment and inventories

of grain, oil seeds, forages and breeding livestockof grain, oil seeds, forages and breeding livestockLabor: Input of operator, unpaid family and hired labor, quality Labor: Input of operator, unpaid family and hired labor, quality

adjusted adjusted Energy: Petroleum fuels, natural gas and electricityEnergy: Petroleum fuels, natural gas and electricity Ag chemicals: Fertilizers, lime and pesticidesAg chemicals: Fertilizers, lime and pesticides Other materials: Seeds, livestock feed, contract labor, machine hireOther materials: Seeds, livestock feed, contract labor, machine hire

Prices: Expected PricesPrices: Expected Prices Corn, soybean and wheat: Commodity-specific futures market price Corn, soybean and wheat: Commodity-specific futures market price

at at planning time for the harvest date adjusted for state-specific planning time for the harvest date adjusted for state-specific

basis basis (or transport and storage cost to nearest river terminal)(or transport and storage cost to nearest river terminal) Ball’s prices for livestock and input groupsBall’s prices for livestock and input groups

Quasi-fixed factorsQuasi-fixed factors Land: Land services including CRP land, quality adjusted acres (Ball)Land: Land services including CRP land, quality adjusted acres (Ball) Adoption rate for GM corn and soybeans, displaces non-GM on a Adoption rate for GM corn and soybeans, displaces non-GM on a

seed per seed basis (NASS and our adjustments)seed per seed basis (NASS and our adjustments) Public Agricultural Research: Stock of real public ag research (H&E)Public Agricultural Research: Stock of real public ag research (H&E) Pre-season precipitation: Deviation of Oct-Mar precipitation from 35 Pre-season precipitation: Deviation of Oct-Mar precipitation from 35

yr norms (H)yr norms (H)

Page 16: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

wt

0 2 9 14 35 t

Figure 4Public Agricultural Research Timing Weights

Page 17: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

V. The Econometric ModelV. The Econometric Model

We add a zero mean random disturbance term to all output We add a zero mean random disturbance term to all output supply and supply and input demand equations except for numeraire input demand equations except for numeraire commodity commodity

Re-parameterize our model to consider autocorrelationRe-parameterize our model to consider autocorrelation

YYitit = = XXitit δ δii + + µµitit, , µµitit = = ρρ µµit-1it-1 + + εεitit,, i i = 1, ...6; = 1, ...6; tt = 1, …45, (12) = 1, …45, (12)

Create pseudo first differencesCreate pseudo first differences

YYitit – – ρYρYit-1it-1 = ( = (XXitit – – ρXρXit-1it-1))δδii + + εεitit.. (13)(13)

Fit model first ignoring cross-equation restrictions and auto-Fit model first ignoring cross-equation restrictions and auto-

correlation and then use residuals to estimate ρ = 0.606 with correlation and then use residuals to estimate ρ = 0.606 with a 99.9 a 99.9 percent confidence interval of (0.46 < percent confidence interval of (0.46 < ρρ < 0.74), < 0.74), which is far from 1which is far from 1

Production system estimated as model of quasi-differenced- Production system estimated as model of quasi-differenced- seemingly unrelated (SUR) regression with cross-equation seemingly unrelated (SUR) regression with cross-equation restrictions (Greene 2008, Zellner 1962, Barten 1969)restrictions (Greene 2008, Zellner 1962, Barten 1969)

VI. Summary Statistics and ResultsVI. Summary Statistics and Results

Page 18: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Table 1. Variable Names and Summary Statistics for U.S. Agriculture in Eight Midwestern States, 1960-2004

Variables Variables MinMin St. DevSt. Dev

QuantitiesQuantities11

Wheat OutputWheat Output Soybean OutputSoybean Output Corn OutputCorn Output

0.180.181.111.112.052.05

0.140.140.900.901.631.63

Livestock OutputLivestock Output 3.15 3.15 1.54 1.54

Capital ServicesCapital Services -1.54 -1.54 0.55 0.55

LaborLabor -3.89 -3.89 1.59 1.59

EnergyEnergy -0.29 -0.29 0.10 0.10

Ag ChemicalsAg Chemicals -0.68 -0.68 0.39 0.39

Other MaterialsOther Materials -2.51 -2.51 1.13.02 1.13.02

PricesPrices22

Soybean OutputSoybean Output Corn OutputCorn Output

1.091.090.95 0.95

0.240.240.16 0.16

Livestock OutputLivestock Output 1.28 1.28 0.39 0.39

Capital ServicesCapital Services 1.03 1.03 0.44 0.44

LaborLabor 0.81 0.81 0.54 0.54

EnergyEnergy 1.25 1.25 0.39 0.39

Farm ChemicalsFarm Chemicals 1.14 1.14 0.30 0.30

Other MaterialsOther Materials 1.53 1.53 0.38 0.38

Continued ->

Page 19: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Table 1. continued

Variables Variables MeanMean St. Dev.St. Dev.

Quasi-Fixed FactorsQuasi-Fixed Factors

Land ServicesLand Services33 0.87 0.87 0.24 0.24

Adoption Rate for GM SoybeanAdoption Rate for GM Soybean 0.110.11 0.240.24

Adoption Rate for GM Corn VarietiesAdoption Rate for GM Corn Varieties 0.04 0.04 0.11 0.11

Public Ag ResearchPublic Ag Research44 30.05 30.05 10.71 10.71

Pre-season PrecipitationPre-season Precipitation55 0.00 0.00 249 249

11Value $1,000,000,000 in 1996 prices of ALValue $1,000,000,000 in 1996 prices of AL22Relative to 1996 AL levelRelative to 1996 AL level33Value $1,000,000,000 in 1996 prices of ALValue $1,000,000,000 in 1996 prices of AL44$1,000,000 in 1996 prices of AL$1,000,000 in 1996 prices of AL55Deviation from meanDeviation from mean

Page 20: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Table 2. Estimate of a System of Output Supply and Input Demand Equations Table 2. Estimate of a System of Output Supply and Input Demand Equations with Symmetry Restrictions with AR(1): Eight Midwestern States, 1960-2004 with Symmetry Restrictions with AR(1): Eight Midwestern States, 1960-2004

(asymptotic t-or z-values in parentheses; N = 43x8 = 344 observations per eq)(asymptotic t-or z-values in parentheses; N = 43x8 = 344 observations per eq)

Page 21: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Table 2 Cont.Table 2 Cont.

Page 22: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Table 3. Output Supply and Input Demand ElasticitiesTable 3. Output Supply and Input Demand Elasticities

Page 23: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Shadow Values of (Quasi-) Fixed Factors Shadow Values of (Quasi-) Fixed Factors _ _

Factor Factor k k ShadowShadow PricePrice

____________________________________________________________________________________________________________________ Land $207 per dollar of land services Land $207 per dollar of land services

(1996 prices)(1996 prices)

GM corn adoption rate $1 billion per 1 percentage pointGM corn adoption rate $1 billion per 1 percentage point

GM soybean adoption rate $ negativeGM soybean adoption rate $ negative

Public agricultural research $ negativePublic agricultural research $ negative

Conclusion: none of these quasi-fixed factors is in equilibrium useConclusion: none of these quasi-fixed factors is in equilibrium use

k

Page 24: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

Table 5. Estimates of Bias Effects in Production DecisionsTable 5. Estimates of Bias Effects in Production Decisions

Page 25: Genetically Modified Crops and Midwestern Farm Production: Evidence at the State Level over 1960-2004 *The author is C.F. Curtiss Distinguished Professor

VII. ConclusionsVII. Conclusions Output supply and input demand functions fitted to aggregate data are consistent Output supply and input demand functions fitted to aggregate data are consistent

with aggregate profit maximization for U.S. Midwestern Farmers, 1960-2004with aggregate profit maximization for U.S. Midwestern Farmers, 1960-2004 Estimates of supply elasticities for wheat is large, modest for corn, very small for Estimates of supply elasticities for wheat is large, modest for corn, very small for soybean and approx zero for livestock soybean and approx zero for livestock Estimates of demand elasticities are largest for farm chemicals and energy but Estimates of demand elasticities are largest for farm chemicals and energy but

relatively small for capital service, labor and other materialsrelatively small for capital service, labor and other materials

Increase in public ag research increases the supply of both outputs and reduces the Increase in public ag research increases the supply of both outputs and reduces the demand for capital services, labor and energy but increases demand for ag demand for capital services, labor and energy but increases demand for ag chemicals and other materials input; and also biases production decisions chemicals and other materials input; and also biases production decisions toward crop output and ag chemical but against capital services and energytoward crop output and ag chemical but against capital services and energy

Increased adoption rate for GM soybean varieties increases the supply of soybean Increased adoption rate for GM soybean varieties increases the supply of soybean and livestock and demand for farm chemicals and other materials; and livestock and demand for farm chemicals and other materials;

and decreases the supply of corn and wheat and the demand for farm energy and decreases the supply of corn and wheat and the demand for farm energy and capital. There is also a bias toward corn, soybean and livestock output and and capital. There is also a bias toward corn, soybean and livestock output and away from wheat. Inputs are biased toward farm chemicals and away from away from wheat. Inputs are biased toward farm chemicals and away from energy and capital services. energy and capital services.

Increased adoption rate for GM corn varieties increases the supply of corn and Increased adoption rate for GM corn varieties increases the supply of corn and slightly increases the demand for all inputs expect for other materials. slightly increases the demand for all inputs expect for other materials.

It biases outputs toward wheat and slightly against other outputs, and toward It biases outputs toward wheat and slightly against other outputs, and toward other material and slightly against other inputs other material and slightly against other inputs

An increase in public agr research increases the supply of all output and the An increase in public agr research increases the supply of all output and the demand for all inputs. It biases outputs toward wheat and away from other demand for all inputs. It biases outputs toward wheat and away from other outputs and toward “other materials” and weakly against the other input outputs and toward “other materials” and weakly against the other input groups. groups.